let r=[0,1]×[0,1] . estimate ∬r4(x y)da by computing two different riemann sums, each with at least six rectangles.

Answers

Answer 1

The estimated value of the double integral using Riemann sum with partition P2 is 0.611.

To estimate the double integral of the function f(x,y) = 4xy over the region r = [0,1] x [0,1], we can use Riemann sums with different partitions of the region.

First, we can divide the region into 6 rectangular subregions of equal size, using the partition:

P1 = {[0,1/3] x [0,1/2], [0,1/3] x [1/2,1], [1/3,2/3] x [0,1/2], [1/3,2/3] x [1/2,1], [2/3,1] x [0,1/2], [2/3,1] x [1/2,1]}

The area of each subregion is (1/3) * (1/2) = 1/6, so the Riemann sum is:

R1 = (1/6) * [f(1/6,1/4) + f(1/6,3/4) + f(1/2,1/4) + f(1/2,3/4) + f(5/6,1/4) + f(5/6,3/4)]

Plugging in the function f(x,y) = 4xy and simplifying, we get:

R1 = (1/6) * [(1/6)*(1/4)4 + (1/6)(3/4)4 + (1/2)(1/4)8 + (1/2)(3/4)8 + (5/6)(1/4)4 + (5/6)(3/4)*4]

= 11/18

Therefore, the estimated value of the double integral using Riemann sum with partition P1 is approximately 0.611.

Alternatively, we can use another partition with 6 rectangular subregions, such as:

P2 = {[0,1/2] x [0,1/3], [1/2,1] x [0,1/3], [0,1/2] x [1/3,2/3], [1/2,1] x [1/3,2/3], [0,1/2] x [2/3,1], [1/2,1] x [2/3,1]}

The area of each subregion is again 1/6, so the Riemann sum is:

R2 = (1/6) * [f(1/4,1/6) + f(3/4,1/6) + f(1/4,1/2) + f(3/4,1/2) + f(1/4,5/6) + f(3/4,5/6)]

Plugging in the function f(x,y) = 4xy and simplifying, we get:

R2 = (1/6) * [(1/4)*(1/6)4 + (3/4)(1/6)4 + (1/4)(1/2)8 + (3/4)(1/2)8 + (1/4)(5/6)4 + (3/4)(5/6)*4]

= 11/18

Therefore, the estimated value of the double integral using Riemann sum with partition P2 is also approximately 0.611.

In both cases, the estimated value of the double integral is the same, which suggests that it is a reasonable estimate.

To learn more about Riemann sum here:

https://brainly.com/question/30404402

#SPJ4


Related Questions

please help me with this problem:
the base of a rectangle is 9/4 of the height and the perimeter is 104 dm. Calculate the perimeter of the square equivalent to four times the rectangle​

Answers

Answer:

[tex]\boxed{384}[/tex]

Step-by-step explanation:

Let B be the base of the rectangle and H the heightWe are given
[tex]B = \dfrac{9}{4}H[/tex]Perimeter is given by 2(B+H) = 104

So
[tex]B + H = \dfrac{104}{2} = 52[/tex]
[tex]\textrm{Substitute }B = \dfrac{9}{4}H[/tex],
[tex]\dfrac{9}{4}H + H = 52[/tex]Multiply throughout by 4:
[tex]4 \cdot \dfrac{9}{4}H + 4H = 4 \cdot 52\\\\\\9H + 4H = 208\\\\13H = 208\\\\H = \dfrac{208}{13} = 16\\\\B = \dfrac{9}{4}H = \dfrac{9}{4}\cdot 16 = 36\\\\\\[/tex]Area of this rectangle = 16 x 36 = 576If we have a square that is the same size of this rectangle, then it's area should also be 576

Since the area of a square of side a is a² and if a² = 576,
[tex]a = \displaystyle \sqrt{576} = 24[/tex]

So each side of a square that is equivalent to the rectangle would be 24A square four times this size would have a side = 4 x 24 = 96The perimeter of a square of side [tex]a[/tex] is [tex]4a[/tex]So  the perimeter of the square equivalent to four times the rectangle​ would be
4 x 96 =  384

Two rectangles are similar.
Rectangle 1: W = 12 in, P = 34 in
Rectangle 2: W = 14 in, P = ?
Provide an answer accurate to the nearest hundredth.

Answers

The answer accurate to the nearest hundredth is 38.5

How to find the nearest hundredth?

To find the nearest hundredth of a number, you can round it to the nearest hundredth. To do this, you need to look at the third digit after the decimal point.

If the digit is less than 5, you can round down.If the digit is greater than or equal to 5, you can round up.

Regarding the rectangles, since the two rectangles are similar, we know that the ratio of their corresponding sides are equal.

W1/W2 = P1/P2 = k (where k is the proportionality constant)

So, P2 = (P1 * W2)/W1 = (34 * 14)/12 = 38.5

Hence, The answer accurate to the nearest hundredth is 38.5

To learn more about How to find the nearest hundredth, Visit

https://brainly.com/question/29169531

#SPJ1

The histogram shows information about the
speed of cars as they pass a checkpoint.
The scale on the frequency density axis
is missing.
Speed of cars
Frequency density
15 20
25
30 35
Speed (mph)
40
45
50
The histogram shows information about
480 cars.
a) How many cars does the first bar represent? (4)
b) Cars with a speed greater than 40 mph are
over the speed limit. Use the histogram to
estimate the number of cars that are over
the speed limit.
+
(2)
+
Total marks: 6

Answers

The bar represent 120 bars The histogram shows information about 480 cars.

How many cars does the first bar represent?​15 to  30  on x axis has    , 24 on y axis (30 - 15) * 24  =  36030 to  35  on x axis has    , 33 on y axis (35 - 30) * 33 =  16535 to  50  on x axis has    , 5 on y axis (50 - 35) * 5=  75360 + 165 + 75  = 600  600  = 4801  = 480/600360  =  360 x 480/600  = 288first bar represent = 288 CarsA histogram is an approximate representation of the distribution of numerical data. The term was first introduced by Karl Pearson.A histogram is used for continuous data, where the bins represent ranges of data, while a bar chart is a plot of categorical variables.

To learn more about first bar represent refers to:

brainly.com/question/2962546

#SPJ1

Is the residual always 0?

Answers

The residual square sum may equal 0. Your model will fit your data more closely if the residual sum of squares is small; conversely, if the residual sum of squares is large, your model will match your data less closely. A value of 0 indicates that your model fits the data perfectly.

What Exactly Is Residual Value?

The estimated value of an asset that is fixed at the end of its useful life or lease term is its residual value, which is often referred to as salvage value. In lease agreements, the residual value is one of the lessor's main methodologies for calculating the lessee's periodic lease payments.

A good residual value is what?

Check out the Car Lease Ratings section of our Lease Kit for a complete list of high-residual vehicle brands and models.

                   A car is probably not a good lease deal if the lease-end residual value is less than 50% of the MSRP (for a 36-month lease). 55% to 65% of MSRP would be a nice residual.

Learn more about Residual Value

brainly.com/question/27864993

#SPJ4

What is called absolute number?

Answers

Any value inside an absolute value in a problem or equation indicates that the value is always positive.

What is called an absolute number?In a wide range of mathematical contexts, generalizations of the absolute value for real numbers occur. Complex numbers, quaternions, ordered rings, fields, and vector spaces are a few examples of objects for which an absolute value is also specified. In a variety of mathematical and physical situations, the absolute value is intimately related to the concepts of magnitude, distance, and norm. Without taking direction into account, absolute value describes how far away from zero a certain number is on the number line. A number can never have a negative absolute value. View some illustrations. 5 is 5 in its entirety.Any value inside an absolute value in a problem or equation indicates that the value is always positive. Absolute values are occasionally utilized with inequality problems and are frequently employed in situations concerning distance.

To learn more about absolute number refer to:

https://brainly.com/question/24368848

#SPJ4

Consider the function g(x)=2[tex]x^{2}[/tex]-x


When g(x) is divided by x+1 the quotient is [tex]\frac{g(x)}{x+1}[/tex] = 2x-3+ [tex]\frac{k}{x+1}[/tex]


What is the value k?

Answers

The value of the constant k in the equation of the division of g(x) by (x + 1); [tex]\frac{g(x)}{x + 1} = 2\cdot x - 3 + \frac{k}{x + 1}[/tex] obtained by the long division of g(x) = 2·x² - x by (x + 1) is 3.

What is the method for the long division of a polynomial?

The method or algorithm of finding the long division of a polynomial, p(x) known as the dividend, by a divisor, g(x) makes use of the equation;

p(x) = q(x) × g(x) + r(x)

Where;

q(x) = The quotient

r(x) = The remainder from the division;

The specified equation; [tex]\frac{g(x)}{x + 1} = 2\cdot x - 3+\frac{k}{x+1}[/tex], indicates that the remainder, r(x) = k.

The value of k in the specified equation, can be found by dividing the function g(x) = 2·x² - x, by (x + 1) as follows;

The expression obtained when g(x) is divided by (x + 1) using long division, is presented as follows;

 [tex]{}[/tex]        2·x - 3

(x + 1) |2·x² - x

[tex]{}[/tex]           2·x² + 2·x

[tex]{}[/tex]                    -3·x

     [tex]{}[/tex]            [tex]{}[/tex]  -3·x - 3

[tex]{}[/tex]                       [tex]{}[/tex]     3

The remainder obtained from the long division of 2·x² - x by (x + 1) is; 3

The result of the long division of 2·x² - x by (x + 1) is therefore;

[tex]\frac{g(x)}{x+1} =2\cdot x - 3 + \frac{3}{x + 1}[/tex]

Comparison of the equation; g(x)/(x + 1) = 2·x - 3 + k/(x + 1) and the equation; g(x)/(x + 1) = 2·x - 3 + 3/(x + 1), indicates that the value of k is 3

Learn more about the long division of polynomials here: https://brainly.com/question/28925622

SPJ1

Problems 1- 14, use the rules of differentiation to find the derivative of the function. 1. y = 14; 2. y=x^9+3 tan x; 3. y = 1/x^4-4cos x

Answers

1 . y'=0 is the derivative of the function y = 14.

2. y' =  9[tex]x^8[/tex]+3[tex]sec^2x[/tex]  is the derivative of the function y= [tex]x^9[/tex]+3tanx

3. y' = [tex]\frac{-4}{x^5}[/tex] + 4sinx is the derivative of the function y = [tex]\frac{1}{x^4}[/tex] - 4cos x

1 . The derivative of a constant is always zero.

A constant function is a function whose value does not depend on the input value.

So y = 4 is a constant function, its derivative is always zero.

So the derivative of y=4 is 0

2. The differentiation of [tex]x^9[/tex]+3tanx is 9[tex]x^8[/tex]+3[tex]sec^2x[/tex]

The power rule states that the derivative of x^n (where n is a constant) is nx^(n-1). So the derivative of x^9 is 9x^8.

The derivative of tanx is [tex]sec^2x[/tex].

And the derivative of 3tanx is 3[tex]sec^2x[/tex]

So, [tex]x^9[/tex]+3tanx  is differentiated as9[tex]x^8[/tex]+3[tex]sec^2x[/tex]

3. The derivative of y = [tex]\frac{1}{x^4}[/tex] - 4cos x can be found using the power rule and the chain rule.

The power rule states that the derivative of x^n (where n is a constant) is nx^(n-1). In this case, [tex]\frac{1}{x^4}[/tex] can be rewritten as [tex]\frac{1}{x^4}[/tex] and the derivative would be -4 [tex]\frac{1}{x^5}[/tex]

The chain rule states that the derivative of (f(g(x)) is f'(g(x))*g'(x). In this case, the inner function is -4cos x, the derivative of cos x is -sin x and the outer function is , [tex]\frac{1}{x^4}[/tex] the derivative of that is -4 [tex]\frac{1}{x^5}[/tex]. So the derivative of -4cos x is -4(-sin x)

So the final derivative of y = [tex]\frac{1}{x^4}[/tex]  - 4cos x is [tex]\frac{-4}{x^5}[/tex] + 4sinx

To know more about derivative click below:

https://brainly.com/question/25324584#

#SPJ4

Please help me and explain

Answers

The value of x in the equation 8 (x - 3) + 7 = 2x (4 - 17) is x = 1/2.

What is an Equation?

An equation is the statement of two expressions located on two sides connected with an equal to sign. The two sides of an equation is usually called as left hand side and right hand side

The given equation is,

8 (x - 3) + 7 = 2x (4 - 17)

Distributive property : p (q + r) = p q + p r

Applying the property here,

8x - (8 × 3) + 7 = 2x × (-13)

8x - 24 + 7= -26x

8x - 17 = -26x

8x + 26x = 17

34x = 17

x = 17/34

x = 1/2

The mistake of Lin happened in the second step where 4 - 17 = -13 but she wrote 13.

Hence the value of x is 1/2 not -1/2 as the solution of Lin.

Learn more about Equations here :

https://brainly.com/question/29657983

#SPJ1

From the set {8, 19, 25}, use substitution to determine which value of x makes the inequality true

Answers

x = 19 and x = 25 make the inequality true.

What is inequality?

In mathematics, a relationship between two expressions or values that are not equal to each other is called 'inequality. ' So, a lack of balance results in inequality.

To use substitution to determine which value of x makes the inequality true, we can substitute each value from the set {8, 19, 25} into the inequality and see if it makes the inequality true or false.

For example, if the inequality is x < 10, we can substitute 8, 19 and 25 into the inequality to see which one makes it true:

8 < 10 is true

19 < 10 is false

25 < 10 is false

So, we can see that only 8 makes the inequality true. Therefore, x = 8 makes the inequality true.

If the inequality is x > 10, we can substitute 8, 19 and 25 into the inequality to see which one makes it true:

8 > 10 is false

19 > 10 is true

25 > 10 is true

Hence, x = 19 and x = 25 make the inequality true.

To learn more about inequality visit,

https://brainly.com/question/25275758

#SPJ1

Look at the picture

Answers

Answer:

1/15

Step-by-step explanation:

dividend=1/3

divisor=5

since

Dividend ÷ Divisor = Quotient.

1/3 ÷5 = 1/15

Therefore, quotient = 1/15

Given f(x) = -4x² + 4x - 1, find f(-6)


Please!!!

Answers

Answer:

Step-by-step explanation:

To find f(-6), we need to substitute -6 for x in the function f(x) = -4x² + 4x - 1.

f(-6) = -4(-6)² + 4(-6) - 1

f(-6) = -4(36) + (-24) - 1

f(-6) = -144 + (-24) - 1

f(-6) = -167

Therefore, f(-6) = -167

Which expression is 0.50.50, point, 5 times as large as 342 + 156342+156342, plus, 156?
Choose 1 answer:
Choose 1 answer:

(Choice A)
A
(342 + 156) \times 0.5(342+156)×0.5left parenthesis, 342, plus, 156, right parenthesis, times, 0, point, 5

(Choice B)
B
342 + 156 \times0.5342+156×0.5342, plus, 156, times, 0, point, 5

(Choice C)
C
(342 +156)\div0.5(342+156)÷0.5

Answers

The expression that is 0.5 times as large as 342 + 156 is (342 + 156) x 0.5

This is because 0.5 is a factor that multiplies the entire sum of 342 + 156.

So the correct answer is (Choice A) (342 + 156) x 0.5

Answer: The correct answer is (A) (342 + 156) × 0.5. This is because in mathematics, multiplication and division should be done before addition and subtraction. Therefore, the parenthesis is solved first, which results in 342 + 156 = 498. Then, 0.5 is multiplied to the result, 498 × 0.5 = 249.

Step-by-step explanation:

Ruben measured how many minutes he meditated each night and the number of hours he slept. Plot the data in a scatter plot.

Meditation (minutes) 444 888 101010 444 181818 444
Sleep (hours) 4.54.54, point, 5 9.59.59, point, 5 8.58.58, point, 5 666 101010 777

Answers

The scatter plot for the given data (See full and correct details attached) is appended accordingly.

What is a scatter plot?

A scatter plot is a collection of dots drawn on two axes, horizontal and vertical. Scatter plots are useful in statistics because they illustrate the amount, if any, of correlation between the values of observed quantities or events (called variables).

Scatter plots aid in the visual representation of correlations between economic factors such as employment and production, inflation and retail sales, and taxes and economic growth.

As you can see there is a slight positive correlation between the number of hours meditated and the numberr of hours slept.

Learn more about Scatter plot:
https://brainly.com/question/13984412
#SPJ1

K
Find the measures of an interior angle and an exterior angle of a regular 15-gon.
The measure of an interior angle is

Answers

The measure of each interior angle of the polygon is 156°.

What is the interior angle of polygon?

In a regular polygon, all interior angles are equal. The interior angle of a polygon = sum of interior angles and the number of sides is the formula for determining the size of an interior angle. A polygon's exterior angles add up to 360°.

Given that the number of sides of the polygon is 15. The sum of the interior angles of the polygon is calculated by the formula:-

Sum = ( n - 2 ) x 180

Sum = ( 15 - 2 ) x 180

Sum = 2340

The measure of each angle is calculated as:-

Angle = 2340 / 15

Angle = 156°

To know more about the interior angle of a polygon follow

https://brainly.com/question/30297817

#SPJ1

Which explains why the commutative property of addition does not work for subtraction?

Answers

The commutative property of addition states that the order of the numbers being added does not affect the result. For example, the sum of 2 + 3 is the same as the sum of 3 + 2, which is 5.

The commutative property of addition does not work for subtraction because subtraction is not commutative. In subtraction, the order of the numbers being subtracted does affect the result. For example, the difference of 3 - 2 is 1, but the difference of 2 - 3 is -1.

The reason for this is that subtraction is the inverse operation of addition and the inverse operation of a commutative operation is not always commutative. In addition, subtraction is not commutative because when we subtract the smaller number from the larger number, we get a positive result but when we subtract the larger number from the smaller number we get a negative result.

To know more about commutative property click on below link:

https://brainly.com/question/778086#

#SPJ4

how to know if a piecewise function is a function

Answers

Answer:

Step-by-step explanation:

a piecewise function is a function that is defined by different formulas or functions for each given interval. In mathematics, a piecewise-defined function (also called a piecewise function or a hybrid function) is a function which is defined by multiple sub-functions, each sub-function applying to a certain interval of the main function's domain (a sub-domain).

during which time interval did dylan maintain the fastest average speed

Answers

The time interval that saw Dylan maintain the fastest average speed was B. between hour 1 and hour 2.

Where did Dylan maintain the fastest speed ?

Dylan maintained the fastest speed at the interval that saw him cover more distance in a shorter amount of time. You can find the speed at these intervals by using the speed formula of distance divided by time.

Speed between hour 0 and 1 :
= 25 miles / 1 hour

= 25 miles per hour

Speed between hour 1 and 2 :

= ( 75 - 25 ) / 1

= 50 miles per hour

Speed between hour 3 and 5 :

= ( 125 - 75 ) / 2

= 25 miles per hour

The fastest speed was therefore between hour 1 and 2.

Find out more on speed at https://brainly.com/question/30144542

#SPJ1

Options for this question are:

between hour 0 and hour 1between hour 1 and hour 2between hour 2 and hour 3between hour 3 and hour 5

What is the exponential of 10?

Answers

The term "exponential of 10" means the numbers in which the base is 10 and the exponent is an integer.

The Exponential of 10 or the "powers of 10" means when the number 10 is multiplied a certain number of times, then the  product is expressed using exponents.

These numbers which are written as the exponents are exponents of 10.

For example : 10² , 10³ represents different exponents of 10 .

In general form of the exponent of 10 or power of 10 is represented as 10ⁿ .

For Example : 10 to the exponent of 5 can be written as 10⁵, and

it's value is calculates as :

⇒ [tex]10^{5}=10\times\ 10 \times 10\times 10\times 10[/tex]

⇒[tex]10^{5}= 100000[/tex] .

Learn more about Exponent here

https://brainly.com/question/4869588

#SPJ4

Graph the image of A(7, −6)
after a reflection in y=x
followed by a reflection in x=−3.

Answers

The image of A After a reflection in y=x followed by a reflection in x=−3. is (0. 7).

What is a reflection?

There are two ways of reflection.

Along x-axis:

(x, y) – (x, -y)

Along y-axis:

(x, y) - (-x, y)

We have,

A = (7, -6)

Reflection rules over y = x.

(x, y) → (y, x)

So,

(7, -6) = (-6, 7)

Now,

Reflection in x = -3

Reflection rules over the y-axis.

(x, y) → (-x, y)

So,

x = -3

There are 3 units between -3 and -6.

So,

3 + 3 = 6 units will be added during reflection over y = -3

i.e

3 units on the left side of y = -3

3 units on the right side of y = -3

So,

(-6, 7) = (-6 + 6, 7) = (0, 7)

Thus,

The image of A is (0. 7).

Learn more about reflections here:

https://brainly.com/question/12463306

#SPJ1

The reflection of image of point in y = x is (-6, 7),

and  reflection in x = −3 is (-13, -6).

What are transformations?

The transformation, or f: X X, is the name given to a function, f, that maps to itself. After the transformation, the pre-image X becomes the picture X. Any operation, or a combination of operations, such as translation, rotation, reflection, and dilation, can be used in this transformation.

Given a point  A(7, −6)

A. a reflection in y = x

Flipping is the term for reflection. A reflection is the shape's mirror image. The line of reflection is the path taken by an image when it reflects.

reflection in y = x

x changed to y and y changed to x

x = -6 and y = 7

coordinates are A'(-6, 7)

B. a reflection in x = −3.

let the coordinates be (a, b)

reflection in x = k

image coordinates will be A" (2k - a, b)

here a = 7, k = -3, and b = -6

2k - a = 2(-3) - 7

2k - a = -13

image coordinates will be A"(-13, -6)

Hence the coordinates are A'(-6, 7),

and reflection in x = -3,

coordinates aere A"(-13, -6).

Learn more about transformations;

https://brainly.com/question/11709244

#SPJ1

Is 1 1 2 3 5 8 an arithmetic sequence?

Answers

No, 1 1 2 3 5 8 is not an arithmetic sequence. An arithmetic sequence is a sequence of numbers in which each term is obtained by adding a constant to the previous term.

Thus, the difference between successive terms is the same. In the given sequence, the difference between terms 1 and 2 is 0, between terms 2 and 3 is 1, between terms 3 and 5 is 2, and between terms 5 and 8 is 3. Therefore, the difference between successive terms is not the same and hence, 1 1 2 3 5 8 is not an arithmetic sequence.

Learn more about Arithmetic Sequence here:

https://brainly.com/question/6561461

#SPJ4

Can someone help me with these pls

Answers

The speed of spin of carousel is 0.286 miles/minutes. The The speed at which something moves in a specific direction is known as its velocity. as the speed of a car driving north on a highway or the speed at which a rocket takes off.

Which math is speed?

based on the distance traveled in a given amount of time. These cars can travel at speeds of more than 150 kilometers per hour (km/h). Meters per second (m/s) is the fundamental unit of speed in the metric system.

Given,

distance spinned=2 miles

time taken=7min

speed=distance/time

speed=2/7=0.286 miles/minute

To know more about metric system visit:-

brainly.com/question/29953513

#SPJ1

How do you find the value of n in exponents?

Answers

We can find the value of n in exponents through various rules based on the given equation.

If x is any real number and n is a positive integer, then [tex]x^n[/tex] is equivalent to repeated multiplication.

We can also write [tex]x^n[/tex] in the following way:

[tex]x^n[/tex] = x * x * x * x * x *...... * x (n times)

This can be referred to as "n raised to the power of x," "n to the power of n," or just "n." In this case, n is the exponent or power, and x is the base.

We may infer a few fundamental guidelines for exponentiation from this concept. There are various methods of finding the exponent based on various rules, namely,

Product ruleQuotient rulePower of a powerPower of a productPower of onePower of ZeroPower of negative oneChange the sign of exponentsFractional exponents

Read more about exponents from:

https://brainly.com/question/30066987

#SPJ4

To find the value of n in exponents, you can use the property that a^n * a^m = a^(n+m)

For example, if you have the expression (2^3)^n, you can use the property above to find the value of n by dividing both sides by 2^3, so (2^3)^n / 2^3 = 1^n. Now you can see that n = 1.

Another way to find the value of n in exponents is to use logarithms. The logarithm base "a" of a^n is n. Therefore, if you know the value of a^n, you can find the value of n by taking the logarithm base "a" of a^n.

For example, if a^n = 8 and a=2, then n = log2(8) = 3.

In summary, there are a couple of ways to find the value of n in exponents, but the most common way is to use the property of exponents or logarithms.

To learn more about exponents:

https://brainly.com/question/13669161

#SPJ4

i need help this is due at 12:10

Answers

Answer:

I believe the answer is 180°

Is x³ an exponential function?

Answers

Yes, is an exponential function. An exponential function is a function in which the variable (x) is in the exponent.

The general form of an exponential function is f(x) = a^x, where a is the base and x is the exponent. In the case of x³, the variable (x) is in the exponent. x³ represents x raised to the power of 3, where x is the base and 3 is the exponent.

Exponential functions are often used to model growth and decay in a variety of natural phenomena, such as population growth, radioactive decay, and compound interest. Understanding exponential functions is important for solving mathematical problems, especially in algebra, calculus, and applied fields such as physics and engineering.

Learn more about exponential function here:

https://brainly.com/question/27161222

#SPJ4

Can somebody help me on this one please I am so confused don’t know none of this stuff

Answers

rotation then reflection.

.

.

.

.

.

.

.

.

.

.

.

.

.

.

Is rotation congruent or similar?

Answers

Answer:

a

Step-by-step explanation:

Contruct an iocele right-angled Triangle 'XYZ' in which angle Y=90° and two ide are 5cm each

Answers

Isosceles right angled triangle XYZ is constructed with the given measure of ∠Y =90° , YX = 5cm and YZ = 5cm each using steps of construction.

Constructed diagram is attached.

As given in the question,

Given measurement to construct a isosceles right angled triangle are:

Measure of ∠Y =90°

Measure of side length

YX = 5cm and YZ = 5cm

Constructed diagram is attached.

Step of construction :

Draw a ray.Take point Y on it and draw an arc of any measure.Take the measure more than half of the radius of the drawn arc.Take each end point as centre and draw an arc on the upper half plane of the ray.Draw ray perpendicular through point Y in the upper half plane.Now take measure of 5cm and point Y as centre and cut an arc on each of the ray.Name the point as 'X' and 'Z'.Join XZ .Isosceles right angled triangle is constructed with the given measurement.

Therefore, construction of isosceles right angled triangle is done as per the above steps of construction.

The above question is incomplete, the complete question is :

Construct an isosceles right-angled Triangle 'XYZ' in which angle Y=90° and two side are 5cm each.

learn more about triangle here

brainly.com/question/2773823

#SPJ4

Find the values of x and y.

40°

Answers

(x,, y,) is a point on the line in the point-slope formula, and m is the slope.

How should slope m be written?

When you know the slope of the line to be investigated and the point supplied is also the y intercept, you may utilize the slope intercept formula y = mx + b. (0, b). The y value of the y intercept point is represented by b in the formula.

The equation of a line can be written in several different formats:

Standard form

Ax+ By = C

A, B, and C must be real numbers and A and B cannot both be zero.

Slope-intercept form

Y = MX + b

M is the slope and b is the y-intercept.

Point-slope form

y-y₁ = m(x-x1)

In the point-slope formula, (x,, y,) is a point on the line and m is the slope.

To learn more about slope to refer:

https://brainly.com/question/19131126

#SPJ1

The average time taken to complete a test follows normal probability distribution with a mean of 70 minutes and a standard deviation of 25 minutes. The probability of a randomly selected student completing the test in 45 minutes or less is approximately equal to %. The probability of a randomly selected student completing the test in 95 minutes is %.

Answers

The probability of a randomly selected student completing the test in 45 minutes or less is approximately equal to 16%.The probability of a randomly selected student completing the test in 95 minutes is 0%.

How to obtain probabilities using the normal distribution?

The z-score of a measure X of a variable that has mean symbolized by [tex]\mu[/tex] and standard deviation symbolized by [tex]\sigma[/tex] is obtained by the rule presented as follows:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The z-score represents how many standard deviations the measure X is above or below the mean of the distribution, depending if the obtained z-score is positive or negative.Using the z-score table, the p-value associated with the calculated z-score is found, and it represents the percentile of the measure X in the distribution.

The mean and the standard deviation for this problem are given as follows:

[tex]\mu = 70, \sigma = 25[/tex]

The probability of 45 minutes of less is the p-value of Z when X = 45, hence:

Z = (45 - 70)/25

Z = -1

Z = -1 has a p-value of 0.16 (rounding).

As for the probability of an exact time, such as 95 minutes, is of 0%, as the normal distribution is continuous.

More can be learned about the normal distribution at https://brainly.com/question/25800303

#SPJ1

Rahul bought a weater and aved r20 when a dicount of 25% wa given. What wa the price of the weater before the dicount ?

Answers

The price of a sweater bought by Rahul before the discount is Rs. 80.

Let us assume the price of the sweater before the discount to be x.

Given that,

The money saved by Rahul will be equal to the discount given for the sweater.

Therefore, we can say that Rs. 20 will be equal to 25% of the price of the sweater before the discount.

The equation we would obtain from the language above would be,

25% of x = 20

Solving this equation further, we can see that,

=> 25% of x = 20

=> 25* 1/100 * x = 20

=> x/4 = 20

=> x = 80

As we assumed x to be the price of the sweater before the discount,

So, the price of a sweater bought by Rahul before the discount is Rs. 80.

Complete question: Rahul bought a sweater and saved Rs. 20 when a discount of 25% was given. What was the price of the sweater before the discount?

To know more about equations visit: brainly.com/question/29657983

#SPJ4

Other Questions
Quick assets (cash, short-term investments, and current receivables) divided by current liabilities is the: Multiple Choice Current liability turnover ratio. Working capital ratio. Current ratio. What is typically the first attribute of an entity? Odina signs a covenant not to compete with her employer, penultimate sales corporation. a court decides that the covenant is overly restrictive. the court will likely:________ Question 4This sentence is an example ofThe approaching car's headlights winked at me.O a simileO onomatopoeiaO a metaphorO hyperboleO personificationO alliteration The area of a sector of a circle of radius 8cm is 45cm. Find the size of the angle subtended at the centre of the circle, correct to one decimal place. (Take = 22/7) Dave spends hours looking at himself in the mirror and believes that he is much more attractive and intelligent than any of his friends. He also often seeks compliments from friends and becomes angry when they are not provided. Based on this description, Dave may have a trait called: 22. Robert Hooke, a French scientist, published Micrographia in which he described manyof his microscopic observations.a. True b. False Why do we see that women make up the majority of older adults that are divorced? In order to study personality development, a researcher studies the same individuals at 7, 14, 21, and 28 years of age. In this case, the researcher is using the _____ method. Transitivity refers to a. the ability to think with abstract concepts. b. being able to compare all items in a set to all other items. c. hypothetical thinking. d. centration. Find the indicated real nth root(s) of a.n=3, a = - 216 Which compound has both covalent and ionic bonds? pls give the explanation thx A NH3B Na2SO4C CH3COOHD NaCl Which statement describes the purpose of the Freedom Charter?to replace the existing constitutionto state core beliefs and demand rightsto announce a new governments creationto reinforce the countrys racial divide Alyssa is training for a triathlon, a timed race that combines swimming, biking, and running. Alyssa has only 20 hours per week that she can devote to training for her race. Which basic principle of individual choice does this scenario illustrate The capital city of arizona is phoenix. what kind of phrase are the bolded words? infinitive phrase noun phrase adjective phrase adverb phrase Select all the correct answers.Exponential function fis represented by the table.2X00-12B-4Function gis represented by the equation.9 (2) = -12 (3)Which statements are true about the two functions?03243Both functions are increasing on all intervals of x.Both functions approach the same value as x approaches ...The functions have the same x-intercept.Both functions approach - as x approaches -...The functions have the same y-intercept. If a firm increases its plowback ratio, this will definitely result in _______ p/e ratio. The more reliable measure for comparing changes in the standard of living over a series of years is:_____ An equestrian club orders magazine subscriptions for new members.Last year they had 32 new members and spent $624 on subscriptions.Use the equation 32m = 624 to find the cost of each subscription. Try itwriting a SummaryWith advancing years I feel I must give this question ofwhat I want to leave behind me greater thought, forbefore long I shall be moving on to fields unknown, andperhaps it may make a difference if I actually know whatI would like to bequeath to a new generation. Perhaps thebest I can do is to pray that the youth of today will havethe ability to live simply and to get joy out of living, thedesire to give of themselves and to make themselvesworthy of giving, and the strength to do without anythingwhich does not serve the interests of the brotherhood ofman. If I can bequeath these desires to my own children,it seems to me I will not have lived in vain.-"What I Hope to Leave Behind,"Eleanor RooseveltBased on the final paragraph and what you rememberfrom the speech overall, write three to four sentencessummarizing what Roosevelt hopes to leave behind.