find y' if x2 y2 = 10.

The surface area of square pyramid is 207.04 square inches.

Surface area is the area of all outer facing surfaces on an object. The total surface area is calculated by adding all the areas on the surface: the areas of the base, top, and lateral surfaces (sides) of the object.

The formula to find the surface area of square pyramid is A=a²+2a√(a²/4+h²)

Here, a=8 inches and h=8 inches

Now, A= a²+2a√(a²/4+h²)

A= a²+2a√(a²/4+h²)

A= 8²+2×8√(8²/4+8²)

A= 64+16√(16+64)

A= 64+16√80

A= 64+16×8.94

A= 207.04 square inches

Therefore, the surface area of square pyramid is 207.04 square inches.

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The graph represents this system of inequalities:

F. y ≤ −x + 4

G. y ≤ 3x − 1

In Mathematics, the point-slope form of a straight line can be calculated by using this mathematical expression:

y - y₁ = m(x - x₁) or y - y₁ = (y₂ - y₁)/(x₂ - x₁)(x - x₁)

Where:

Next, we would determine the linear equation representing the line of f(x) which passes through the points (0, 4) and (4, 0) by using the point-slope form as follows:

y - y₁ = (y₂ - y₁)/(x₂ - x₁)(x - x₁)

y - 0 = (4 - 0)/(0 - 4)(x - 4)

y - 0 = -1(x - 4)

y = -x + 4

Therefore, an inequality representing the line of f(x) is y ≤ -x + 4

For the line of g(x), we have:

y - y₁ = (y₂ - y₁)/(x₂ - x₁)(x - x₁)

y - (-1) = (5 - (-1))/(2 - 0)(x - 0)

y + 1 = 3(x - 0)

y = 3x - 1

Therefore, an inequality which represents the line of g(x) is y ≤ 3x - 1.

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Complete Question:

In the graph, the area below f(x) is shaded and labeled A, the area below g(x) is shaded and labeled B, and the area where f(x) and g(x) have shading in common is labeled AB. Graph of two intersecting lines. The line f of x is solid and goes through the points 0, 4, and 4, 0 and is shaded below the line. The other line g of x is solid, and goes through the points 0, negative 1 and 2, 5 and is shaded below the line. The graph represents which system of inequalities?

y ≤ −3x − 1

y ≤ −x − 4

y > −3x + 1

y ≤ −x − 4

y < 3x − 1

y ≤ −x + 4

y ≤ 3x − 1

y ≥ −x + 4

The conversion from torr to atm involves multiplying the torr value by a conversion factor of 1/760. This is because 1 atm is equal to 760 torr.

Given, that convert torr to atm.

Atmosphere (atm) and torr are both units of pressure measurement. Torr is a unit of pressure in the centimeter-gram-second (CGS) system, while atm is a unit of pressure in the International System of Units (SI).

The conversion from torr to atm involves multiplying the torr value by a conversion factor of 1/760. This is because 1 atm is equal to 760 torr.

For example:

To convert 2.77 atm to torr, multiply 2.77 by 760, which gives 2,108 torr.  In conclusion, 2.77 atm is equal to 2,108 torr.

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The angle that is a vertical angle to AEB is CED.

When we have the intersection of two lines, we define the vertical angles as the pair of angles that share a vertex and don't share sides.

So these angles are only connected by the vertex.

So a vertical angle to AEB should also have the vertex E, and no common sides to AEB, the only angle that meets that requiriment is CED.

Then we conclude that the vertical angle to AEB is CED.

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Answer: 17mm

Step-by-step explanation: 153/9 is 17

The value of c for the given function at x = 0 to be continuous is c = 8/15.

The following three requirements must all be met for a function to be regarded as continuous at a point:

In other words, a function is continuous at a place if you can draw it without moving your hand and the function's graph doesn't have any gaps or leaps at that location. Calculus' central idea of continuity is crucial for defining derivatives and integrals.

According to the question

Given function =  f(x)= 12x−4sin(3x)/5x3

We require f(0) = c, where c is the value given to the function at x = 0, in order to make the function continuous at that point. We may assess the limit of f(x) as x gets closer to zero to determine c.

The limit of f(x) as x approaches 0 may be determined using L'Hopital's rule as follows:

lim x→0 f(x) = lim x→0 (12x - 4 * sin(3x)) / (5x^3)

= lim x→0 (12 - 4 * 3 * cos(3x)) / (15x^2)

= 8 / 15.

So, c = 8 / 15. Therefore, the function f(x) = (12x - 4 * sin(3x)) / (5x^3), x ≠ 0 and c, x = 0 is continuous at x = 0 with c = 8 / 15.

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The Volume of Each Shape is Shown below.

Volume' is a mathematical quantity that shows the amount of three-dimensional space occupied by an object or a closed surface. The unit of volume is in cubic units such as m³, cm³, in³ etc.

Given:

1. r = 6 inch, height = 6 inch

So, Volume of Cone = 1/3 πr²h

                                  = 1/3 x 3.14 x 6 x 6 x 6

                                   = 226.08 inch³

2. diameter = 6cm

r = 3 cm,

so, volume of each piece

= 4/3 πr³

= 4/3 x 3.14 x 3 x 3 x 3

= 113 cm³

now, volume of 20 candies

= 20 x 113

=  2260 cm³ of chocolate.

3. The height of the cone shape, h = 84 inches

radius = 8 inches

The cost per cubic inch is $2.25.

The cost of nickel for the sculpture is given by

= 2.25 x 1/3πr²h

= 2.25 x 1/3 x 3.14 x 8 x 8 x 84

= $12660.48.

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The pair of variables with an inverse relationship is y = 1/x. This relationship can be seen by graphing the two variables on a coordinate plane and observing the shape of the graph.

As x increases, y decreases and as x decreases, y increases. This is because the equation y = 1/x can be written as y = c/x, where c is a constant. Since c is a constant, as the value of x increases, the value of y decreases, and vice versa.

For example, if x = 4, then y = 1/4, or 0.25. If x increases to 8, then y decreases to 1/8, or 0.125. On the other hand, if x decreases to 2, then y increases to 1/2, or 0.5. As can be seen, as x increases, y decreases, and as x decreases, y increases, which shows the inverse relationship between the two variables.

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The value of t for which the linear functions are parallel is given as follows:

t = 5.

Linear functions are parallel when they have the same slope.

Given two points, the slope is calculated as the change in y divided by the change in x.

Considering points (-4, -7) and (2,-3), the slope is given as follows:

m = (-3 - (-7))/(2 - (-4)) = 4/6.

Considering points (-4,1) and (2,t), the slope is given as follows:

m = (t - 1)/(2 - (-4)) = (t - 1)/6.

The two lines will be parallel when:

4/6 = (t - 1)/6.

Hence the value of x is obtained as follows:

t - 1 = 4.

t = 5.

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The limit as h→0 of f(x+h) − f(x) / h is 0. the denominator of the fraction is 0, the limit is undefined.

To evaluate this limit, we need to plug in the given value for x and the function f(x). We are given that f(x) = x2 and x = 3.

Therefore, we have:

limh→0 f(3+h)−f(3) h

Since f(3) = 3^2 = 9, we can rewrite the limit as:

limh→0 f(3+h)−9

We can now plug in the value of h=0 to get the value of the limit:

limh→0 f(3+0)−9 0

Since the denominator of the fraction is 0, the limit is undefined.

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The required equation is C = 8 + 0.25m, where m represents the number of mats used per month and C represents the total cost in dollars.

Let's use "m" to represent the number of center floor mats used per month, and "C" to represent the total cost in dollars. The total cost can be expressed as the sum of a fixed monthly fee of $8 and an additional fee of $0.25 per center floor mat used:

C = 8 + 0.25m

This equation expresses the relationship between the number of center floor mats used (m) and the total cost (C) in dollars.

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Probability determines the likelihood of an event occurring: P(A) = f / N

P(A) = f / N indicates the likelihood of an event occuring. Odds and probability are connected, but odds are affected by probability. Before calculating the chances of an event occurring, you must first calculate probability.

Finding the chance of a simple event occurring is simple: add the probabilities together. For instance, if you have a 10% chance of winning $10 and a 25% chance of winning $20, your total chances of winning are 10% + 25% = 35%. According to probability, heads have a 12 chance, thus we may expect 50 heads. But when we attempt it, we could get 48 heads, or 55 heads, or anything else, but in most circumstances, we’ll get something close to 50.

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A. The circular base of the bucket is larger.

B. The bale has a larger volume.

A. The circular base of the bucket has a larger area than the rectangular base of the bale.

The formula for the area of a circle is π * r^2, where r is the radius. The diameter of the bucket is 3 feet, so the radius is 3/2 feet. The area of the circular base is therefore π * (3/2)^2 = 7.07 square feet.

The rectangular base of the bale has length 2 feet and width 3 feet, so its area is 2 * 3 = 6 square feet.

Since 7.07 > 6, the circular base of the bucket is larger.

B. The bale has a larger volume than the bucket.

The formula for the volume of a rectangular prism is l * w * h, where l is the length, w is the width, and h is the height. The bale has length 2 feet, width 3 feet, and height 5 feet, so its volume is 2 * 3 * 5 = 30 cubic feet.

The formula for the volume of a cylinder is π * r^2 * h, where r is the radius and h is the height. The radius of the bucket is 3/2 feet and the height is 5 feet, so the volume of the bucket is π * (3/2)^2 * 5 = 22.36 cubic feet.

Since 30 > 22.36, the bale has a larger volume.

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The complete question goes thus:

At a farm, animals are fed bales of hay and buckets of gain.Each bale of hay is in the shape of a rectangular prism.The base side lengths 2 feet and 3 feet,and the height is 5 feet. Each bucket of grain is a cylinder with diameter of 3 feet. The height of the bucket is 5 feet as the height of bale. A. Which is larger in area, the rectangular base of the bale or the circular base of the bucket? Explain how you know B. Which is larger in volume, the bale or the bucket? Explain how you know

92% is the percent of decrease.

A relation is a function if it has only One y-value for each x-value.

The function [tex]M(t)=975.(0.92)^{t}[/tex]

Function represents the number of milligrams of a medication in a patients body as a function of time.

t represents the time.

0.92×100=92%

975 is the initial value and 0.92 is the percent of decrease.

Hence, 92% is the percent of decrease.

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The bearing of point X from point Z is 280°

To find the bearing of point X from point Z, we need to use the principle of alternate angles in each point and sum of angles of a triangle

The triangle formed is as follows

angle x = 100 - 65 = 35

angle y = (180 - 140) + 65 = 105

angle z = 180 - angle y + angle x = 180 - 35 + 105 = 40

The bearing of point X from point Z,

= 360 - angle z - alternate angle from y

= 360 - 40 - 40

= 280

Bearing of X from Z =  280

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The probability that a randomly selected person from the city will be a woman is 17,000 / 190,000, or approximately 0.089.

1. Calculate the total number of women: 17,000

2. Calculate the total population of the city: 190,000

3. Divide the number of women by the total population: 17,000 / 190,000

4. The probability is approximately 0.089

The probability that a randomly selected person from the city will be a woman is 17,000 / 190,000, or approximately 0.089.

The probability that a randomly selected person from the city of Akron, Ohio will be a woman is 0.089. This means that out of every 100 people, approximately 8.9 of them will be female. The city has a population of 190,000 and 17,000 of them are female. This means that approximately 8.9 percent of the city's population is female.

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The linear regression equation that best fits the data is given as follows:

y = 1.2x - 21.3.

Hence the projected test score for an student with a homework score of 45 is given as follows:

32.7.

To find the regression equation, also called line of best fit or least squares regression equation, we need to insert the points (x,y) in the calculator. These points are given on a table or in a scatter plot in the problem.

The points for this problem are given as follows:

(78, 66), (89, 76), (54, 42), (86, 90), (74, 68), (73, 73), (86, 84), (63, 54), (64, 54)

Inserting these points into the calculator, the line of best fit is given as follows:

y = 1.2x - 21.3.

The projected test score for an student with a homework score of 45 is found replacing x by 45, hence:

y = 1.2(45) - 21.3

y = 32.7.

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The value of k given sequence is =300 and the value of the term Sk=4875,

In mathematics, we may come across different types of numbers, and patterns. One of the number patterns includes sequences. The sequence is a specified collection of objects in which repetitions are allowed and order matters. Formally, a sequence is a function from natural numbers to the elements at each position. Similar to a set, it contains members, and they are called elements or terms. The number of elements is called the length of the sequence. Unlike a set, the same elements can appear multiple times at different positions in a sequence, and the order does matter.

value of k

U1 =1.3

U2= 1.4

Uk = 31.2

a = 1.3

d = 1.4 - 1.3 = 0.1

Uk = 1.3 + (k - 1)(0.1)

=> 1.3 + (k - 1)(0.1) = 31.2

=>  (k - 1)(0.1) = 29.9

=> k - 1 = 299

=> k = 300

Sk  = (300/2)(1.3 + 31.2)

= 150 * (32.5)

= 4875

F is the sum of the terms for which the term is not a multiple of 3

3rd term = 1.5

6th term = 1.8

300th term = 31.2

Total terms = 100

Sum = (100/2)(1.5 + 31.2)  =  1635

F = 4875 - 1635   = 3240

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To find the width of Wyoming, we need to find the area of the state and divide by the width.

Area = population density x total population

Area = 2.16 x 564,000 people

Area = 1,222,624 square kilometers

Width = Area / Length

We don't have the length, so we'll have to rearrange the formula to solve for it:

Width = Area / Length

Length = Area / Width

Length = 1,222,624 square kilometers / Width

We'll solve for width:

Width = 1,222,624 square kilometers / Length

Since we don't know the length, we cannot solve for width.

16 is the number which shows a proportional relationship between x and y.

The ratio is defined as the comparison of two quantities of the same units that indicates how much of one quantity is present in the other quantity.

here, we have,

the ratio of x:y = 0.8 : 4

let, the number for y be a

so that, x: y is  proportional .

i.e. 3.2 : a = 0.8 : 4

or, a = 16

Hence, 16 is the solution.

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f(-2) and f(2) does not exist. Limit when x tend to -2, 0 and 4 does not exist. f(0) = 5 and f(4) = -1. Limit when x tend to 2 converges to 0.5.

f(-2) does not exist as shown in the figure there is no definite value at -2. Also limit does not exist at x = -2 as right limit approaches positive infinity where left limit approaches negative infinity.

f(0) equals 5 and not 3.5 as we can see that at 3.5 it is a hole implying it is not defined, while at 5 it is a solid dot. Limit does not exist at f(0) as the left limit approaches 3.5 and the right limit approaches 5.

f(2) does not exist as there is a hole at that point in the graph. Limit as x tend to 2 approaches 0.5 as both right and left limit approaches 0.5.

f(4) equals -1 as the solid dot is at that point. As x tend to 4 the limit diverges to positive infinity implying the limit does not exist.

--The question is not readable, answering to the question below and graph attached--

"Use the graph of the function f to decide whether the value of the given quantity exists. (If an answer does not exist, enter DNE.)

(a) f(−2)

(b) lim x→−2 f(x)

(c) f(0)

(d) lim x→0 f(x)

(e) f(2)

(f) lim x→2 f(x) 0.5

(g) f(4)

(h) lim x→4 f(x) "

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The measure of angle D is ∠D = 65°.

Two triangles are said to be similar if there corresponding sides are proportional and their corresponding angles are equal.

Given is that triangle ΔABC is similar to triangle ΔDEF.

We can write -

∠D + x + 90° = 180°

∠D = 90° - x

Since both the triangles are similar, we can write -

∠D = ∠A

{90° - x} = {2x + 15}°

3x = 75°

x = 25°

∠D = 90 - x = 65°

∠D = 65°

Therefore, the measure of angle D is ∠D = 65°.

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The value of the variable x for the function f(x) = x² + 4x for which

f(f(x) ) = f(x) is equal to x = -1 or x = -3.

The function f(x) = x² + 4x

Substitute the value in the required function we get,

Right hand side

= f ( f(x))

= f ( x² + 4x )

= ( x² + 4x )² + 4 ( x² + 4x )

= x⁴ + 8x³ + 16x² + 4x² + 16x

= x⁴ + 8x³ + 20x² + 16x

Left hand side

f(x)

= x² + 4x

Equate left hand side is equal to right hand side we get,

x⁴ + 8x³ + 20x² + 16x = x² + 4x

⇒x⁴ + 4x³ + 4x³ + 16x² + 4x² + 16x =  x² + 4x

⇒x² ( x² +4x ) + 4x ( x² + 4x )+ 4 ( x² + 4x ) = x² + 4x

⇒( x² + 4x ) ( x² + 4x + 4 ) = x² + 4x

⇒ x² + 4x + 4 = 1

⇒ ( x + 2 )²  - 1² =0

⇒ ( x + 2 -1 ) ( x+ 2 + 1) = 0

⇒ ( x+ 1 ) ( x+ 3 ) = 0

⇒ x = -1  or x = -3

Therefore, the value of x = -1 or x = -3 for the condition f(f(x)) = f(x).

The above question is incomplete , the complete question is:

Let function f(x) = x² + 4x for what value of x is f(f(x)) = f(x).

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Answer:

104976

Step-by-step explanation:

First multiply 6 by 2 and you get 12. Now add 6 to it and you get 18. Now power 18 to 4

18 times 18 times 18 times 18

and you get 104976

The value of h for which b in the plane spanned by a1 and a2 is 11.

A vector b is in the plane spanned by two vectors a1 and a2 if it can be written as a linear combination of a1 and a2. This means that there exist scalars x and y such that:

b = xa1 + ya2

[5, 4, h] = x[1, 4, -1] + y[-6, -20, 2]

Solving for x and y, we have:

5 = x - 6y

4 = 4x - 20y

h = -x + 2y

Using the first two equations, we can solve for x and y:

x = 5 + 6y

20y + 4 = 4x = 4(5 + 6y)

20y + 4 = 20 + 24y

4y = -16

y = -16/4 = -4

Substituting this value of y back into the first equation:

x = 5 + 6y

= 5 + 6 * -4

= 5 - 24

= -19

Finally, substituting x and y into the third equation:

h = -x + 2y

= -(-19) + 2 * (-4)

= 19 - 8

= 11

So for h = 11, the vector b is in the plane spanned by a1 and a2.

--The question is incomplete, answering to the question below--

"Let a1 = [1 4 -1], a2 = [-6 -20 2], and b = [5 4 h]. For what value(s) of h is b in the plane spanned by a1 and a2?"

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Answer: All values/solutions of P must be greater than 2 to be true to the inequality 10p-8>12

Step-by-step explanation:

When solving inequalities, we treat it like an equation, solving for the variable, in this case, p.

10p - 8 > 12

Lets isolate p

10p - 8 > 12

       +8   +8

10p > 20

/10     /10

p > 2

After solving, we now know that all values of P must be greater than 2.

For the graph of the cubic root function, the function has no intercept.

The cartesian plane is a two-dimensional coordinate plane that is formed when two parallel lines meet. The X-axis is the horizontal line, and the Y-axis is the vertical line. On the Cartesian plane, the coordinate point (x, y) indicates that the point is on the right of the origin if the sign of x is positive; otherwise, the point is on the left of the origin.

Given the graph of the cubic root function,

The points where a line crosses an axis are known as the x-intercept and the y-intercept, respectively.

the function of the graph is y = ∛x

when x = 0, y = 0

the function does not have any intercept.

Hence option C is correct.

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The height of his kite on this blustery day if an angle of elevation is 40°, 64.3 meter

An angle is a mathematical term, which we can define, when two straight lines or rays meet at a common endpoint. The common point is called the vertex of an angle. The word angle comes from a Latin word named ‘angulus,’.

Interior angles:- The inner angle made by the intersection of two polygonal sides.

Exterior angles:- The outer angle made by the intersection of two polygonal sides.

Given that,

Edward is flying a kite on a beautiful sunny day at the beach,

An angle of elevation of 40°

kite string let out = 100 meter

The height of his kite = ?

Suppose, height  = h

if we consider horizontal distance of kite from the Edward and Vertical distance from the Edward

It will form a right angle triangle

Now, we can use sine formula in the right angle triangle,

α =  40°

L  = 100 meter

h  = ?

It is known that,

sinα  = height/hypotenuse  

sin40° =  h/100

h  = 0.643 x 100

    =  64.3

Hence, the height of kite is 64.3 meter

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Answer:

0.00000016

Step-by-step explanation:

Raise 0.02 to the power of 4.

0.000000256.

The expression (0.02)^4 represents the fourth power of 0.02. In mathematical terms, "^" symbol is used to indicate exponentiation, so (0.02)^4 is equal to 0.02 multiplied by itself 4 times.

To calculate this expression, we can multiply 0.02 by itself 4 times:

0.02 * 0.02 * 0.02 * 0.02 = (0.02)^4 = 0.000000256

So, the result of (0.02)^4 is approximately equal to 0.000000256.