Answers
Answer:
40
Step-by-step explanation:
This is an example of a composite function. And, in order to answer the given problem, we need to calculate first the inner function.
In this example, we have:
[tex]f(x) = x^{2} - 3x + 6\\g(x) = 5x - 10[/tex]
And, we are tasked to calculate the [tex]g(f(-4))[/tex]. Let's calculate first the [tex]f(-4)[/tex].
[tex]f(x) = x^{2} + 3x + 6\\f(-4) = (-4)^{2} + 3(-4) + 6\\f(-4) = 16 - 12 + 6\\f(-4) = 4 + 6\\f(-4) = 10[/tex]
Let's substitute this value to the function of g to get the final answer.
[tex]g(x) = 5x - 10\\g(f(-4)) = 5(10) - 10\\g(f(-4)) = 50 - 10\\g(f(-4)) = 40[/tex]
Thus, the final answer was 40.
Related Questions
HOW FAR FROM HOME PLATE
TO SECOND BASE?
The catcher at home plate often needs
to make a quick throw to second base.
According to the measurements shown on
the baseball diamond, the exact distance
is √16,200 feet. How far is that in decimal
form? (Round to the nearest hundredth.)(please hurry )
Answers
The catcher must throw the ball in a distance of 127.2 feet to force a runner out at second base.
What is the distance that the ball have to be throw?From the figure we understands that it is a right angled triangle.
A right triangle or right-angled triangle, or more formally an orthogonal triangle, formerly known as a rectangled triangle, is a triangle with one right angle, i.e. two perpendicular sides. Trigonometry is founded on the relationship between the sides and other angles of a right triangle.The hypotenuse of a right triangle is formed by the line from home plate to second base. The triangle's two sides are each 90 feet.
We can calculate the length of the hypotenuse using the Pythagorean theorem:
90² + 90² = c²
= 8100 + 8100 = c²
= 16200 = c²
c = √16200
c = 127.2
c = 127 feet
As a result, the distance that the catcher must throw the ball to get a runner out at second base is 127 feet.
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Xochitl went into a movie theater and bought 6 bags of popcorn and 4 drinks, costing a total of $65. Alonso went into the same movie theater and bought 9 bags of popcorn and 8 drinks, costing a total of $107.50. Determine the price of each bag of popcorn and the price of each drink.
Answers
The cost of bag of popcorn is $7.5 and that of one drink is $5.
How to find the general equation of a Straight line?The formula for finding the general equation of a straight line is -
[y] = [m[y] = [m]x + [c]
where -
[m] → is slope of line which tells the unit rate of change of [y] with respect to [x].
[c] → is the y - intercept i.e. the point where the graph cuts the [y] axis.
We have Xochitl who went into a movie theatre and bought 6 bags of popcorn and 4 drinks, costing a total of $65, Alonso went into the same movie theatre and bought 9 bags of popcorn and 8 drinks, costing a total of $107.50.
Assume that the cost of one popcorn bag is $[x] and one drink is $[y].
Then we can write -
6x + 4y = 65
6x + 4y = 659x + 8y = 107.5
Plot the graph of both equations and the points of intersection would be the solution set. Refer to the graph below. We get x = $7.5 and y = $5.
Therefore, the cost of bag of popcorn is $7.5 and that of one drink is $5.
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Answer:
$7.5 and 5
Step-by-step explanation:
i did this on my assignment
Suppose that the relation His defined as follows.
H={(−3, 1), (−4, −4), (1, −3), (0, 8)}
Give the domain and range of H.
Write your answers using set notation.
domain = []
range = 0
Answers
Domain of the relation will be {-3,-4,1,0} and
Range of the relation will be {1,-4,-3,8}.
What is range and domain of a function?
Domain
The set of all possible values which qualify as inputs to a function is known as the domain of the function, or it can also be defined as the entire set of values possible for independent variables. The domain can be found in – the denominator of the fraction is not equal to zero and the digit under the square root bracket is positive. (In the case of a function with fraction values).
Range
The set of all the outputs of a function is known as the range of the function or after substituting the domain, the entire set of all values possible as outcomes of the dependent variable.
Now,
As inputs in the given relation are {-3,-4,1,0}
and outputs are {1,-4,-3,8}.
Hence,
Domain of the relation will be {-3,-4,1,0} and
Range of the relation will be {1,-4,-3,8}
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In \triangle QRS,△QRS, \overline{SQ}\cong \overline{RS} SQ ≅ RS and \text{m}\angle R = 21^{\circ}.m∠R=21 ∘ . Find \text{m}\angle Q.m∠Q
Answers
The measure of ∠Q is equivalent to 21°.
What are congruent triangles?Congruent triangles have both the same shape and the same size.
Given is that in △QRS, SQ ≅ RS and m ∠R=21°.
Now, it is given that SQ ≅ RS, this means that -
SQ = RS
Angles opposite to equal sides are equal.
∠R = ∠Q = 21°
Therefore, the measure of ∠Q is equivalent to 21°.
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solve 3x+2y=10 , 3x-y=4 for graphing.
Answers
Answer:
im sorry but i need the points
The sum of three consecutive numbers is ninenty- nine. What is the smallest of the three numbers?
Answers
Answer: 32
Step-by-step explanation:
32+33+34 = 99
They are consecutive numbers.
In quadrilateral QRST, point Q has coordinates (5, -6) and is
translated 6 units left and 5 units down. What are the coordinates
of the translated point Q'?
O (10,0)
Answers
By applying the required transformation, the coordinates of the translated point Q' are (-1, -11).
What is translation?A translation is a type of transformation in geometry that moves every point of a figure in a fixed direction and by a fixed distance, without changing its size or shape. It is one of the basic geometric transformations along with rotation, reflection, and dilation.
What are coordinates?Coordinates are a set of values that determine the position of a point in a certain space. In a two-dimensional space, coordinates are usually represented by an ordered pair of numbers (x, y), where x is the horizontal distance from a fixed point called the origin and y is the vertical distance from the origin. In a three-dimensional space, coordinates are represented by an ordered triple of numbers (x, y, z). Coordinates are often used to locate points in space, to describe the position of objects, and to plot graphs.
To find the coordinates of the translated point Q', we can use the rule that in a translation, the x-coordinate is decreased by the horizontal translation distance and the y-coordinate is decreased by the vertical translation distance.
Given that point Q has coordinates (5, -6) and is translated 6 units left and 5 units down, we can find the coordinates of the translated point Q' as follows:
x' = x - 6 (horizontal translation distance)
y' = y - 5 (vertical translation distance)
So the coordinates of the translated point Q' are:
x' = 5 - 6 = -1
y' = -6 - 5 = -11
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Translate to an algebraic expression: one-fifth of a number, k
Answers
The mathematical expression for the given algebraic expression is,
⇒ k / 5
What is an expression?Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
We have to given that;
The algebraic expression is,
⇒ One-fifth of a number, k
Now, We can write the mathematical expression for the given algebraic expression is,
⇒ One-fifth of a number, k
⇒ 1/5 of k
⇒ 1/5 × k
⇒ k / 5
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Madison has a loyalty card good for a 15% discount at her local grocery store. What
number should she multiply the prices on the tags by to find the price she would have
to pay, before tax, in one step?
Answers
Madison should multiply the price on the tag by (1-0.15) = 0.85 to find the price she would have to pay
How may math issues involving discounts be solved?Discount Formulas can be used to solve Discount problems in mathematics. It aids in boosting sales. Where M.P. (Marked Price) denotes the item's full retail cost without any discounts. The selling price, or S.P., is what consumers pay for the item. A percentage of the marked price is the discount.
The loyalty card gives a 15% discount so Madison should multiply the price on the tag by (1-0.15) = 0.85 to find the price she would have to pay, before tax, in one step.
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Find a formula for the
n
th term,
T
n
, of the following arithmetic sequence:
−
9
,
−
18
,
−
27
,
−
36
,
.
.
.
Answers
Answer:
x+9
Step-by-step explanation:
for example x is 18 , add 9 to it will become 18+9=27
2) A robot vacuum cleans a dirty floor using multiple passes. During each pass, 17% of the dirt is removed. If the floor initially has 460.0 ml of dirt, how much dirt will remain after 9 passes?
Answers
86 ml of dirt will remain after 9 passes
What is an equation?An equation is an expression showing the relationship between numbers and variables.
Let y represent the amount of dirt on the floor after x passes, hence:
y = abˣ
During each pass, 17% of the dirt is removed, therefore b = 100% - 17% = 0.83
If the floor initially has 460.0 ml of dirt, then a = 460.
The equation becomes:
y = 460(0.83)ˣ
After 9 passes:
y = 460(0.83)⁹ = 86
86 ml of dirt will remain
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H(x) = (x-1)^2 -9 plot the x intercept
Answers
Answer:
x = -2 and 4
Step-by-step explanation:
You want a plot of the x-intercepts of H(x) = (x -1)² -9.
X-interceptsThe x-intercepts are the points where the graph crosses the x-axis, the points where H(x) = 0. Solving, we get ...
H(x) = (x -1)² -9
9 = (x -1)² . . . . . . . . add 9
±3 = x -1 . . . . . take the square root
±3 +1 = x = {-2, 4} . . . . . add 1
PlotThe attached graph shows the coordinates of the x-intercept points on the x-axis. The coordinates of the vertex of the parabola are also shown.
Twenty percent of a town’s voters favor letting a major discount store move into their neighborhood, 63% are against it, and17% are indifferent. What is the probability that a randomly selected voter from this town will either be against it or be indifferent? Explain why this probability is not equal to 1.0.
Answers
The required probability is 0.8
What is probability?Probability is a measure of the likelihood of an event occurring. The probability formula is defined as the possibility of an event happening is equal to the ratio of the number of favorable outcomes and the total number of outcomes. Probability of event to happen P(E) = Number of favorable outcomes/Total Number of outcomes.
Given here: Twenty percent of a town’s voters favor letting a major discount store move into their neighborhood, 63% are against it, and 17% are indifferent.
Thus total percentage of voters that are either against or be indifferent is equal to P( against or indifferent)=80%
=0.8
The probability is not equal to one because there is also percentage of voters that are in favour which accounts for 20%
Hence, The required probability is 0.8
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What are the features of the quadratic function graphed in the figure?
Answers
Vertex (3, -4) with x-intercepts (1, 0), (5, 0), and (0, 5) and an axis of symmetry of 3. As a result, choice B is the right response.
The characteristics of the quadratic function graphed in the figure must be identified.
f(x) = ax2 + bx + c, where a, b, and c are numbers and an is not equal to zero, is a quadratic function. A parabola is the shape of a quadratic function's graph. Vertex (3, -4) has an axis of symmetry of three and an x-intercepts of one, five, and five. Choice B is the appropriate response as a result.It is necessary to identify the traits of the quadratic function graphed in the figure.A parabola can have different "widths" or "steepnesses," as well as different opening directions, but they all have the same basic "U" shape.This is how the whole process occurs in the given featuresTo know more about quadratic functions here
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(a)
Two friends, Jeanette and Zoe, are growing out their hair. They plan to cut it off at a certain point and donate it to a charity that makes wigs for people with cancer. Jeanette's hair is already 29 centimeters long and grows at a constant rate of 1 centimeter per month. Zoe's hair is 12 centimeters and growing at a speed of 2 centimeters per month. If the girls get their hair cut on a certain day, they will have exactly the same length to donate. How long will their hair be? How long will that take?
Part A:
Using the variables y for total growth and x for rate of change answer the questions below.
Create the equation for Jeanette's hair growth:
Create the equation for Zoe's hair growth
Answers
Answer:
Step-by-step explanation:
J: y = 29 cm + (1 cm/mo)x
Z: y = 12 cm + (2 cm/mo)x
29 cm + (1 cm/mo)x = 12 cm + (2 cm/mo)x
Solve for x to find how many months it will take for them to have the same length of hair:
29 cm - 12 cm = (2 cm/mo)x - (1 cm/mo)x
17 cm = (1 cm/mo)x
x = (17 cm) / (1 cm/mo) = 17 months
Plug this value for x (17 months) into the equations to find how long their hair will be:
J: y = 29 cm + (1 cm/mo)(17 mo) = 46 cm
Z: y = 12 cm + (2 cm/mo)(17 mo) = 46 cm
This shows that it will take 17 months for each girl's hair to be 46 cm long.
Aunt Janelle uses the ratio 5 cups of milk to 2 cups of cocoa for her hot chocolate recipe. If she used 8 cups of cocoa, how many cups of milk does she need?
Answers
The number of cups of milk that she will need would be = 20 cups.
What is a ratio?A ratio is defined as the expression that shows the relationship between two numbers of the same unit.
The ratio used by Aunt Janelle to make hot chocolate is as follows;
The quantity of milk to cocoa = 5 cups : 2 cups respectively.
Therefore the cups of milk to 8 cups would be = X
That is, 5 cup of milk = 2 cups of cocoa
X cup of milk = 8 cups of cocoa
make X the subject of formula;
X = 5 × 8/2
X= 40/2
X = 20
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In a fruit punch drink, the 3 ingredients
are apple juice, orange juice and
cranberry juice. If 4 of the drink is apple
juice and % is orange juice then write
the ratio of cranberry juice to apple juice
to orange juice in its simplest form.
Answers
3: 4=6: 8 We discovered an analogous ratio by multiplying both terms by 2, as the ratio was already in lowest terms.
What is the simplest definition of ratio?The proportion between two or more items in terms of number, amount, or size. When the second number in the ordered pair, b, is not equal to 0, the ratio is expressed as a/b. An equation in which two ratios are made equal is known as a percentage. As an illustration, you could express the ratio as 1: 3 if there is 1 guy and 3 girls (for every one boy there are 3 girls) 40% are girls, and 14% are boys.
Comparing two numbers by dividing them is how ratios work. Your formula would be A/B if you were contrasting one data point (A) with another data point (B). By doing so, you are multiplying information A by information B.
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19 out of 36 in a class are girls calculate 19 as a percentage to 1 decimal point
Answers
The value of percent in 1 decimal point is, 52.7%.
What is mean by Percentage?A number or ratio that can be expressed as a fraction of 100 or a relative value indicating hundredth part of any quantity is called percentage.
Given that;
There 19 out of 36 in a class are girls.
Hence, The percentage of girls is,
⇒ 19 / 36 × 100 %
⇒ 1900/36 %
⇒ 52.7%
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find the taylor series up to the degree 4 term at a = 8 for f(x) = ex.
Answers
The Taylor series up to the degree 4 terms is:
e^8 + (x - 8)e^8 + (x - 8)^2/2! e^8 + (x - 8)^3/3! e^8 + (x - 8)^4/4! e^8
The Taylor series of a function f(x) at point a is an infinite sum of terms that approximates the value of the function near point a. The general form of the Taylor series of f(x) at a is:
f(x) = f(a) + (x - a)f'(a) + (x - a)^2/2! f''(a) + (x - a)^3/3! f'''(a) + ...
Where,
f'(a) is the first derivative of f(x) at a.f''(a) is the second derivative of f(x) at a.f'''(a) is the third derivative of f(x) at a.In the case of e^x, the function is infinitely differentiable, so all its derivatives are equal to itself. Hence the Taylor series at a=8 is:
e^8 + (x-8)e^8 + (x-8)^2/2! e^8 + (x-8)^3/3! e^8 + (x-8)^4/4! e^8 + ....
by taking the degree 4 terms we can find the Taylor series of e^x at a = 8 up to the degree 4 terms, which is
e^8 + (x-8)e^8 + (x-8)^2/2! e^8 + (x-8)^3/3! e^8 + (x-8)^4/4! e^8
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What is the third angle of the triangle if the angles are 15 and 86
Answers
Answer:
79 degrees
Step-by-step explanation:
there are 180 degrees in a triangle
if you deduct the sum of 15 and 86, which is 101, the third angle must measure 79 degrees
15+86+x=180
x= 180-101
x = 79
The third angle is 79 degrees
pls answer the first question
Answers
Need help quick please.
Answers
y=2x²+4x+4 and y=3x²+6x+9 are two instances for the provided standard form, y=ax²+bx+c.
What is equation?In its most basic form, an equation is a mathematical statement that indicates that two mathematical expressions are equal. 3x + 5 = 14, for example, is an equation in which 3x + 5 and 14 are two expressions separated by a 'equal' sign. A condition on a variable (or variables) such that two expressions in the variable (variables) have equal value is referred to as an equation. • The solution or root of the equation is the value of the variable for which the equation is fulfilled.
Here,
given standard form,
y=ax²+bx+c
examples of this,
y=2x²+4x+4
y=3x²+6x+9
The 2 examples for given standard form, y=ax²+bx+c is y=2x²+4x+4 and y=3x²+6x+9.
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How do I solve this?
Answers
general equation of the tangent line, expressed through the x-coordinate of the point, at which it touches the function.
How do you find the equation of a tangent line?The equation of the tangent line can be found using the formula y – y1 = m (x – x1), where m is the slope and (x1, y1) is the coordinate points of the line1) Find the first derivative of f(x). 2) Plug x value of the indicated point into f '(x) to find the slope at x. 3) Plug x value into f(x) to find the y coordinate of the tangent point. 4) Combine the slope from step 2 and point from step 3 using the point-slope formula to find the equation for the tangent lineA tangent to a circle at point P with coordinates is a straight line that touches the circle at P. The tangent is perpendicular to the radius which joins the centre of the circle to the point P. As the tangent is a straight line, the equation of the tangent will be of the form y = m x + c
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Kami needs to score at least an 83 on her quiz in order to make an A for the report card.Write the inequality.
Answers
The inequality for the expression is x≥83
What is inequality?inequality, In mathematics is a statement of an order relationship. The signs in inequality includes: greater than, greater than or equal to, less than, or less than or equal to—between two numbers or algebraic expressions.
greater than( >)
less than (<)
less than or equal to ≤
greater than or equal to ≥
Kami needs to score at least 83 on her quiz, this means that kami need to score a mark greater than or equal to 83 in her quiz.
If we represent the score of kami by x, this means the expression can be represented as:
x ≥ 83
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9. Write 3 numbers that are divisible by
both 2 and 5.
Answers
In this question, we use the theory of LCM (Least Common Multiple) for finding the numbers which are divisible by 2,5 and 10. As we know, in arithmetic, the LCM is the smallest or least positive integer that is divisible by both a and b. So, in this question we need to calculate the LCM of 2,5
Which is divisible by 2 and 5?step 1
Solution
LCM of 2,5,10 is 10
So, if a number is divisible by 10 then it will be divisible by 2,5,10
Like 60,100,120,450,600
step-by-step answer:
For example, let us take two positive integers 4 and 6. Multiples of 4 are: 4,8,12,16,20,24… Multiples of 6 are: 6,12,18,24…. The common multiples for 4 and 6 are 12,24,36,48…and so on.
2, 5 and 10 (LCM by Division Method).
LCM of 2, 5 and 10 = 2X5
= 10
we get LCM of 2, 5 and 10 is 10.
So, if a number is divisible by 10
Then it will be divisible by 2,5,10.
Therefore, any number which is multiple of 10 or which is divisible by 10. We say it will be divisible by 2,5,10.
Like- 10, 20, 30, 40, 50, 60, 70, 80 etc.
Thus, 10, 20, 30, 40, 50 are 5 numbers which are divisible by 2,5 and 10.
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Which function increases at a faster rate on 0 to infinity, f(x) = x2 or g(x) = 2x? Explain your reasoning.
Answers
The function that increases at a faster rate on 0 to infinity is g(x) = 2ˣ
What is an average rate?
An average rate measure of how much the function changed per unit, on average, over that interval. It is derived from the slope of the straight line connecting the interval's endpoints on the function's graph.
The functions are given as:
f(x) = x² --- quadratic
g(x) = 2ˣ --- exponential
The exponential function has the same base as the power of the quadratic function.
This means that the exponential function would increase faster from the point where f(x) = g(x)
This is illustrated using the following table
x 0 1 2 3 4 5
f(x) 0 1 4 9 16 25
g(x) 1 2 4 8 16 3
Hence, the function that increases at a faster rate on 0 to infinity is g(x) = 2ˣ
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Suppose you found that the correlation between the life expectancy of citizens in a nation and the average number of TVs in households in that nation is r=0.89. Does that mean that watching TV helps you live longer?
Answers
Yes , watching TV helps you live longer by using correlation coefficient.
How to interpret a correlation coefficient?
The statistical measure of how well changes in the value of one variable predict changes in the value of another is called a correlation coefficient. The value rises or falls together when the variables are positively linked.
The r represents the correlation coefficient which has a value 0.89 for the given case.
we can say that there is a positive association between the life expectancy of citizen and the average number of TVs in households.
the r value is close to +1 which means that the association is close to linear relation .
so we put it like
R² = 0.89² = 0.7921
now 0.7921 signifies that almost 79% variation in life.
So we can say that watching TV helps you live longer.
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Kali’s school is selling tickets to a choral performance. On the first day of ticket sales the school sold 1 adult ticket and 8 student tickets for a total of $60. The school took in $48 on the second day by selling 5 adult tickets and 4 student tickets. What is the price each of one adult ticket and one student ticket?
Answers
Using simultaneous equations, the price of one adult ticket is $4 and one student ticket is $7.
What are simultaneous equations?Simultaneous equations are two or more equations solved concurrently.
Sales of Tickets:
Adult Student Sales Revenue
First day of ticket sales 1 8 $60
Second day of ticket sales 5 4 $48
Let the price per adult ticket = a and students ticket = s
Equations:Equation 1: a + 8s = 60
Equation 2: 5a + 4s = 48
Multiply equation 1 by 5:
Equation 3: 5a + 40s = 300
Subtract equation 2 from equation 3:
5a + 40s = 300
-
5a + 4s = 48
36s = 252
s = 7
= $7
In equation 1, substitute s = 7:
a + 8s = 60
a + 8(7) = 60
a + 56 = 60
a = 4
= $4
Thus, the price of one adult ticket is $4 while the price of one student ticket at Kali's school is $7.
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sketch the region enclosed by the given curves. x = 7y2, x = 4 + 6y2
Find its area.
Answers
The enclosed area between the 2 equations, x = 7y² and x = 4 + 6y² is 32/3 sq units
Here equation 1 is x = 7y²
and equation 2 is x = 4 + 6y²
To find the area enclosed between the region, we need to first find the points where these two lines meet.
This implies,
eq 1 = eq 2
or, 7y² = 4 + 6y²
or, y² = 4
or, y = ±2
Now if we see the graph with respect to y, the area between the y-axis and eq 2 is greater than that of the y-axis and equation 1.
Now area is enclosed between 2 lines with respect to x. Hence it will be
= ∫eq 2 dy - ∫eq 1 dy with limts of 2 and -2
= ∫4 + 6y²dy - ∫7y²dy with limits 2 and -2
= [4y + 2y³ - 7/3 y³] with limits 2 and -2
= 8 + 16 - 56/3 + 8 + 16 - 56/3 sq. units
= 48 - 112/3
= 32/3 sq units
Hence the enclosed area is 32/3 sq units
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Using the maxima and minima of the function, produce upper and lower estimates of the integral
I=∫∫De^5(x2+y2)dA where D is the circular disk: x^2+y^2≤4
Answers
In calculus, we can find the maximum and minimum value of any function or variable without on looking at the graph of the function.
Maxima will be the giant point on the curve within the given range and minima would be the minimum point on the curve. The combination of both is extrema.
Since 0 ≤ x^2 + y^2 ≤ 6, we have e^ (6*0) ≤ e^ (6(x^2 + y^2)) ≤ e^ (6*6) on D.
So, ∫∫ 1 dA ≤ ∫∫ e^ (6(x^2 + y^2)) dA ≤ ∫∫ e^36 dA
==> 6π ≤ ∫∫ e^ (6(x^2 + y^2)) dA ≤ 6π * e^36, since the area of D is 6π.
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