Set up the integral (or integrals) needed to compute the area between the curves. Use the smallest possible number of integrals. x= -5 x= 3 y= 9x y=x^2-10
Answers
The area between the curves is 61.5 square units.
How did we arrive at this value?To compute the area between the curves y = 9x and y = x^2 - 10, find the points of intersection between the curves.
Setting the two equations equal to each other:
x^2 - 10 = 9x
Move all to one side:
x^2 - 9x - 10 = 0
Factor the quadratics:
(x - 10)(x + 1) = 0
So, the points of intersection are x = -1 and x = 10.
Now, determine which curve is above the other in the interval between -5 and 3. Evaluating the y-coordinates of each curve at a point in this interval, say x = 0.
y = 9x, y = 0 at x = 0, so the curve passes across the origin.
y = x^2 - 10, y = -10 at x = 0.
Therefore, the curve y = 9x is above y = x^2 - 10 in the interval [-5, 3].
To compute the area between the curves, take the integral of the top curve minus the integral of the bottom curve over the interval of intersection:
∫(-1 to 3) [9x - (x^2 - 10)] dx
Simplify:
∫(-1 to 3) [ -x^2 + 9x + 10] dx
Then, integrate each term of the polynomial:
[ (-1/3) x^3 + (9/2) x^2 + 10x ] evaluated from x = -1 to x = 3
Plug into the limits of integration and then simplify:
= [ (81/2) - (19/3) ] - [ (-1/3) - (17/2) ]
= 61.5
Therefore, the area between the curves is 61.5 square units.
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Related Questions
What is the arc measure of major arc AC on circle P in degrees
Answers
An arc is a segment of a circle. An arc measure is the measure of an angle that the arc creates in the center of a circle, while an arc length is the span of the arc. This measure can be given in degrees or radians. We can easily convert between the two using the fact that pi radians = 180 degrees.
while eating your yummy pizza, you observe that the number of customers arriving to the pizza station follows a poisson distribution with a rate of 18 customers per hour. on average, how many customers arrive in each 10 minutes interval?
Answers
In every 10 minutes an average of 3 customers will arrive to the pizza station
Given,
The number of customers arriving to the pizza station follows a poisson distribution with a rate of 18 customers per hour.
We have to find the average number of customers arrives in each 10 minutes.
Here,
The chance that X represents the number of successes of a random variable in a Poisson distribution is provided by the following formula:
P (X = x) = (e^-μ × μ^x) / x!
Where,
The number of successes is x.
The Euler number is e = 2.71828.
μ is the average over the specified range.
Now,
Rate of 18 customers per hour;
μ = 18 n
n is the number of hours.
Number of customers arrive in each 10 minutes
10 minutes = 10/60 = 1/6
Then,
μ = 18 x 1/6 = 3
That is,
In every 10 minutes an average of 3 customers will arrive to the pizza station.
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water is placed in a Cinderella bucket on a bench the bucket has a diameter of 12 in and a height of 12 in The bench is capable of supporting 200 lb The water weighs about 64.2 pounds per cubic foot how how much does the bucket in the water weigh
Answers
EXPLANATION
Let's see the facts:
Bucket diameter = 12 inches
Bucket height = 12 inches
Bench capability = 200lb
Water density = 64.2 pounds/ ft^3
Considering that the bucket is a cylinder, first we need to convert the inches units to feets units:
1 feet = 12 inches
So, the diameter would be:
Diameter = 12inches/12inches/feet = 1 feet
Then, the height would be
Height = 12 inches / 12inches/feet = 1 feet
The volume of a cylinder is given by the following formula:
\(\text{Volume}_{cylinder}=\pi h(\frac{d}{2})^2\)Substituting terms:
\(\text{Volume}_{bucket}=\pi\cdot1\cdot(\frac{1}{2})^2=\pi\cdot\frac{1}{4}=\frac{\pi}{4}=0.78ft^3\)The amount of water that can placed on this bucket is:
\(\text{Amount of water=density of water}\cdot volume\text{ of bucket}\)Replacing terms:
\(\text{Amount of water = }\frac{64.2\text{ pounds}}{ft^3}\cdot0.785ft^3=50.4\text{ pounds}\)Answer: The water on the bucket weights 50.4 pounds.
Fill in the blanks below in order to justify whether or not the mapping shown
represents a function.
Set A
co
5
H
The mapping diagram above|
Set B
✓in
-2
3
O
7
શ function since
where there
Answers
Answer:
It is not a function
Step-by-step explanation:
A function is a rule from x to y that applies to all elements of x. Every element of x should have one image only.
Here, element "1" has two images 3 and 7. Therefore it's not a function.
4. Write the equation of a line that passes through the point (-8, 2) and is parallel to the
line 3x – 2y = 12.
Answers
Answer:
y = 1.5x +14
Im pretty sure this is right but i am so sorry if this is wrong
Ann wants to set up chairs in rows of 8. If she sets 14 rows, how many seats will she have?
Answers
Answer:
112
Step-by-step explanation:
8×14 if each row has 8 chairs, and there's 14 rows that means 8×14 which equals 112 :)
Answer:
14 x 8=112
8 chairs are row multiply by the of rows
John put $3, 000 in his savings at 2% annually for 3 years. What did he earn in simple interest?
Answers
Answer:
End Balance: $5,160.00
Total Interest: $2,160.00
Step-by-step explanation:
Total Interest =$3000 × 2% × 3 × 12
=$2,160.00
End Balance =$3000 + $2,160.00
=$5,160.00
Answer:
can we get the options
Step-by-step explanation:
Brandon discovered that his daily routine of buying a slice of pizza and a soda at lunch was costing him more than 18,000$ per year.
A. This statement does not make sense because this would mean that a slice of pizza and a soda costs him about 5$ a day.
B This statement makes sense because this would mean that a slice of pizza and a soda costs him about 5$
C.
This statement makes sense because this would mean that a slice of pizza and a soda costs him about 49$ a day.
D.
This statement does not make sense because this would mean that a slice of pizza and a soda costs him about 49$ a day.
Answers
I’m sorry if it’s wrong :(
Is UVW= XYZ? If so, name the postulate that applies. A. Congruent - ASA B. Congruent - AAA C. Might not be congruent D. Congruent - SSS
Answers
Might not be congruent
Reason:
To determine triangle congruence, we need information about at least one pair of sides. Unfortunately we don't have such info. Instead we are given the three corresponding angle pairs are congruent. This means the triangles are similar, but we don't know if they are congruent or not.
Consider an equilateral triangle that's really small. All angles here are 60 degrees. Then consider a much bigger equilateral triangle. The angles are still 60 degrees each. These two triangles are similar, but they aren't congruent (since the side lengths don't match up).
The example in the previous paragraph shows why there is no such thing as the "AA congruence theorem" or "AAA congruence theorem", where A stands for "angle".
The list of congruence theorems are:
SSS = side side side SAS = side angle sideASA = angle side angleAAS or SAA = similar to ASA, but this time the side is not between the angles.HL = hypotenuse leg (works for right triangles only)HA = hypotenuse acute angle (works for right triangles only)LL = leg leg (works for right triangles only)Side note: SSA isn't a valid congruence theorem because it could lead to ambiguity.
The postulate applied in triangles ΔUVW and ΔXYZ is AAA congruency.
What is triangle congruency?There are ways to prove that two triangles are congruent.
- Side-Side-Side (SSS) Congruence.
The three sides of one triangle are equal to the corresponding three sides of another triangle.
- Side-Angle-Side (SAS) Congruence.
The two sides and the included angle of one triangle are equal to the corresponding two sides and included angle of another triangle.
- Angle-Side-Angle (ASA) Congruence.
The two angles and the included side of one triangle are equal to the corresponding two angles and included side of another triangle.
- Angle-Angle-Side (AAS) Congruence.
We have,
ΔUVW and ΔXYZ
∠U ≅ ∠X (corresponding angles)
∠V ≅ ∠Y (corresponding angles)
∠W ≅ ∠Z (corresponding angles)
This means,
AAA congruency.
Thus,
The postulate applied in triangles ΔUVW and ΔXYZ is AAA congruency.
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MATH
Systems of Linear Equations
1. Determine if each system of equations below is linear or nonlinear.
A. -9x+8y = 9x 7y+8=8x
Linear or nonlinear?
D. 6y+x=12 y-x=1-x
B.
2.3y+1.2x = 0
1.1x+0.1y 1.2
C.
2 7-3y=- 2x+9= 3y
Linear or nonlinear?
Linear or nonlinear?
E. 45x + y = 12 y+x² = 1-x²
Linear or nonlinear?
G
0.2x+9.1y9.1√x
7x+1=8√y
Linear or nonlinear?
F. x+8y = 81 x-7y = 32
Linear or nonlinear?
H.
98317y= 1010 + 2965x
-71389y=5692x - 1001
3 xx y-5= 1 zy+3x=-21
Linear or nonlinear?
Linear or nonlinear?
Linear or nonlinear?
2. Find the solution, if one exists, for each of the graphs shown below that are representing different systems of linear equations.
A.
B.
Solution:
Solution:
C.
D.
Solution:
Solution:
2. Find the solution, if one exists, for each of the graphs shown below that are representing different systems of linear equations.
A.
B.
Solution:
Solution:
C.
D.
Solution:
Solution:
Answers
The system of equations -9x+8y = 9x and 7y+8=8x is linear.
A system of equations is considered linear if each equation in the system is linear, meaning that the highest power of any variable in each equation is 1.
In this case, the first equation -9x+8y = 9x is linear because the highest power of any variable is 1 (x is raised to the first power).
Similarly, the second equation 7y+8=8x is also linear because the highest power of any variable is 1 (x is raised to the first power and y is not raised to any power).
Therefore, the system of equations is linear.
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have a random argument with yourselves
Answers
Answer:
ok
Step-by-step explanation:
CAN SOMEONE PLEASE HELP ME WITH THIS
Answers
Answer:
about 100 feet
Step-by-step explanation:
It cost Jocelyn $5.60 to send 56 text messages. How much would it cost to send 198 text messages?
Answers
Answer:
$19.80
Step-by-step explanation:
56÷5.60=.10
.10×198=19.8
Answer:
$19.80
Step-by-step explanation:
First, the unit rate of each text message is .1 so if we multiply 198 x .1 we get $19.80 which is your answer.
Hope this helps!
Find the surface area of a cylinder with a height of 9 ft and diameter of 4
Answers
Answer:50.2654812288
Step-by-step explanation:
The two circles :
Sa = πr²
= π x 2²
= 12.5663706144
= 12.5663706144 x 2
= 25.1327412288
The rectangle :
C x h = 2πr
= 25.13274
= 25.13274 + 25.1327412288
= 50.2654812288
Step-by-step explanation:
50.2654858683848
because it is equivalent to this. Also I can tutor you
Rajiv used 34 of a bag of sugar to make cookies. With the sugar he has left over, he will make 3 cakes. What fraction of the original bag of sugar will he use for each cake?
Answers
Answer:
I'm assuming it was 3/4. not 34.
if so, 1/4 of the bag is left.
1/4 ÷ 3= 1/12
Answer:
3 = 1/2
Step-by-step explanation:
1. If x is 3, what is 3x + 2x? Plz I need help
Answers
Answer:
15
Step-by-step explanation:
3*3+2*3=15
Answer:
15
Step-by-step explanation: If x equals 3, then you would do 3x3 = 9 and 2x3 = 6. Then add to get 15.
Anne bought a piece of ribbon that is 7 over 9 m long. She used 3 over 18 m of it to tie a birthday present. She then used the remaining ribbon to form squares of sides 1 over 16 m. What was the maximum number of squares she could form?
Answers
Answer:
9 squares
Step-by-step explanation:
Anne bought a piece of ribbon = 7 over 9 m long = 63 m²
she used = 3 over 18 m = 54 m²
left = 9 m²
maximum number of squares she could form of 1 m = 9
The average cost of an item is defined as the total cost to produce divided by the number produced.A shoe company that pays $240,000 in rent and employee salaries per year figures it also must pay $3.50 in materials per shoe set it produces Write the equation needed to solve the problem. Use the equation to find the number of shoe sets the company would need to produce for the average cost of each set to be $7.50. Work out the problem, show all of your steps, and provide explanations.
Answers
Answer:
Step-by-step explanation:
Average cost = Total cost to produce / number of items produced
Fixed cost per year = $240,000
Variable cost = $3.50s
Where s = number of shoes produced
Total cost= fixed cost + variable cost
Total cost = $240,000 + $3.50s
When average cost = $7.50
Average cost = Total cost to produce / number of items produced
7.50 = $240,000 + $3.50s / s
Cross product
7.50s = $240,000 + $3.50s
Collect like terms
7.50s - 3.50s = 240,000
4s = 240,000
divide both sides by 4
s = 240,000 / 4
= 80,000
s = 80,000
SOLVE FOR R
-7 - 7r= -10r + 8
R =
Answers
Answer:
the answer is 5
Step-by-step explanation:
(Add 10r to both sides)
-7-7r+10r= 8
Then -7+3r = 8
(Add 7 to both sides)
3r = 8+7
3r = 15
Divide both sides by 3.
r = 5
find the measure of the angel x
Answers
Answer:
80°+30°=180°
=110=180
x=70°
answer
Answer:
80 - 30 = 50
Step-by-step explanation:
bcz sum of two interior angle is equal to one exterior angle
How many tiles can fit in a rectangular floor with length 14 ft and width 6 ft if the the square tiles has an edge of 3/4 ft.
Answers
A rectangular floor with a length of 14 ft and a width of 6 ft, square tiles with an edge length of 3/4 ft, a total of 144 tiles can fit.
To determine how many square tiles can fit in a rectangular floor, we need to calculate the total number of tiles that can fit both horizontally and vertically.
Given:
Length of the rectangular floor = 14 ft
Width of the rectangular floor = 6 ft
Edge length of square tile = 3/4 ft
First, let's calculate the number of tiles that can fit horizontally:
Length of the rectangular floor / Edge length of square tile = 14 ft / (3/4 ft) = 14 ft × (4/3 ft) = 56/3 ft
Since we want a whole number of tiles, we need to round down or take the floor value:
Number of tiles horizontally = floor(56/3) = 18 tiles
Next, let's calculate the number of tiles that can fit vertically:
Width of the rectangular floor / Edge length of square tile = 6 ft / (3/4 ft) = 6 ft × (4/3 ft) = 24/3 ft
Again, we round down or take the floor value:
Number of tiles vertically = floor(24/3) = 8 tiles
To find the total number of tiles, we multiply the number of tiles horizontally by the number of tiles vertically:
Total number of tiles = Number of tiles horizontally × Number of tiles vertically = 18 tiles × 8 tiles = 144 tiles
Therefore, in a rectangular floor with a length of 14 ft and a width of 6 ft, square tiles with an edge length of 3/4 ft, a total of 144 tiles can fit.
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the temperature at sunrise is 42°F. each hour the temperature rises 6°F. write an equation that models the temperature y in degree farenheit after x hours . what is the graph of the equation
Answers
The Slope-Intercept form of an equation of a line is:
\(y=mx+b\)Where "m" is the slope of the line and "b" is the y-intercept.
According to the information given in the exercise, each hour the temperature rises 6 °F, then you can identify that the slope is:
\(m=6\)Knowing that the temperature at sunrise is 42 °F, you can identify that the value of "b" is the following:
\(b=42\)Then, the equation that models the temperature "y" (in degrees Farenheit) after "x" hours, is:
\(y=6x+42\)In order to graph it, you can also find the x-intercept. By definition, when the line cuts the x-axis, the value of "y" is:
\(y=0\)Substituting this value into the equation and solving for "x", you get:
\(\begin{gathered} y=6x+42 \\ 0=6x+42 \\ -42=6x \\ \\ \frac{-42}{6}=x \\ \\ x=-7 \end{gathered}\)Knowing the y-intercept and the x-intecept, you can graph the equation.
The answers
- Equation:
\(y=6x+42\)- Graph:
Find the measure of the following angles.
1) M
2) M
3) m
4) m
5) M
Answers
Same directions as question #1
Sn = ( -1 )n + 1
Answers
The sum of the sequence based on the function Sn = ( -1 )n + 1 will be -6.
How to depict the information?The formula for finding the nth term in an arithmetic sequence given as:
= a + (n - 1)d
Here, Sn is given as ( -1 )n + 1. This is used to illustrate the sum in the sequence. Based on the function given, let's assume that n = 5. Therefore, the 5th term will be:
= (-1)n + 1
= (-1)5 + 1
= (-1)6
= -6
Here is the complete question:
Find the 5th term of a sequence given the function Sn = ( -1 )n + 1.
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find by a digit to make the number divisible by 3 1234?
Answers
A digit to make the number divisible by 3 is by adding the digit 2 to the number 1234.
To make the number 1234 divisible by 3, we can find the sum of its digits and determine if it is divisible by 3. If the sum of the digits is divisible by 3, then the original number is also divisible by 3.
Let's calculate the sum of the digits in 1234:
1 + 2 + 3 + 4 = 10
The sum of the digits is 10. Since 10 is not divisible by 3, we need to add or subtract a digit to make the sum divisible by 3.
To find the digit we need to add or subtract, we can use the fact that the difference between the original sum and the next multiple of 3 is the required digit.
The next multiple of 3 greater than 10 is 12 (12 - 10 = 2). Therefore, we need to add 2 to the number 1234 to make it divisible by 3.
1234 + 2 = 1236
we obtain the number 1236, which is divisible by 3.
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Julie thinks this will mean the prices will be reduced to $0 after the four reductions because 4 x
25% = 100%.
Explain why Julie is wrong
Answers
Answer:
4x25/100=1
Step-by-step explanation:
How I came up with it
4÷100=25
25÷25=1
Julie will only get a 1% discount
Hope it helps
Ayuda operaciones y respuesta es para ahora
Answers
The perimeter of the given window is 48 centimeter.
From the given figure,
Perimeter of window = 2(Length+Breadth)
= 2(10+14)
= 2×24
= 48 centimeter
Perimeter of house = 2(Length+Breadth)
= 2(37+35)
= 2×72
= 144 centimeter
Perimeter of roof = 2(Length+Breadth)
= 2(37+5)
= 2×42
= 84 centimeter
Therefore, the perimeter of the given window is 48 centimeter.
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Number bond of 10
8+6+2=
Answers
Answer:
260
Step-by-step explanation:
Answer:260
Step-by-step explanation:
A penguin starts at 15 meters above sea level and ends at 7 meters below sea level. What is the change in elevation?
Answers
Answer:
22 meters
Step-by-step explanation:
If the penguin goes from 15 meters above sea level to sea level (0 meters), they traveled 15 meters in elevation.
Then they traveled another 7 meters when going 7 meters below sea level.
15 + 7 = 22
Hope this helps :)
When compared with the independent variable, how many of the graphs represent a linear relationship?
Answers
We can see from the graphs that only two of the graphs represents a linear relationship.
What is a linear relationship?A linear relationship is one which obeys the relation; y = mx + c. The slope of a straight line graph remains the same irrespective of the pair of points used to measure the slope along the line.
The required graphs are attached to this question. We can see from the graphs that only two of the graphs represents a linear relationship.
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