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Mkey [24]
3 years ago
11

What is the volume of the figure? Enter the answer in the box.

Mathematics
1 answer:
Whitepunk [10]3 years ago
8 0

Answer:

217,600

Step-by-step explanation:

Multiply all the sides

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The function h(t) = −5t2 + 20t shown in the graph models the curvature of a satellite dish: graph of parabola starting at zero c
ipn [44]

Answer:

Part 1) Option B: 0 ≤ x ≤ 4

Part 2) Option C: (5x − 1)(2x − 3)

Part 3) Option C: The crop yield decreased by 10 pounds per acre from year 10 to year 20.

Part 4) Option B: f(x) = (2x + 1)(2x − 1)

Part 5) Option A: The company earned 85 billion dollars in 2008

Part 6) Option C: (3, 0) and (5, 0)

Step-by-step explanation:

Part 1) we have

h(t)=-5t^{2}+20t

This is a vertical parabola open downward

The vertex is a maximum

The x-intercepts are the points (0,0) and (4,0)

The vertex is the point (2,20) ---> The x-coordinate of the vertex is the midpoint of the x-intercepts

so

The domain is the interval ----> [0,4]

0\leq t\leq 4

The range is the interval ----> [0,20]

0\leq h(t)\leq 20

Part 2) we have

V=10x^{2} -17x+13

where

x is the time in minutes

V is the volume in gallons

we know that

When the trough is empty, the volume is equal to zero

so

For V=0

10x^{2} -17x+3=0

The formula to solve a quadratic equation of the form

ax^{2} +bx+c=0

is equal to

x=\frac{-b(+/-)\sqrt{b^{2}-4ac}} {2a}

in this problem we have

10x^{2} -17x+3=0

so

a=10\\b=-17\\c=3

substitute in the formula

x=\frac{-(-17)(+/-)\sqrt{-17^{2}-4(10)(3)}} {2(10)}

x=\frac{17(+/-)\sqrt{169}} {20}

x=\frac{17(+/-)13} {20}

x=\frac{17(+)13} {20}=\frac{3}{2}

x=\frac{17(-)13} {20}=\frac{1}{5}

so

10x^{2} -17x+3=10(x-\frac{3}{2})(x-\frac{1}{5})

simplify

10(x-\frac{3}{2})(x-\frac{1}{5})=(2x-3)(5x-1)

Part 3) we have

f(x)=-x^{2}+20x+100

we know that

To find the average rate of change, we divide the change in the output value by the change in the input value

the average rate of change is equal to

\frac{f(b)-f(a)}{b-a}

In this problem we have

f(a)=f(10)=-(10)^{2}+20(10)+100=200  

f(b)=f(20)=-(20)^{2}+20(20)+100=100  

a=10

b=20

Substitute

\frac{100-200}{20-10}

-\frac{100}{10}=-10  ----> is a decreasing function

therefore

The crop yield decreased by 10 pounds per acre from year 10 to year 20.

Part 4) we have

f(x)=4x^{2} -1

<em>Find out the x-intercepts</em>

Remember that the x-intercepts are the values of x when the value of the function is equal to zero

so

For f(x)=0

4x^{2} -1=0

Solve for x

4x^{2}=1

x^{2}=\frac{1}{4}

take square root both sides

x=(+/-)\frac{1}{2}

so

f(x)=4x^{2} -1=4(x-\frac{1}{2})(x+\frac{1}{2})=(2x-1)(2x+1)

Part 5) we have

t^{2}+14t+85

Remember that

The y-intercept of a function is the value of the function (output value) when the value of x (input value) is equal to zero

In this problem

The expression represent a company's net sales, in billions, from 2008 to 2018

t is the number of years since the end of 2008

so

For t=0 -----> represent the end of 2008

(0)^{2}+14(0)+85=85\ billion\ dollars

therefore

The company earned 85 billion dollars in 2008.

Part 6) What are the x-intercepts of the parabola?

we have the points (2,3),(4,-1),(6,3)

This is a vertical parabola open upward

The vertex represent a minimum

In this problem the vertex is the point (4,-1)

The equation of a vertical parabola in vertex form is equal to

y=a(x-h)^2+k

where

a is a coefficient

(h,k) is the vertex

we have

(h,k)=(4,-1)

substitute

y=a(x-4)^2-1

take the point (2,3) and substitute in the quadratic equation to solve for a

For x=2, y=3

3=a(2-4)^2-1

3=4a-1

4a=4

a=1

The quadratic equation is

y=(x-4)^2-1

Find out the x-intercepts

Remember that the x-intercepts are the values of x when the value of the function is equal to zero

so

For y=0

(x-4)^2-1=0

Solve for x

(x-4)^2=1

take square root both sides

(x-4)=(+/-)1

x=4(+/-)1

x=4+1=5\\x=4-1=3

therefore

The x-intercepts are the points (3,0) and (5,0)

7 0
3 years ago
Read 2 more answers
Find at least 3 numbers that are palindromes and have square roots that are palindromes
Artemon [7]

Hey there!

Palindromes are numbers that can be written the same way backwards, such as 101 and 12321. You're looking for some numbers which are palindromes, and so are their square numbers.

Alright, I'll give you four of those:

  1. 121 is a palindrome, and its square root is 11, both palindromes. 11 x 11 = 121
  2. 484 is a palindrome, and its square root is 22, both palindromes. 22 x 22 = 484
  3. 10201 is a palindrome, and its square root is 101, both palindromes. 101 x 101 = 10201
  4. 12321 is a palindrome, and its square root is 111, both palinromes. 111 x 111 = 12321

Hope this helps!

7 0
2 years ago
Read 2 more answers
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