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2 years ago

Look at picture y=_the height of the baseball after 5 seconds is ___ feet

Mathematics

1 answer:

Wittaler [7]2 years ago

5 0

Answer:

y = -2(x -3)² +24
16 feet

Step-by-step explanation:

We expect the equation for y to be quadratic. Since the table is obviously symmetrical about x=3, we can start with the vertex form ...

y = a(x -3)² +b

Filling in the values from the first two table points, we get

For (x, y) = (0, 6):

6 = a(0 -3)² + b ⇒ 9a +b = 6

For (x, y) = (2, 22):

22 = a(2-3)² +b ⇒ a +b = 22

Subtracting the second equation from the first gives ...

(9a +b) -(a +b) = (6) -(22)

8a = -16 . . . . . . collect terms

a = -2 . . . . . . . . divide by 8

The second equation above tells us ...

b = 22 -a = 22 -(-2) = 24

So, our equation for y is ...

y = -2(x -3)² +24

The value of y for x=5 is ...

y = -2(5 -3)² +24 = 16

The height of the ball after 5 seconds is 16 feet.

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The object below was made by placing a cone on top of a cylinder. The base of the cone is congruent to the base of the cylinder.

Ber [7]

Answer:

Part 1) The volume of the object is $32\pi\ cm^{3}$ or $100.48\ cm^{3}$

Part 2) see the procedure

Step-by-step explanation:

The picture of the question in the attached figure

Part 1) What is the volume, in cubic centimeters, of the object?

we know that

The volume of the object is equal to the volume of the cylinder plus the volume of the cone

Find the volume of the cone

The volume of the cone is equal to

$V=\frac{1}{3}\pi r^{2} h$

we have

$r=4/2=2\ cm$ -----> the radius is half the diameter

$h=3\ cm$

substitute the values

$V=\frac{1}{3}\pi (2^{2})(3)=4\pi\ cm^{3}$

Find the volume of the cylinder

The volume of the cylinder is equal to

$V=\pi r^{2} h$

we have

$r=4/2=2\ cm$ -----> the radius is half the diameter

$h=(10-3)=7\ cm$

substitute the values

$V=\pi (2^{2})(7)=28\pi\ cm^{3}$

Part 2) Then explain how you found the volume of the total shape

The volume of the total shape is equal to the volume of the cylinder plus the volume of the cone

$4\pi\ cm^{3}+28\pi\ cm^{3}=32\pi\ cm^{3}$ ------> exact value

Find the approximate value of the volume

assume

$\pi=3.14$

$32(3.14)=100.48\ cm^{3}$

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Alexxandr [17]

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2 years ago

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Vaselesa [24]

Answer:

The answer is 5.

Step-by-step explanation:

(2x+3)(x+1) Use the FOIL METHOD

2x²+2x+3x+3

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3 years ago

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Find the percent of tip:

r-ruslan [8.4K]

The answer is 14%

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2 years ago

27 + (8-5) -am looking for the answer of number 7

Rasek [7]

Answer:

The answer to the equation from question 7 is 14.

Step-by-step explanation:

In question 7, we are given an equation.

2³ + (8 - 5)² - 3

First, subtract 5 from 8 in the parentheses.

2³ + 3² - 3

Next, solve the exponents for 2³ and 3².

8 + 9 - 3

Add 8 to 9.

17 - 3

Subtract 3 from 17.

So, the answer to this equation from question 7 is 14.

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3 years ago

Look at picture y=_the height of the baseball after 5 seconds is ___ feet​

Look at picture y=_the height of the baseball after 5 seconds is ___ feet