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Nuetrik [128]
3 years ago
12

What is the exact volume of a cylinder that has a height of 1.8 ft and a radius of 6.1 ft?

Mathematics
1 answer:
lozanna [386]3 years ago
3 0
Cylinder area=height times area of base (area of base=area of circle)

height =1.8
radius=6.1
area of circle=pi times r^2


area of circle=pi times 6.1^2=37.21π
times height

1.8 times 37.21π=66.978π

volume=66.978π ft^3
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If a ball is thrown into the air with a velocity of 34 ft/s, its height (in feet) after t seconds is given by y = 34t − 16t2. Fi
Finger [1]

<u>ANSWER: </u>

If a ball is thrown into the air with a velocity of 34 feet per second, then velocity of the ball after 1 second is 2 feet per second

<u>SOLUTION: </u>

Given, a ball is thrown into the air with a velocity of 34 feet per second

Initial velocity (u) = 34 feet per second

And also given a relation between displacement and time = \mathrm{y}=34 \mathrm{t}-16 \mathrm{t}^{2} --- eqn 1

We need to find the velocity when t = 1 ; v = ?

We know that, v = u + at and \mathrm{s}=\mathrm{ut}+\frac{1}{2} \mathrm{at}^{2}

where v is instantaneous velocity and u is initial velocity

a is acceleration

t is time interval  

s is displacement

using the displacement and time relation eqn (1) we get

Now, when t = 1, displacement s = 34(1) – 16(1)

\mathrm{ut}+\frac{1}{2} \mathrm{at}^{2}=34-16

34 \times 1+\frac{1}{2} \times a \times 1^{2}=18

34+\frac{a}{2}=18

\begin{array}{l}{\frac{a}{2}=18-34} \\\\ {\frac{a}{2}=-16} \\ {a=-16 \times 2} \\ {a=-32}\end{array}

here, -ve sign indicates that object is in deceleration . so acceleration is -32 ft/s

now put a value in v = u + at

v = 34 + (-32)(1)

v = 34 – 32

v = 2 ft/s

Hence, velocity of the ball after 1 second is 2 ft/s

6 0
2 years ago
This graph represents a quadratic function. What is the function’s equation written in factored form and in vertex form?
creativ13 [48]

Answer:

Part a) The function’s equation written in vertex form is

f(x)=2(x-2)^2-8

Part b) The function’s equation written in factored form is equal to

f(x)=2x(x-4)

Step-by-step explanation:

Part a) What is the function’s equation written in vertex form?

we know that

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

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

where

a is a coefficient

(h,k) is the vertex

Looking at the graph

The vertex is the point (2,-8)

substitute

f(x)=a(x-2)^2-8

Find the value of the coefficient a

take one point from the graph

(0,0)

substitute in the equation

0=a(0-2)^2-8\\0=4a-8\\4a=8\\a=2

therefore

The function’s equation written in vertex form is

f(x)=2(x-2)^2-8

Part b) What is the function’s equation written in factored form?

we know that

The equation of a vertical parabola written in factored form is equal to

f(x)=a(x-x_1)(x-x_2)

where

a is a coefficient

x_1 and x_2 are the zeros or x-intercepts of the function

Remember that the x-intercept is the value of x when the value of the function is equal to zero

Looking at the graph

The zeros or x-intercepts of the function are

x=0 and x=4

so

f(x)=a(x-0)(x-4)

f(x)=ax(x-4)

Find the value of the coefficient a

take one point from the graph

(2,-8)

substitute

-8=a(2)(2-4)\\-8=-4a\\a=2

therefore

The function’s equation written in factored form is equal to

f(x)=2x(x-4)

4 0
3 years ago
Two less than 2 times a number is the same as the number plus 64. What is the number?
Alex Ar [27]
Set it up as an equation. "A number" is x.

2x-2=x+64

Move all of the x terms to one side by subtracting x from both sides, then add 2 to both sides to isolate x.

X=66

The number is 66
8 0
2 years ago
Students are playing a game similar to blackjack (with a standard 52 card deck)- trying to get as close to 21 points without goi
son4ous [18]
1/2 wee player a just got 2 so it is out
7 0
3 years ago
Can someone please help me out?
jek_recluse [69]

Answer:

Ligh blue

Step-by-step explanation:

6 0
2 years ago
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