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3 years ago

Daniel kicks a soccer ball and the trajectory is modeled by f(t) =− 16t^2+ 32t .

Mathematics

1 answer:

vagabundo [1.1K]3 years ago

3 0

Answer:

f(1) = 16

Domain: 0 ≤ t ≤ 2

Step-by-step explanation:

Given

f(t) = -16t²+ 32t

Solving (a): f(1)

Substitute 1 for t in f(t)

f(t) =− 16t²+ 32t .

f(1) =− 16 * (1)²+ 32 * 1

f(1) = -16 * 1 + 32

f(1) = -16 + 32

f(1) = 16

Solving (b): The domain

The implication of the given parameter in (b) is that t ≤ 2.

Since t represents time, t can't be negative.

Hence, a reasonable domain is

0 ≤ t ≤ 2

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Which of the following is not geometric sequence

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C. The sequence is a sequence of squares. There is no common ratio.

D. The common ratio is 1/2.

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A and D are geometric sequences.

B and C are not geometric sequences.

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4 years ago

6x-1/5 = 3/1 Solve for x in simplest form.

lawyer [7]

6x-1/5=3
add 1/5 to both sides
6x=1/5+3
convert 3 to fraction with 5 as denomenatory
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8 0

3 years ago

Read 2 more answers

Twenty seven pears are packed in bags of three. Five bags of pears are sold. How many pears are left

aliya0001 [1]

Answer:

$Pears\ Left = 12$

Step-by-step explanation:

Given

$Pears = 27$

$Bags\ Sold = 5$

Required

Determine the number of bags sold

First, we need to determine the number of bags for 27 pears;

Since they are packed in 3s

$Bags = 27/3$

$Bags = 9$

Hence:

9 bags were used for 27 pears;

After 5 bags were sold, we have:

$Bags\ Left = 9 - 5$

$Bags\ Left = 4$

Recall that the pears are packed in 3s

So:

$Pears\ Left = 4 * 3$

$Pears\ Left = 12$

4 0

3 years ago

Let x = wavelength and y = frequency. The equation that models the inverse relation is

Vikki [24]

Answer:

y = (3 × 10^8 m/s)/x

Step-by-step explanation:

Speed of a wave is given by the product of wavelength and frequency.

Thus; speed = frequency × wavelength

If x = wavelength and y = frequency then speed will be;

speed = yx

Thus to get wavelength, y;

y = speed/x , but speed is 3 × 10^8 m/s

Thus;

y = (3 × 10^8 m/s)/x

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3 years ago

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Need Help

klio [65]

The smallest amount of material needed is 54 square centimeters

<h3>How to determine the amount of material needed?</h3>

The given parameters are:

Volume = 36 cubic centimeters

Represent length with x, width with y and height with z.

So, we have

x = 3y

The volume is calculated as:

V = xyz

This gives

V = 3y²z

Substitute 36 for V

3y²z = 36

Divide by 3

y²z = 12

Make z the subject

z = 12/y²

The surface area is:

S = 2(xy + xz + yz)

This gives

S = 2(3y² + 3yz + yz)

Evaluate the like terms

S = 2(3y² + 4yz)

Expand

S = 6y² + 8yz

Substitute z = 12/y²

S = 6y² + 8y * 12/y²

This gives

S = 6y² + 96/y

Differentiate

S' = 12y - 96/y²

Set to 0

12y - 96/y² = 0

Multiply through by y²

12y³ - 96 = 0

Add 96 to both sides

12y³ = 96

Divide by 12

y³ = 8

Take the cube root of both sides

y = 2

Recall that:

x = 3y and z = 12/y²

This gives

x = 3 * 2 = 6

z = 12/2² = 3

Recall that:

S = 2(xy + xz + yz)

So, we have:

S = 2(6 * 2 + 3 * 3 + 2 * 3)

Evaluate

S = 54

Hence, the smallest amount of material needed is 54 square centimeters