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3 years ago

11

Write the following sentence using mathematical symbols. The difference of z and two-thirds is the same as the product of z and

two-thirds.

1 answer:

charle [14.2K]3 years ago

3 0

Answer:

Step-by-step explanation:

z - 2/3 = (2/3)z

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The graph h = −16t^2 + 25t + 5 models the height and time of a ball that was thrown off of a building where h is the height in f

Thepotemich [5.8K]

Answer:

part 1) 0.78 seconds

part 2) 1.74 seconds

Step-by-step explanation:

step 1

At about what time did the ball reach the maximum?

Let

h ----> the height of a ball in feet

t ---> the time in seconds

we have

$h(t)=-16t^{2}+25t+5$

This is a vertical parabola open downward (the leading coefficient is negative)

The vertex represent a maximum

so

The x-coordinate of the vertex represent the time when the ball reach the maximum

Find the vertex

Convert the equation in vertex form

Factor -16

$h(t)=-16(t^{2}-\frac{25}{16}t)+5$

Complete the square

$h(t)=-16(t^{2}-\frac{25}{16}t+\frac{625}{1,024})+5+\frac{625}{64}$

$h(t)=-16(t^{2}-\frac{25}{16}t+\frac{625}{1,024})+\frac{945}{64}\\h(t)=-16(t^{2}-\frac{25}{16}t+\frac{625}{1,024})+\frac{945}{64}$

Rewrite as perfect squares

$h(t)=-16(t-\frac{25}{32})^{2}+\frac{945}{64}$

The vertex is the point $(\frac{25}{32},\frac{945}{64})$

therefore

The time when the ball reach the maximum is 25/32 sec or 0.78 sec

step 2

At about what time did the ball reach the minimum?

we know that

The ball reach the minimum when the the ball reach the ground (h=0)

For h=0

$0=-16(t-\frac{25}{32})^{2}+\frac{945}{64}$

$16(t-\frac{25}{32})^{2}=\frac{945}{64}$

$(t-\frac{25}{32})^{2}=\frac{945}{1,024}$

square root both sides

$(t-\frac{25}{32})=\pm\frac{\sqrt{945}}{32}$

$t=\pm\frac{\sqrt{945}}{32}+\frac{25}{32}$

the positive value is

$t=\frac{\sqrt{945}}{32}+\frac{25}{32}=1.74\ sec$

8 0

3 years ago

Someone help ASAP<br> serious answers only or i will report

nadezda [96]

T represents hours, so if c(1.5)=c(t) as it mentioned in the problem, then 1.5 equals hours, and c represents cost, so if cost + time equals nine then I think it's a

3 0

3 years ago

18) -32.-132, -232, -332, ..<br> Find a

Valentin [98]

Answer:

Step-by-step explanation:

next term is -432

5 0

2 years ago

What is the value of x ?? If u cant see numbers let me know

Hoochie [10]

Answer:

X = 58°

Step-by-step explanation:

105° = (2x -11)°

105° + 11° = 2x

116°= 2x

Divide both sides by 2

X = 58°.

4 0

2 years ago

Read 2 more answers

(8.4 x 102) (2.5 x 106)

MaRussiya [10]

Answer:

the answer to (8.4 × 102) (2.5 × 106) = 227,052

7 0

3 years ago