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2 years ago

Are these answers correct?

Mathematics

2 answers:

Rainbow [258]2 years ago

8 0

Answer:

Yes, your answers are correct!

Step-by-step explanation:

Leona [35]2 years ago

8 0

Answer:

yes

Step-by-step explanation:

you are correct!

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2 years ago

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Step-by-step explanation:

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2 years ago

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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

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

2 years ago

Alyssa scored x goals during the soccer game yesterday. Today she scored 3 times as many goals. She scored a total of 4 goals du

damaskus [11]

Answer:

Alyssa had scored 3 goals today.

Step-by-step explanation:

Given:

Number of goals scored yesterday = $x$

Total number of goals scored in 2 games = 4

We need to find the number of goals scored today.

Solution:

Now Given:

Today she scored 3 times as many goals than yesterday.

So we can say that;

Number of goals scored today = $3x$

Now we know that;

Total number of goals scored in 2 games is the sum of Number of goals scored yesterday and Number of goals scored today.

framing in equation form we get;

$x+3x=4\\\\4x=4$

Dividing both side by 4 we get;

$\frac{4x}{4} =\frac{4}{4}\\\\x=1$

Number of goals scored yesterday = 1

Number of goals scored today = $3x = 3\times1 =3$

Hence Alyssa had scored 3 goals today.

6 0

3 years ago