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2 years ago

The point-slope equation of a line is....? HELP ME

Mathematics

1 answer:

Kay [80]2 years ago

8 0

Y-y1=m(x-x1) she kdhkshs jshdkhd

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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

PLEASEEE HELP ME WHAT IS THE ANSWER!!

blagie [28]

Answer:

Number 3 is correct.

129.19m

Step-by-step explanation:

You might be wondering how did I got 32⁰, well, that's because they are alternate angles.

Now, we're trying to find the opposite side of the triangle.

Using the laws,

we got cos32⁰=x/243.8

243.8cos32⁰=x

129.19⁰

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3 0

2 years ago

Find the map ratio if 10 cm on the map is represented by 10 km

olga nikolaevna [1]

I think this is the answer :)

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Which expression shows the distance you would drive from the gym to the office along this road?

-Dominant- [34]

B because absolute value means the distance of a point on a number line from 0. So the absolute value of -6 is 6 and you add that to 4

3 0

2 years ago

Is the square root of 4 plus the square root of 16 rational

Ahat [919]

Yes because square root of 4 is 2 and square root of 16 is 4. 4+2=6

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2 years ago

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