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3 years ago

Using SQRT(2)=1.414 and SQRT(3)=1.732 approximate SQRT(75)-SQRT(48)

1 answer:

3 0

√2 ≈ 1.414 and √3 ≈ 1.732

√75 = √(25x 3) = 5√3 OR 5x1.414 = 7.07
√48 = √(16x 3) = 4√3 OR 4x1.732 = 6.92

So √75 - √48 = 7.07 - 6.92 ≈ 0.15

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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

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

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3 years ago

1. What is the value of x?<br> 41°<br> 72<br> Your answer

Mazyrski [523]

Triangles add up to 180°, so the answer is 67

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3 years ago

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This equation shows how the cost of a charity gala depends on the number of attendees. d = 5.1a + 11.6 The variable a represents

aleksandr82 [10.1K]

$98.30=5.1a+11.6
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Gnoma [55]

Answer:

Step-by-step explanation:

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Answer:

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