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harina [27]
3 years ago
15

30 Points! A soccer ball hit from the ground into the air and is modeled by the function

Mathematics
1 answer:
gavmur [86]3 years ago
5 0

Answer:

A)

At t = 3/2

B)

36 feet

Step-by-step explanation:

The soccer ball is modeled by the function:

h(t)=-16t^2+48t

Where h(t) represents the height in feet of the ball over time t.

Note that this is a quadratic equation.

Part A)

Since this is a quadratic, the maximum height will be reached when the ball reaches its vertex.

So, we will find the x-coordinate of the vertex.

The vertex is given by:

\displaystyle \Big (-\frac{b}{2a} , h( -\frac{b}{2a} )  \Big)

In this case, a = -16 and b = 48. Thus, the t-coordinate is:

\displaystyle t=-\frac{48}{2(-16)}=-\frac{48}{-32}=\frac{3}{2}

The ball will reach is maximum height at t = 3/2.

Part B)

To find the maximum height, we can simply substitute the value back into the function and evaluated. Therefore:

\displaystyle\begin{aligned} h(\frac{3}{2})&=-16\Big(\frac{3}{2}\Big)^2+48\Big(\frac{3}{2}\Big)\\\\ &=-16\Big(\frac{9}{4}\Big)+24(3)\\ \\ &=-36+72\\\\ &= 36 \end{aligned}

The maximum height of the ball is 36 feet.

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myrzilka [38]

Part A.

What we can do to solve this problem is to assume that the acceleration of Bryan is constant so that the velocity function is linear. The standard form of a linear function is in the form:

y = m x + b

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v = m t + b

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The slope m can be calculated by:

m = (v2 – v1) / (t2 – t1)

m = (12 – 15) / (7 – 4)

m = -1

Since slope is negative therefore this means the cyclist are constantly decelerating. The equation then becomes:

v = - t + b

Now finding for b by plugging in any data pair:

15 = - (4) + b

b = 19

So the complete equation is:

v = - t + 19

This means that the initial velocity of the cyclists at t = 0 is 19 km / h.

 

Part B. What we can do to graph the equation is to calculate for the values of v from t = 0 to 12, then plot all these values in the Cartesian plane then connect the dots.

6 0
4 years ago
The ratio of width to length of a rectangle is 7:10.The width of the rectangle is 91 cm.
kvasek [131]

Answer:

Length= 130 cm

For, Width= 91 cm

Step-by-step explanation:

Ratio of the width to the length of the rectangle = 7:10

Width of the rectangle= 91 cm

\frac{Width}{Length} =\frac{7}{10}

As, Width = 91 cm

\frac{91}{Length} =\frac{7}{10}

On, Cross multiplication the fraction:

91*10=7*Length

7*Length=910

Dividing by '7' both the sides:

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6 0
3 years ago
Operations with Radical Expressions
lisov135 [29]

Answer: 30\sqrt{11}

<u>Step-by-step explanation:</u>

  3\sqrt{50} * \sqrt{22}

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= 3\sqrt{5*5*2*2*11}

= 3*5*2\sqrt{11}

= 30\sqrt{11}

******************************************

Answer: 6\sqrt{30}

<u>Step-by-step explanation:</u>

  \sqrt{20} * \sqrt{3} * \sqrt{18}

= \sqrt{2*2*5} * \sqrt{3} * \sqrt{3*3*2}

= \sqrt{2*2*5*3*3*3*2}

= 2*3\sqrt{5*3*2}

= 6\sqrt{30}

********************************************

Answer: -\sqrt{5}

<u>Step-by-step explanation:</u>

  4\sqrt{20} - 3\sqrt{45}

= 4\sqrt{2*2*5} - 3\sqrt{3*3*5}

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********************************************

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<u>Step-by-step explanation:</u>

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Answer: 46\sqrt{2}

<u>Step-by-step explanation:</u>

  4\sqrt{32} + 6\sqrt{50}

= 4\sqrt{2*2*2*2*2} + 6\sqrt{2*5*5}

= 4*2*2\sqrt{2} + 6*5\sqrt{2}

= 16\sqrt{2} + 30\sqrt{2}

= 46\sqrt{2}





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4 years ago
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ankoles [38]
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Hope this answer is helpful


Please mark me as brainliest
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4 years ago
What is the volume of the cylinder pictured below?
Vera_Pavlovna [14]

Answer:

Answer is 80.36

Step-by-step explanation:

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Pls mark brainleist

Hope this helps

Thanks!!

8 0
3 years ago
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