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fomenos
2 years ago
15

Amy launched a ball into the air. The height of the ball can be represented by the equation h = -16t^2 + 96t + 112, where h is t

he height, in units, and t is the time, in seconds, after the ball was launched. Graph the equation from t = 0 to t = 7 seconds
And then the second question is state the coordinates of the vertex and explain its meaning in the context of the problem.

Please help me and show work
Mathematics
1 answer:
Sidana [21]2 years ago
3 0

Answer:

Vertex is (3, 256)

Step-by-step explanation:

The vertex means that at 3 seconds, the highest point the ball will reach is 256 units in the air.

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Solve the equation: k^2+5k+13=0
mr_godi [17]

Step-by-step explanation:

k² + 5k + 13 = 0

Using the quadratic formula which is

x =  \frac{ - b \pm \sqrt{ {b}^{2} - 4ac } }{2a}  \\

From the question

a = 1 , b = 5 , c = 13

So we have

k =  \frac{ - 5 \pm \sqrt{ {5}^{2} - 4(1)(13) } }{2(1)}  \\  =  \frac{ - 5 \pm \sqrt{25 - 52} }{2}  \\  =  \frac{ - 5 \pm \sqrt{ - 27} }{2}  \:  \:  \:  \:  \:  \:  \\  =  \frac{ - 5  \pm3 \sqrt{3}  \: i}{2}  \:  \:  \:  \:  \:  \:

<u>Separate the solutions</u>

k_1 =  \frac{ - 5 + 3 \sqrt{3} \: i }{2}  \:  \:  \:  \: or \\ k_2 =  \frac{ - 5 - 3 \sqrt{3}  \: i}{2}

The equation has complex roots

<u>Separate the real and imaginary parts</u>

We have the final answer as

k_1 =  -  \frac{5}{2}  +  \frac{3 \sqrt{3} }{2}  \: i \:  \:  \:  \: or \\ k_2 =  -  \frac{5}{2}  -  \frac{3 \sqrt{3} }{2}  \: i

Hope this helps you

8 0
2 years ago
1. Write a polynomial function of minimum degree with real coefficients whose zeros include those listed. Write the polynomial i
Katena32 [7]
Polynomial with real coefficients always has even number of complex roots. We know that one of them is 2 + 5i so the second one will be  2 - 5i and:

f(x)=\big(x-4\big)\big(x-(-8)\big)\big(x-(2+5i)\big)\big(x-(2-5i)\big)=\\\\=(x-4)(x+8)(x-2-5i)(x-2+5i)=\\\\=(x^2-4x+8x-32)(x^2-2x+5ix-2x+4-10i-5ix+10i-25i^2)\\\\=\big(x^2+4x-32\big)\big(x^2-4x+4-25\cdot(-1)\big)=\\\\=(x^2+4x-32)(x^2-4x+29)=\\\\=x^4-4x^3+29x^2+4x^3-16x^2+116x-32x^2+128x-928=\\\\=\boxed{x^4-19x^2+244x-928}

Answer B.
8 0
3 years ago
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Answer:

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A. (0,-6)
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If 2 coins can be exchanged for 3.3782 dubloons, how many dubloons can be obtained for 9 coins?
Shtirlitz [24]

Answer:

5.33

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