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Gnesinka [82]
3 years ago
6

All ball is thrown into the air with an upward velocity of 24 ft/s. Its height h in feet after t seconds is given by the functio

n h=-16t^2+24t+7. a. In how many seconds does the ball reach its maximum height? Round to the nearest hundredth if necessary. What is the ball's maximum height?
Mathematics
1 answer:
VARVARA [1.3K]3 years ago
7 0
//I'm going to use differentiation to show you how to do this, although I would normally use mechanics.

dh/dt = -32t + 24
-32t + 24 = 0 when maximum
32t = 24
t = 24/32
t = 3/4

//To find the maximum height just substitute "t" in

h = -16 (9/16) + 24(3/4) + 7
h = -9 + 18 + 7
h = 16ft
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9. Given the point (6,-8) values of the six trig function.
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Answer:

Here's what I get.

Step-by-step explanation:

9. (6, -8)

The reference angle θ is in the fourth quadrant.

∆AOB is a right triangle.

OB² = OA² + AB² = 6² + (-8)² = 36 + 64 = 100

OB = √100 = 10  

\sin \theta = \dfrac{-8}{10} = -\dfrac{4}{5}\\\\\cos \theta =\dfrac{6}{10} = \dfrac{3}{5}\\\\\tan \theta = \dfrac{-8}{6} = -\dfrac{4}{3}\\\\\csc \theta = \dfrac{10}{-8} = -\dfrac{5}{4}\\\\\sec \theta = \dfrac{10}{6} = \dfrac{5}{3}\\\\\cot \theta = \dfrac{6}{-8} = -\dfrac{3}{4}

10. cot θ = -(√3)/2

The reference angle θ is in the second quadrant.

∆AOB is a right triangle.

OB² = OA² + AB² = (-√3)² + (2)² = 3 + 4 = 7

OB = √7

\sin \theta = \dfrac{2}{\sqrt{7}} = \dfrac{2\sqrt{7}}{7}\\\\\cos \theta = \dfrac{-\sqrt{3}}{\sqrt{7}} = -\dfrac{\sqrt{21}}{7}\\\\\tan \theta = \dfrac{2}{-\sqrt{3}} = -\dfrac{2\sqrt{3}}{3}\\\\\csc \theta = \dfrac{\sqrt{7}}{2} \\\\\sec \theta = \dfrac{\sqrt{7}}{-\sqrt{3}} = -\dfrac{\sqrt{21}}{3}\\\\\cot \theta = -\dfrac{\sqrt{3}}{2}

3 0
3 years ago
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astraxan [27]

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Step-by-step explanation:

hope it helps

5 0
2 years ago
Can anyone Help me please
m_a_m_a [10]
The partial variation is A

7 0
3 years ago
Can you help me with this??<br> please explain
zepelin [54]
Hello!

We separate this into three sections

we are looking for a graph that has a line where x is greater than -3 and less than -2 while the circles not shaded since it does have the or equal to sign

The graphs that have this is the first and the third

Next we can look for the graph that has x greater than or equal to -2 and less than 3 with the one at -2 shaded but the one at 3 not

The graph that follows this is the third graph

The answer is the third one

Hope this helps!
7 0
3 years ago
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