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irga5000 [103]
3 years ago
5

A ball is thrown vertically upward from the ground with an initial velocity of 111 ft/sec. Use the quadratic function h(t) = −16

t2 + 111t + 0 to find how long it will take for the ball to reach its maximum height (in seconds), and then find the maximum height (in feet). (Round your answers to the nearest tenth.)
Mathematics
1 answer:
ddd [48]3 years ago
4 0

Answer:

t=3.5 seconds

Step-by-step explanation:

Given

h(t) = −16t^2 + 111t + 0

h'(t)= -32t + 111

Maximum height occurs when h(t) = 0 and the ball begins to fall

h(t)= -32t + 111=0

-32t + 111=0

-32t=-111

Divide both sides by -32

t=3.46872

Approximately, t=3.5 seconds

Recall,

Maximum height occurs when h(t) = 0

h(t)= -32t + 111=0

= -32(3.46872)+111

= -110.99904+111

= 0.00096 ft

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The complete formula for circumference is:


C=\pi d


Since we know the circumference of the circle is 314 inches, we can then solve for d, the diameter:


314=\pi d


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4 0
3 years ago
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alexgriva [62]

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6 0
3 years ago
Please help I don’t know if I’m doing this correctly
solmaris [256]

Answers:

  1. Exponential and increasing
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=========================================================

Explanation:

Problems 1, 2, and 5 are exponential functions of the form y = a(b)^x where b is the base of the exponent and 'a' is the starting term (when x=0).

If 0 < b < 1, then the exponential function decreases or decays. Perhaps a classic example would be to study how a certain element decays into something else. The exponential curve goes downhill when moving to the right.

If b > 1, then we have exponential growth or increase. Population models could be one example; though keep in mind that there is a carrying capacity at some point. The exponential curve goes uphill when moving to the right.

In problems 1 and 5, we have b = 2 and b = 1.1 respectively. We can see b > 1 leads to exponential growth. I recommend making either a graph or table of values to see what's going on.

Meanwhile, problem 2 has b = 0.8 to represent exponential decay of 20%. It loses 20% of its value each time x increases by 1.

---------------------

Problems 3 and 4 are linear functions of the form y = mx+b

m = slope

b = y intercept

This b value is not to be confused with the previously mentioned b value used with exponential functions. They're two different things. Unfortunately letters tend to get reused.

If m is positive, then the linear function is said to be increasing. The line goes uphill when moving to the right.

On the other hand if m is negative, then we go downhill while moving to the right. This line is decreasing.

Problem 3 has a negative slope, so it is decreasing. Problem 4 has a positive slope which is increasing.

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2.) Opposite angles are equal
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