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Paha777 [63]
3 years ago
13

We are standing on the top of a 320 foot tall building and launch a small object upward. The object's vertical altitude, measure

d in feet, after t seconds is h ( t ) = − 16 t 2 + 128 t + 320 . What is the highest altitude that the object reaches?
Mathematics
1 answer:
STALIN [3.7K]3 years ago
6 0

Answer:

The highest altitude that the object reaches is 576 feet.

Step-by-step explanation:

The maximum altitude reached by the object can be found by using the first and second derivatives of the given function. (First and Second Derivative Tests). Let be h(t) = -16\cdot t^{2} + 128\cdot t + 320, the first and second derivatives are, respectively:

First Derivative

h'(t) = -32\cdot t +128

Second Derivative

h''(t) = -32

Then, the First and Second Derivative Test can be performed as follows. Let equalize the first derivative to zero and solve the resultant expression:

-32\cdot t +128 = 0

t = \frac{128}{32}\,s

t = 4\,s (Critical value)

The second derivative of the second-order polynomial presented above is a constant function and a negative number, which means that critical values leads to an absolute maximum, that is, the highest altitude reached by the object. Then, let is evaluate the function at the critical value:

h(4\,s) = -16\cdot (4\,s)^{2}+128\cdot (4\,s) +320

h(4\,s) = 576\,ft

The highest altitude that the object reaches is 576 feet.

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Katena32 [7]

Hey there!!

Equation Given : x + 3x - 36

In order to solve this, we will need to combine the like terms.

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Like terms are terms which have the same variable, in the equation given, the variable mentioned is x and hence, the like terms are x and 3x.

Now, we will need to combine x and 3x.

Let's take x as 1x and 3x as 3x.

Now, we will need to add both these like terms.

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x will be common, we will need to add 1 and 3

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5 0
3 years ago
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Chanelle deposits $7,500 into the bank. She does not withdraw or deposit money for 6 years. She earns 6% interest during that ti
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Answer: a. $2700

b. $10200

Step-by-step explanation:

a. The interest she would have earned at the end of the 6 years can be gotten using the formula

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= $7500 × 6% × 6

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= $7500 × 0.06 × 6

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5 0
3 years ago
Please help me out with this equation! <br> i will mark you as brainliest
BigorU [14]
<h3>Answer:  -19, -15, -9, -1, 9   (choice A)</h3>

===================================================

Explanation:

If we plug in x = -2, then we get,

y = x^2 + 7x - 9

y = (-2)^2 + 7(-2) - 9

y = 4 - 14 - 9

y = -10 - 9

y = -19

So x = -2 leads to y = -19. The answer is between A and D.

---------

If you repeat those steps for x = -1, then you should get y = -15

Then x = 0 leads to y = -9

x = 1 leads to y = -1

Finally, x = 2 leads to y = 9

The outputs we get are: -19, -15, -9, -1, 9 which is choice A

Choice D is fairly close, but we won't have a second copy of -15, and  we don't have an output of -19.

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A tv has a listed price of $896.99 before tax. If the sales tax rate is 7.75%, find the total cost of the tv with sales tax incl
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Answer:69.52

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