The formula for the time it takes to travel a distance of d at an average speed v is (d)/(v)

Ja'Von kicks a soccer ball into the air. The function f(x) = –16(x – 2)2 + 64 represents the height of the ball, in feet, as a f

Dima020 [189]

Answer:

The maximum height the ball reaches is 64 feet

Step-by-step explanation:

The given function is f(x) = -16·(x - 2)² + 64

From the equation, the path described by the ball is an inverted n-shaped parabola

The maximum height is therefore, the tip of the parabola

At the maximum height, the slope = 0 because the tip is momentarily flat

Since the slope (y₂ - y₁)/(x₂ - x₁) = The derivative Δy/Δx, we find the derivative of the function and equate it to zero to find the coordinates at the maximum height

Δy/Δx = dy/dx = d(-16·(x - 2)² + 64)/dx = -32·(x - 2) = -32·x + 64

To check if it is a maximum, we have;

d²y/dx² = d(-32·x + 64)/dx = -32 which is negative, indicating that the slope is reducing and we at the maximum point of the slope

Therefore for the maximum height Δy/Δx = dy/dx = -32·x + 64 = 0

64 = 32·x

x = 64/32 = 2 seconds

We now have the x-value at the slope, the f(x) value, is therefore;

f(2) = -16·(2 - 2)² + 64 = 64 feet

Therefore, the maximum height the ball reaches is 64 feet.

3 0

3 years ago

A jewelry store bought a gold necklace and marked it up 110% from the original cost of $23.52. Later on, Dean purchased the gold

gladu [14]

Answer: The Solution is in the photo

4 0

2 years ago

If f(x)=8-10x and g(x) =5x +4, what is the value of (fog)(-2)?

swat32

Answer:

68

Step-by-step explanation:

Any function is evaluated by putting the argument value where the variable is, then doing the arithmetic. When the argument is another function value, that function value is evaluated first.

__

The "o" in (fog) is a stand-in for the "ring operator" (∘) which is the operator used to signify a composition. A composition is evaluated right-to-left. That means (f∘g)(x) ≡ f(g(x)). The value of g(x) is found first, and is operated on by the function f.

Writing the composition in the form f(g(x)) lets you identify the layers of parentheses. As with any expression evaluation, the Order of Operations applies. It tells you to evaluate the expression in the innermost parentheses and work your way out.

To evaluate (f∘g)(-2) = f(g(-2)), we must first evaluate g(-2). That is ...

g(x) = 5x +4

g(-2) = 5(-2) +4 = -10 +4 = -6 . . . . . put -2 where x is, do the math

Now that we know g(-2) = -6, we know this expression is ...

f(-6) = 8 -10(-6) = 8 +60 = 68 . . . . . substitute for x in 8-10x

Then the value we're looking for is ...

(f∘g)(-2) = 68

8 0

1 year ago

In 12 hours, the temperature fell steadily from 17degrees to -7degrees f. what was the average change in temperature per hour?

Zarrin [17]

If the temperature changed from 17 degree F to -7 , the change was
17+7=24 degrees F
the average change was 24/12=2 , 2 degrees per hour
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7 0

2 years ago

If f(x) = 3^(x + 4), find f(2).<br><br> A. 729<br> B. 243<br> C. 81<br> D. 18

Umnica [9.8K]

Answer:

f(2) = 729

Step-by-step explanation:

f(x) = 3^(x + 4)

Let x =2

f(2) = 3^(2 + 4)

f(2) = 3^(6)

f(2) = 729

4 0

3 years ago