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3 years ago

What is x minus the square root of 2

Mathematics

1 answer:

Zielflug [23.3K]3 years ago

6 0

Answer:

x - sqrt(2)

Step-by-step explanation:

x - sqrt(2)

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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

Jean cost $45, they are now priced $40. find the percent of change from $45 to $40

Kisachek [45]

The percent of change is 9%

3 0

3 years ago

What is the slope of a line that is perpendicular to the line represented by the equation y=-2/5x+4/5

enot [183]

Answer:

$\frac{5}{2}$

Step-by-step explanation:

recall for a line whose equation is

y = mx + b,

the slope of this line is m

the slope of a line that is perpendicular to this line is - $\frac{1}{m}$

in this case,

m = - $\frac{2}{5}$

hence - $\frac{1}{m}$ = $\frac{5}{2}$

6 0

3 years ago

Complete the solution of the equation. Find the value of y when x equals -4. 5x + 2y = -20

guajiro [1.7K]

6 0

3 years ago

The table below shows the cube roots of different numbers:

Mila [183]

part A)

$\bf \begin{array}{|c|cccccc|ll} \cline{1-7} x&8&27&64&125&&x\\ \cline{1-7} y&\stackrel{\sqrt[3]{8}}{2}&\stackrel{\sqrt[3]{27}}{3}&\stackrel{\sqrt[3]{64}}{4}&\stackrel{\sqrt[3]{125}}{5}&&\sqrt[3]{x} \\ \cline{1-7} \end{array}~\hspace{10em}y = \sqrt[3]{x}$

part B)

f(x) = 10 + 20x

so if you rent the bike for a few hours that is

1 hr.............................10 + 20(1)

2 hrs..........................10 + 20(2)

3 hrs..........................10 + 20(3)

so the cost is really some fixed 10 + 20 bucks per hour, usually the 10 bucks is for some paperwork fee, so you go to the bike shop, and they'd say, ok is 10 bucks to set up a membership and 20 bucks per hour for using it, thereabouts.

f(100) = 10 + 20(100) => f(100) = 2010.

f(100), the cost of renting the bike for 100 hours.

4 0

3 years ago