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3 years ago

14

A helicopter descends at a rate of 450 feet per minute write the equation and sole the change in altitude of the helicopter afte

r 5 minutes?

1 answer:

sweet [91]3 years ago

8 0

Just divide the 450 by 5

You might be interested in

Every evening Jenna emptied her pocket and put your change in a jar at the end of the week she counts her money one week she had

Lelu [443]

Answer:

Jenna had 25 quarters and 15 dimes.

Step-by-step explanation:

Let Q = the number of quarters and D = the number of dimes.

Then:

1) Q+D = 40 "One week she had 40 coins, all of them dimes and quarters...."

2) 0.25Q+0.1D = $7.75 "...she had a total of $7.75."

Rewrite equation 1) as: D = 40-Q and substitute into equation 2).

2a) 0.25Q+0.1(40-Q) = 7.75 Simplify the left side.

2b) 0.25Q+4-0.1Q = $7.75 Subtract 4 from both sides.

2c) 0.25Q-0.1Q = 3.75 Combine the like-terms on the left side.

2d) 0.15Q = 7.75 Divide both sides by 0.15

2e) Q = 25 and:

D = 40-Q

D = 40-25

D = 15

Jenna had 25 quarters and 15 dimes.

3 0

3 years ago

If you are offered one slice from a round pizza (in other words, a sector of a circle) and the slice must have a perimeter of 24

VARVARA [1.3K]

Answer:

A 12 in diameter will reward you with the largest slice of pizza.

Step-by-step explanation:

Let $r$ be the radius and $\theta$ be the angle of a circle.

According with the graph, the area of the sector is given by

$A=\frac{1}{2}r^2\theta$

The arc lenght of a circle with radius $r$ and angle $\theta$ is $r \theta$

The perimeter of the pizza slice is composed of two straight pieces, each of length r inches, and an arc of the circle which you know has length s = rθ inches. Thus the perimeter has length

$2r+r\theta=24 \:in$

We need to express the area as a function of one variable, to do this we use the above equation and we solve for $\theta$

$2r+r\theta=24\\r\theta=24-2r\\\theta=\frac{24-2r}{r}$

Next, we substitute this equation into the area equation

$A=\frac{1}{2}r^2(\frac{24-2r}{r})\\A=\frac{1}{2}r(24-2r)\\A=12r-r^2$

The domain of the area is

$0$

To find the diameter of pizza that will reward you with the largest slice you need to find the derivative of the area and set it equal to zero to find the critical points.

$\frac{d}{dr} A=\frac{d}{dr}(12r-r^2)\\A'(r)=\frac{d}{dr}(12r)-\frac{d}{dr}(r^2)\\A'(r)=12-2r$

$12-2r=0\\-2r=-12\\\frac{-2r}{-2}=\frac{-12}{-2}\\r=6$

To check if $r=6$ is a maximum we use the Second Derivative test

if $f'(c)=0$ and $f''(c)$ , then f(x) has a local maximum at x = c.

The second derivative is

$\frac{d}{dr} A'(r)=\frac{d}{dr} (12-2r)\\A''(r)=-2$

Because $A''(r)=-2$ the largest slice is when r = 6 in.

The diameter of the pizza is given by

$D=2r=2\cdot 6=12 \:in$

A 12 in diameter will reward you with the largest slice of pizza.

3 0

3 years ago

10 POINTS!!! FULL ANSWER WITH FULL STEP BY STEP SOLUTION PLEASE. DO BOTH PARTS OF 1 AND ALL OF 2.

diamong [38]

One A
y = e^x
dy/dx = e^x The f(x) = the differentiated function. Any value that e^x can have, the derivative has the same value. x is contained in all the reals.
One B
y = x*e^x
y' = e^x + xe^x Using the multiplication rule.
You want the slope and the value of the of y to be the same. The slope is y' of the tangent line
xe^x = e^x + xe^x
e^x = 0
This happens only when x is very "small" like x = - 4444444

y = e^x * ln(x) Using the multiplication rule again, we need the slope of the line with is y'
y1 = e^x
y1' = e^x
y2 = ln(x)
y2' = 1/x
y' = e^x*ln(x) + e^x/x So at x = 1 the slope of the line =
y' = e^1*ln(1) + e^1/1
y' = e*0+e = e
y = mx + b
y = ex + b
to find b we use y= e^x ln(x)

e^x ln(x) = e*x + b
e^1 ln(1) = e*1 + b
ln(1) = 0
0 = e + b
b = - e

line equation and answer.
y = e*x - e

8 0

3 years ago

And I oop- T^T<br><br> Send help

Rufina [12.5K]

I sent help but no one answered :(

Jk, I got you fam

12(t + 2) + 4 ≥ - 8

12t + 24 + 4 ≥ - 8

12t + 28 ≥ - 8

12t ≥ - 8 - 28

12t ≥ - 36

t ≥ - 36 ÷ 12

t ≥ - 3

Solution:

t ≥ -3

4 0

3 years ago

Read 2 more answers

Write as an equation: If a number is decreased by five, and then the result is multiplied by two, the result is 26.

kvasek [131]

Answer:

18

Step-by-step explanation:

Because when 18-5=13 x 2=26

5 0

2 years ago