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2 years ago

The length of a rectangle is three times its width. if the area of the rectangle is 75 in2, find its perimeter.

Mathematics

1 answer:

UkoKoshka [18]2 years ago

7 0

Answer:

40 in

Step-by-step explanation:

For a width of w, the length is 3w and the area and perimeter are ...

A = LW = (3w)(w) = 3w^2

P = 2(L+W) = 2(3w +w) = 8w

We are given the area, so we can find w to be ...

75 in^2 = 3w^2

25 in^2 = w^2 . . . . . divide by 3

5 in = w . . . . . . . . . square root

Then the perimeter is ...

P = 8w = 8(5 in) = 40 in

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Molly Invests $8,600 into her son's college fund, which earns 3% annual interest

8_murik_8 [283]

Answer:

n= 13.8 years

Step-by-step explanation:

First, we need to determine the daily interest rate:

Daily interest rate= 0.03 / 365

Daily interest rate= 0.000082

Now, using the following formula we can determine the number of days and years:

n= ln(FV/PV) / ln(1+i)

n= ln(13,000 / 8,600) / ln(1.000082)

n= 5,039 days

In years:

n= 5,039/365

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2 years ago

?÷2/3 = 3/4 10 POINTS!!!

FromTheMoon [43]

The answer is 1/2. Multiply 3/4 by 2/3.

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3 years ago

Read 2 more answers

Use the chain rule calculate dw/dr , dw/ds and dw/dt

Liono4ka [1.6K]

Answer:

$\frac{dw}{dr} = \frac{8\cdot r}{4\cdot r^{2}-t^{2}+5\cdot s^{2}}$ , $\frac{dw}{ds} = \frac{10\cdot s}{4\cdot r^{2}-t^{2}+5\cdot s^{2}}$ , $\frac{dw}{dt} = -\frac{2\cdot t}{4\cdot r^{2}-t^{2}+5\cdot s^{2}}$

Step-by-step explanation:

We proceed to derive each expression by rule of chain. Let be $w = \ln (x+2\cdot y + 3\cdot z)$ , $x = r^{2}+t^{2}$ , $y = s^{2}-t^{2}$ and $z = r^{2}+s^{2}$ :

$\frac{dw}{dr} = \frac{\frac{dx}{dr}+2\cdot \frac{dy}{dr} +3\cdot \frac{dz}{dr} }{x+2\cdot y + 3\cdot z}$

$\frac{dx}{dr} = 2\cdot r$

$\frac{dy}{dr} = 0$

$\frac{dz}{dr} = 2\cdot r$

$\frac{dw}{dr} = \frac{8\cdot r}{(r^{2}+t^{2})+2\cdot (s^{2}-t^{2})+3\cdot (r^{2}+s^{2})}$

$\frac{dw}{dr} = \frac{8\cdot r}{4\cdot r^{2}-t^{2}+5\cdot s^{2}}$ (1)

$\frac{dw}{ds} = \frac{\frac{dx}{ds}+2\cdot \frac{dy}{ds} +3\cdot \frac{dz}{ds} }{x+2\cdot y + 3\cdot z}$

$\frac{dx}{ds} = 0$

$\frac{dy}{ds} = 2\cdot s$

$\frac{dz}{ds} = 2\cdot s$

$\frac{dw}{ds} = \frac{10\cdot s}{(r^{2}+t^{2})+2\cdot (s^{2}-t^{2})+3\cdot (r^{2}+s^{2})}$

$\frac{dw}{ds} = \frac{10\cdot s}{4\cdot r^{2}-t^{2}+5\cdot s^{2}}$ (2)

$\frac{dw}{dt} = \frac{\frac{dx}{dt}+2\cdot \frac{dy}{dt} +3\cdot \frac{dz}{dt} }{x+2\cdot y + 3\cdot z}$

$\frac{dx}{dt} = 2\cdot t$

$\frac{dy}{dt} = -2\cdot t$

$\frac{dz}{dt} = 0$

$\frac{dw}{dt} = -\frac{2\cdot t}{(r^{2}+t^{2})+2\cdot (s^{2}-t^{2})+3\cdot (r^{2}+s^{2})}$

$\frac{dw}{dt} = -\frac{2\cdot t}{4\cdot r^{2}-t^{2}+5\cdot s^{2}}$ (3)

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2 years ago

When you have a compound inequality like so, but the variable is a negative, how do you graph it? Do you just graph it normally

Dvinal [7]

You can never have a negative variable, meaning you have to divide by -1 on both sides.
Therefore, the answer would be...
x< 3
You reverse the inequality symbol because you are dividing by a negative number
Hope this helps

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3 years ago

Find the area of the semicircle.

Oliga [24]

So since this is half a circle, we have to divide the area of a circle by 2. So that would give us 1/2 pi* r^2. We find the radius by dividing 10 by 2. So the radius is 5. Plugging that in for r in 1/2(pi)(r^2) we get 1/2(pi)(5^2) which is 25pi/2. Turning pi into 3.14 we have (25(3.14))/2 which is 78.5/2 which is approximately 39.25 units^2

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2 years ago