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3 years ago

The length of a rectangle it twice it's within. If the perimeter of the rectangle is 30 cm, find its area.

Mathematics

1 answer:

Xelga [282]3 years ago

6 0

w - width

2w - length (l)

30 cm - perimeter

w + w + 2w + 2w = 6w - perimeter

The equation:

6w = 30 <em>divide both sides by 6</em>

w = 5 cm

2w = 2(5) = 10

l = 10 cm

The area of a rectangle: A = lw.

Substitute:

A = (5)(10) = 50

<h3>Answer: The area is 50cm²</h3>

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A population of insects increases at the rate of 200 10t 13t2 what is the change in the population of insects between day 0 and

RUDIKE [14]

Answer:

762 days

Step-by-step explanation:

Given

$Rate = 200 + 10t + 13t^2$

Let the rate be R.

So the rate change with time is represented as:

$\frac{dR}{dt} = 200 +10t + 13t^2$

So:

$dR = (200 + 10t + 13t^2)\ dt$

To get the number of insects between day 0 and day 3, we need to integrate dR and set the bounds to 0 and 3

i.e.

$dR = (200 + 10t + 13t^2)\ dt$ becomes

$\int\limits^3_0 {dR} \, =\int\limits^3_0 (200 + 10t + 13t^2)\ dt$

$R =\int\limits^3_0 (200 + 10t + 13t^2)\ dt$

Integrate

$R = 200t + \frac{10t^2}{2} + \frac{13t^3}{3} [3,0]$

Solve for R by substituting 0 and 3 for t

$R = (200*3 + \frac{10*3^2}{2} + \frac{13*3^3}{3}) - ( 200*0 + \frac{10*0^2}{2} + \frac{13*0^3}{3})$

$R = (200*3 + \frac{10*9}{2} + \frac{13*27}{3}) - (0 + \frac{10}{2} + \frac{0}{3})$

$R = (200*3 + 5*9 + 13*9) - (0)$

$R = 600 + 45 + 117 - 0$

$R =762$

<em>The population of insect between the required interval is 762</em>

4 0

3 years ago

On his 8 tests, Hong earned a total of 568 points. What was his mean number if points earned per test?

madam [21]

Answer:

He earned 71 points per test on average.

Step-by-step explanation:

Divide the total amount of points by the amount of tests to find the average (mean.)

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3 years ago

What is the difference? Complete the equation. -4 - 2 1/2

Lina20 [59]

Answer: - 6 1/2

Step-by-step explanation:

We should note that:

=-4 - 2 1/2

= -6 1/2

For example, let's assume you owe Bob $4 and then you owe Bill $2 1/2. To calculate the total amount owed, you would have $6 1/2.

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3 years ago

What is 8.4/4 - 4.9+1.6/25

WINSTONCH [101]

Answer:

-2.736

Step-by-step explanation:

FOLLOW PEMDAS

8.4/4= 2.1

1.6/25= .64

2.1-4.9= -2.8

-2.8+.064=

-2.736

7 0

3 years ago

A boy stands 1 meter away from a lamppost. He is 1.8 meters tall and casts a shadow 2 meters long in the light from the lamp. Ho

Charra [1.4K]

A boy stands 1 meter away from a lamppost. He is 1.8 meters tall and casts a shadow 2 meters long in the light from the lamp

The diagram is attached below using the given information

We have two similar triangle

Triangle ACD is similar to triangle ABE. So the sides are in proportional

$\frac{DC}{EB} =\frac{AC}{AB}$

AC = AB + BC = 3m

$\frac{x}{1.8}=\frac{3}{2}$

2x = 1.8 * 3 (cross multiply)

2x = 5.4

Divide by 2 on both sides

x = 2.7

Height of Lamppost is 2.7 meter

3 0

3 years ago

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