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2 years ago

The height of two similar pails are 12cm and 8cm.The larger pail can hold 2litres. What is the capacity of the smaller pail?

Mathematics

1 answer:

Vedmedyk [2.9K]2 years ago

7 0

Answer:

1.33 liters

Step-by-step explanation:

Volume of any shape is given by cross sectional area multiplied by height. Therefore, V=Ah

Where A is area and h is height

Since their cross sections are the same, then volume depends on height.

If 12cm equals 2 liters

8cm equals x

X=(2*8)/12=1.3333333333333 liters

Approximayely, the smaller pail has capacity of 1.33 liters

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Two one hundred is 200.
15 tens is 150.
Six ones is the same.
$200 + 150 + 6 = 456$

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2 years ago

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Sometimes a change of variable can be used to convert a differential equation y′=f(t,y) into a separable equation. One common ch

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Answer:

$y=\frac{-7t^2+22t-7}{7t-22}$

Step-by-step explanation:

We are given that

Initial value problem

$y'=(t+y)^2-1$ , y(3)=4

Substitute the value $z=t+y$

When t=3 and y=4 then

z=3+4=7

$y'=z^2-1$

Differentiate z w.r.t t

Then, we get

$\frac{dz}{dt}=1+y'$

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Integrate on both sides

$-\frac{1}{z}dz=t+C$

$z=-\frac{1}{t+C}$

Substitute t=3 and z=7

Then, we get

$7=-\frac{1}{3+C}$

$21+7C=-1$

$7C=-1-21=-22$

$C=-\frac{22}{7}$

Substitute the value of C then we get

$z=-\frac{1}{t-\frac{22}{7}}$

$z=\frac{-7}{7t-22}$

$y=z-t$

$y=\frac{-7}{7t-22}-t$

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$y=\frac{-7t^2+22t-7}{7t-22}$

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2 years ago

The net of a triangular prism is shown below. What is the surface area of the prism? A. 128 cm^2 B. 152 cm^2 C. 176 cm^2 D. 304

shtirl [24]

Answer:

B. 152 cm²

Step-by-step explanation:

To find the surface area using a net, do this:

Take apart the figure. We see that there are three rectangles and two triangles. Find the area of each ( $A=l*w$ ) and then add the values together:

The first rectangle on the left is the same as the one on the right.

$5*8=40$

Two measures are 40 cm².

The middle rectangle is:

$6*8=48$

48 cm²

The formula for the area of a triangle is $A=\frac{1}{2}*b*h$ :

$A=\frac{1}{2}*6*4\\\\A=\frac{1*6*4}{2}\\\\A=\frac{24}{2}\\\\ A=12$

The area of the two triangles is 12 cm².

Now add the values:

$40+40+48+12+12=152$

The area of the figure is 152 cm².

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2 years ago

In 2004, a magazine's circulation was about 1,000,000 readers. In 2014, the magazine had about 2,000,000 readers. Write a linear

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Answer:

$r(t)=100,000t+600,000$

Step-by-step explanation:

Let

r ----> the number of readers (y-coordinate or dependent variable)

t ----> the number of years after 2000 (x-coordinate or independent variable)

Remember

2004 ----> represent t=4 years

2014 ----> represent t=14 years

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step 1

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The formula to calculate the slope between two points is equal to

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substitute the values

$m=\frac{2,000,000-1,000,000}{14-4}$

$m=\frac{1,000,000}{10}$

$m=100,000\frac{readers}{year}$

step 2

Find the equation of the line in point slope form

$r-r1=m(t-t1)$

we have

$m=100,000\\point\ (4,1,000,000)$

substitute

$r-1,000,000=100,000(t-4)$

step 3

Convert to slope intercept form

$r=mt+b$

isolate the variable r

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step 4

Convert to function notation

$r(t)=100,000t+600,000$

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