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2 years ago

How much work is done lifting a 100 Newton book onto a shelf that is 2 meters high on Earth?

Mathematics

1 answer:

Igoryamba2 years ago

4 0

We want to find the work done by lifting a book a given distance.

The answer is 200 N*m

We know that the book weighs 100 Newtons and that we lift it a distance of 2 meters.

Remember that the work needed to lift an object of mass M to a height H is:

W = M*g*H

where g is the gravitational acceleration.

Knowing that:

weight = M*g

We can replace the things we know to get the work:

W = 100N*2m = 200 N*m

If you want to learn more, you can read:

brainly.com/question/13662169

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4 years ago

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3 years ago

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4 years ago

Sketch the region enclosed by y=3x and y=x^2 . Then find the area of the region.

kolezko [41]

Answer:

$A=4.5u^2$

Step-by-step explanation:

The integral of a function gives you the area under the curve, the subtraction of one of the areas from the other will give you the area in between.

The limits of integration are the points where the curves intersect each other(take the curves has a system of equation and solve for x and y):

$y=3x, y=x^2\\3x=x^2\\x^2-3x=0\\x(x-3)=0\\x_1=0\\x-3=0\\x_2=3$

$y_1=3x_1=3(0)=0\\y_2=3x_2=3(3)=9$

The integral will be the subtraction of the curve $y=3x$ and $y=x^2$ (In the graph you can see y=3x is the upper curve):

$\int\limits^3_0 {3x-x^2} \, dx =\left\frac{3x^2}{2}-\frac{x^3}{3}\right|^3_0=\frac{3(3)^2}{2}-\frac{(3)^3}{3}-\left(\frac{3(0)^2}{2}-\frac{(0)^3}{3}\right)\\\int\limits^3_0 {3x-x^2} \, dx =\frac{27}{2}-\frac{27}{3} =13.5-9=4.5u^2$

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3 years ago