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3 years ago

Multiplication of numbers with their uncertainty

1 answer:

3 0

if you're adding or subtracting quantities with uncertainties, you add the absolute uncertainties. If you're multiplying or dividing, you add the relative uncertainties. If you're multiplying by a constant factor, you multiply absolute uncertainties by the same factor, or do nothing to relative uncertainties

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Multiple-Choice Integration, Picture Included, Please Include Work

ValentinkaMS [17]

$\displaystyle\int_0^2\sqrt{4-x^2}\,\mathrm dx$

Recall that a circle of radius 2 centered at the origin has equation

$x^2+y^2=4\implies y=\pm\sqrt{4-x^2}$

where the positive root gives the top half of the circle in the x-y plane. The definite integral corresponds to the area of the right half of this top half. Since the area of a circle with radius $r$ is $\pi r^2$ , it follows that the area of a quarter-circle would be $\dfrac{\pi r^2}4$ .

You have $r=2$ , so the definite integral is equal to $\dfrac{2^2\pi}4=\pi$ .

Another way to verify this is to actually compute the integral. Let $x=2\sin u$ , so that $\mathrm dx=2\cos u\,\mathrm du$ . Now

$\displaystyle\int_0^2\sqrt{4-x^2}\,\mathrm dx=\int_0^{\pi/2}\sqrt{4-(2\sin u)^2}(2\cos u)\,\mathrm du=4\int_0^{\pi/2}\cos^2u\,\mathrm du$

Recall the half-angle identity for cosine:

$\cos^2u=\dfrac{1+\cos2u}2$

This means the integral is equivalent to

$\displaystyle2\int_0^{\pi/2}(1+\cos 2u)\,\mathrm du=2u+\sin2u\bigg|_{u=0}^{u=\pi/2}=\pi$

4 0

3 years ago

How do you solve this problem<br> (2x+8)2=64

asambeis [7]

Answer:

Step-by-step explanation:

If (2x+8)2 = 64, then I would solve it by making sure the numbers in the parentheses equal 32. This is because it would get multiplied by 2 after you find the answer and 32 x 2 is 64. So what times 2 is 24? 12. 12 x 2 is 24, plus 8 is 32, and multiply 32 by 2 and you get 64 :) I'm not the best at explaining btw ;-;

7 0

3 years ago

Read 2 more answers

The band sold $498 worth of tickets for their spring concert. Adult tickets cost $5 each and student tickets cost $3 each. If th

saw5 [17]

Let: A = adult tickets; S = student tickets

a. 498 = 5A + 3S
118 = A + S

b. S = 118 - A
498 = 5A + 3(118 - A)
498 = 5A + 354 - 3A
498 - 354 = 2A
144 = 2A
A = 72

118 = S + A
118 = 72 + S
118 - 72 = S
S = 46

c. Therefore, there were 72 adult tickets and 46 student tickets sold.

5 0

4 years ago

Please help with test offering big points pt 3

kirill [66]

Answer:

Step-by-step explanation:

because if you do 1000 divided buy 25 its 69420 so if you do 69420 divided by 69420 its 1 and 1x1000 its 1000 divided by 54 its 25 so its 25

7 0

3 years ago

A cell phone provider offers a plan that costs $30 per month plus $0.10 per text message sent or received. A compatible plan cos

WITCHER [35]

Answer: There would have to be 200 text messages fro both plans to cost the same each month.

Step-by-step explanation:

8 0

3 years ago

Multiplication of numbers with their uncertainty​

Multiplication of numbers with their uncertainty