Ivan runs 7 miles in 60 minutes. at the same rate how many miles would he run in 24 minutes

Electric charge is distributed over the disk x2 + y2 ≤ 16 so that the charge density at (x, y) is rho(x, y) = 2x + 2y + 2x2 + 2y

professor190 [17]

Answer:

Required total charge is $256\pi$ coulombs per square meter.

Step-by-step explanation:

Given electric charge is dristributed over the disk,

$x^2=y^2\leq 16$ so that the charge density at (x,y) is,

$\rho (x,y)=2x+2y+2x^2+2y^2$

To find total charge on the disk let Q be the total charge and $x=r\cos\theta,y=r\sin\theta$ so that,

$Q={\int\int}_Q\rho(x,y) dA$ where A is the surface of disk.

$=\int_{0}^{2\pi}\int_{0}^{4}(2x+2y+2x^2+2y^2)dA$

$=\int_{0}^{2\pi}\int_{0}^{4}(2r\cos\theta+2r\sin\theta+2r^2 \cos^{2}\theta+2r^2\sin^2\theta)rdrd\theta$

$=2\int_{0}^{2\pi}\int_{0}^{4}r^2(\cos\theta+\sin\theta)drd\theta+2\int_{0}^{2\pi}\int_{0}^{4}r^3drd\theta$

$=\frac{2}{3}\int_{0}^{2\pi}(\sin\theta+\cos\theta)\Big[r^3\Big]_{0}^{4}d\theta+2\int_{0}^{2\pi}\Big[\frac{r^4}{4}\Big]d\theta$

$=\frac{128}{3}\int_{0}^{2\pi}(\sin\theta+\cos\theta)d\theta+128\int_{0}^{2\pi}d\theta$

$=\frac{128}{3}\Big[\sin\theta-\cos\theta\Big]_{0}^{2\pi}+128\times 2\pi$

$=\frac{128}{3}\Big[\sin 2\pi-\cos 2\pi-\sin 0+\cos 0\Big]+256\pi$

$=256\pi$

Hence total charge is $256\pi$ coulombs per square meter.

3 0

2 years ago

An option to buy a stock is priced at $150. If the stock closes above 30 next Thursday, the option will be worth $1000. If it cl

valentina_108 [34]

Answer:

Step-by-step explanation:

An option to buy a stock is priced at $150. If the stock closes above 30 next Thursday, the option will be worth $1000. If it closes below 20, the option will be worth nothing, and if it closes between 20 and 30, the option will be worth $200. A trader thinks there is a 50% chance that the stock will close in the 20-30 range, a 20% chance that it will close above 30, and a 30% chance that it will fall below 20.

a) Let X represent the price of the option

$1000 20/100 = 0.2

$200 50/100 = 0.5

$0 30/100 = 0.3

b) Expected option price

$= \sum x.P(X=x)\\\\ = 1000 * 0.2 + 200 * 0.5 + 0 = \$ 300$

Therefore expected gain = $300 - $150 = $150

c) The trader should buy the stock. Since there is an positive expected gain($150) in trading that stock option.

7 0

3 years ago

Fator by grouping ab+2a+5b+10

Alenkasestr [34]

Ab + 2a + 5b + 10

= a(b + 2) + 5(b + 2)

= (b + 2) (a + 5)

3 0

2 years ago

WILL GIVE BRAINLIEST

Anna11 [10]

Answer:

Sarah is paid $20 an hour at her new job. She wishes to graph her total pay y, as a function of the number of hours, x. She wants to be sure her graph shows her pay for 10 and 20 hours of work.

a. What is a good scale to use for the x-axis? Explain your reasoning.

b. What is a good interval to use for the y-axis? Explain your r

Step-by-step explanation:

3 0

2 years ago

A sample of 100 was taken from a population, with the mean of the sample

Elis [28]

Answer: I think the answer might be A

Step-by-step explanation:

3 0

2 years ago

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