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2 years ago

When y varies proportionally with x, what is k when x = 50 and y = 375?

Mathematics

1 answer:

Andrei [34K]2 years ago

5 0

Answer:

x/375=50/100 if its a percent

Step-by-step explanation:

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Look at the following survey and then answer the question.

wolverine [178]

Answer:

c 32 out of 80 were surveyed

7 0

3 years ago

Tyler can shovel the driveway in 2 hours Dakota can complete the job in 90 minutes if they work together how long will it take

topjm [15]

One JOB = 1 and 2 hours = 120 min

Tyler Rate per minute: 1/120 (in 1 minute he performes 1/120 of the job)
Dakota<span> Rate per minute: 1/90 (in 1 minute he performes 1/90 of the job)

Tyler's + Dakota's rate per 1 minute = 1/120 + 1/90 = 7/360 (Job/minutes)

7/360 of the job was performed in 1 minute
</span>a complete JOB =1 to be performed in x minutes (Rule of three)

x = 1x1/(7/360) that equals to 360/7 and x (time of both) = 51 min 42

5 0

2 years ago

The boundary of a lamina consists of the semicircles y = 1 − x2 and y = 16 − x2 together with the portions of the x-axis that jo

oksano4ka [1.4K]

Answer:

Required center of mass $(\bar{x},\bar{y})=(\frac{2}{\pi},0)$

Step-by-step explanation:

Given semcircles are,

$y=\sqrt{1-x^2}, y=\sqrt{16-x^2}$ whose radious are 1 and 4 respectively.

To find center of mass, $(\bar{x},\bar{y})$ , let density at any point is $\rho$ and distance from the origin is r be such that,

$\rho=\frac{k}{r}$ where k is a constant.

Mass of the lamina=m= $\int\int_{D}\rho dA$ where A is the total region and D is curves.

then,

$m=\int\int_{D}\rho dA=\int_{0}^{\pi}\int_{1}^{4}\frac{k}{r}rdrd\theta=k\int_{}^{}(4-1)d\theta=3\pi k$

Now, x-coordinate of center of mass is $\bar{y}=\frac{M_x}{m}$ . in polar coordinate $y=r\sin\theta$

$\therefore M_x=\int_{0}^{\pi}\int_{1}^{4}x\rho(x,y)dA$

$=\int_{0}^{\pi}\int_{1}^{4}\frac{k}{r}(r)\sin\theta)rdrd\theta$

$=k\int_{0}^{\pi}\int_{1}^{4}r\sin\thetadrd\theta$

$=3k\int_{0}^{\pi}\sin\theta d\theta$

$=3k\big[-\cos\theta\big]_{0}^{\pi}$

$=3k\big[-\cos\pi+\cos 0\big]$

$=6k$

Then, $\bar{y}=\frac{M_x}{m}=\frac{2}{\pi}$

y-coordinate of center of mass is $\bar{x}=\frac{M_y}{m}$ . in polar coordinate $x=r\cos\theta$

$\therefore M_y=\int_{0}^{\pi}\int_{1}^{4}x\rho(x,y)dA$

$=\int_{0}^{\pi}\int_{1}^{4}\frac{k}{r}(r)\cos\theta)rdrd\theta$

$=k\int_{0}^{\pi}\int_{1}^{4}r\cos\theta drd\theta$

$=3k\int_{0}^{\pi}\cos\theta d\theta$

$=3k\big[\sin\theta\big]_{0}^{\pi}$

$=3k\big[\sin\pi-\sin 0\big]$

$=0$

Then, $\bar{x}=\frac{M_y}{m}=0$

Hence center of mass $(\bar{x},\bar{y})=(\frac{2}{\pi},0)$

3 0

2 years ago

Compare the fractions 2/3 5/7

andrey2020 [161]

Step-by-step explanation:

2/3 is not greater than 5/7 and the answer to the question "Is 2/3 greater than 5/7?" is no. When comparing fractions such as 2/3 and 5/7, you could also convert the fractions (if necessary) so they have the same denominator and then compare which numerator is larger.

8 0

2 years ago

Write and solve an equation for:

geniusboy [140]

Answer:

n = - 12

Step-by-step explanation:

n + 6 = 2n/4

4 (n+6) = 2n

4n + 24 = 2n

4n - 2n = - 24

2n = -24

n = - 24/2

n = - 12

6 0

2 years ago