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3 years ago

6

A factory machine produces 5/10 kilograms of chocolate every 1/6 mins. At what rate does the machine produce chocolate

1 answer:

katovenus [111]3 years ago

3 0

5/10 kilogram per 1/6 minutes = 5/10 * 6 = 30/10 = 3 kilograms/min
3 kilograms/min * 60 min/hour = 180 kilograms/hour
180 kilograms/hour * 24 hours/day = 4320 kilograms/day
4320 kilograms/day * 365.25 days/year = 1,577,880 kilograms/year

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4(4x-2) + 1 =16x - 7. Solutions

Talja [164]

Answer:

4(4x - 2) + 1 = 16x - 7

16x - 8 + 1 = 16x - 7

16x - 7 = 16x - 7

-7 = -7

0 = 0

6 0

3 years ago

Conplete the square to solve the quadratic equation. x<br><img src="https://tex.z-dn.net/?f=1%20%7Bx%7D%5E%7B2%7D%20%20-%206x%20

o-na [289]

Answer:

$\large\boxed{x=4\pm2\sqrt6}$

Step-by-step explanation:

$x^2-6x+12=2x+20\qquad\text{subtract}\ 2x\ \text{and}\ 12\ \text{from both sides}\\\\x^2-8x=8\\\\x^2-2(x)(4)=8\qquad\text{add}\ 4^2=16\ \text{to both sides}\\\\x^2-2(x)(4)+4^2=8+4^2\qquad\text{use}\ (a-b)^2=a^2-2ab+b^2\\\\(x-4)^2=24\iff x-4=\pm\sqrt{24}\\\\x-4=\pm\sqrt{4\cdot6}\\\\x-4=\pm\sqrt4\cdot\sqrt6\\\\x-4=\pm2\sqrt6\qquad\text{add 4 to both sides}\\\\x=4\pm2\sqrt6$

6 0

3 years ago

First make a substitution and then use integration by parts to evaluate the integral. (Use C for the constant of integration.) x

e-lub [12.9K]

Answer:

$(\frac{x^{2}-25}{2})ln(5+x)-\frac{x^{2}}{4}+\frac{5x}{2}+C$

Step-by-step explanation:

Ok, so we start by setting the integral up. The integral we need to solve is:

$\int x ln(5+x)dx$

so according to the instructions of the problem, we need to start by using some substitution. The substitution will be done as follows:

U=5+x

du=dx

x=U-5

so when substituting the integral will look like this:

$\int (U-5) ln(U)dU$

now we can go ahead and integrate by parts, remember the integration by parts formula looks like this:

$\int (pq')=pq-\int qp'$

so we must define p, q, p' and q':

p=ln U

$p'=\frac{1}{U}dU$

$q=\frac{U^{2}}{2}-5U$

q'=U-5

and now we plug these into the formula:

$\int (U-5)lnUdU=(\frac{U^{2}}{2}-5U)lnU-\int \frac{\frac{U^{2}}{2}-5U}{U}dU$

Which simplifies to:

$\int (U-5)lnUdU=(\frac{U^{2}}{2}-5U)lnU-\int (\frac{U}{2}-5)dU$

Which solves to:

$\int (U-5)lnUdU=(\frac{U^{2}}{2}-5U)lnU-\frac{U^{2}}{4}+5U+C$

so we can substitute U back, so we get:

$\int xln(x+5)dU=(\frac{(x+5)^{2}}{2}-5(x+5))ln(x+5)-\frac{(x+5)^{2}}{4}+5(x+5)+C$

and now we can simplify:

$\int xln(x+5)dU=(\frac{x^{2}}{2}+5x+\frac{25}{2}-25-5x)ln(5+x)-\frac{x^{2}+10x+25}{4}+25+5x+C$

$\int xln(x+5)dU=(\frac{x^{2}-25}{2})ln(5+x)-\frac{x^{2}}{4}-\frac{5x}{2}-\frac{25}{4}+25+5x+C$

$\int xln(x+5)dU=(\frac{x^{2}-25}{2})ln(5+x)-\frac{x^{2}}{4}+\frac{5x}{2}+C$

notice how all the constants were combined into one big constant C.

7 0

3 years ago

Angela practices piano for 5 hours on Sundays amd for 3 hours on all other days of the week. How many hours doea Angela practice

Kitty [74]

Answer:8 x 365=2920

Step-by-step explanation:

First, you add 5 + 3 which equals 8. Then there is 365 days in a year so you would multiply 8 times 365 which equals 2920.

Pretty sure this is right, hope it helps.

7 0

3 years ago

What's the answer for 24

scZoUnD [109]

X= -2 or X= 3 either one works.

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3 years ago