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3 years ago

How do you find the least common multiple of these two expressions. 10x^5v^8 and 25x^4v^7u^2

2 answers:

8 0

$10x^5v^8=5x^4v^7\cdot2xv\\\\25x^4v^7u^2=5x^4v^7\cdot5u^2\\\\LCM(10x^5v^8;\ 25x^4v^7u^2)=5x^4v^7\cdot2xv\cdot5u^2=50x^5v^8u^2$

Ahat [919]3 years ago

4 0

$10x^{5} v^{8}= 1*2*5*x*x*x*x*x*v*v*v*v*v*v*v*v \\ 25 x^{4} v^{7} u^{2}=1*5*5*x*x*x*x*v*v*v*v*v*v*v*u*u \\$
Underline all the numbers which are common in both the factorisations. Write them down:
$5 x^{4} v^{7}$
There, you have your LCM of both the expressions.

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A 2 liter bottle is filled completely with water from a faucet in 10 seconds. How much water was filled into the bottle each sec

telo118 [61]

Answer:

A 0.2 L water was filled into the bottle from faucet each seconds.

Step-by-step explanation:

Unit rate is defined as the rates are expressed as a quantity of 1, such as 3 feet per second or 6 miles per hour, they are called unit rates.

Given the statement: A 2 liter bottle is filled completely with water from a faucet in 10 seconds.

⇒ In 10 sec a 2L bottle is completely filled with water from a faucet.

Unit rate per second = $\frac{2}{10} = \frac{1}{5} = 0.2 L$

Therefore, 0.2 L water was filled into the bottle each seconds.

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3 years ago

For neighborhood parks of a given size, the equation yˆ=7.219x+2.033 models the number of children at a park, where x is the num

Soloha48 [4]

I'm not 100% sure, but I believe the answer would be:
D. For every additional adult at the park, the number of children increases by about 7.
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2 years ago

Read 2 more answers

Which points lies on the line described by the equation? y+4=(x-3)

NikAS [45]

Hello :
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3 years ago

Consider the line integral Z C (sin x dx + cos y dy), where C consists of the top part of the circle x 2 + y 2 = 1 from (1, 0) t

pashok25 [27]

Direct computation:

Parameterize the top part of the circle $x^2+y^2=1$ by

$\vec r(t)=(x(t),y(t))=(\cos t,\sin t)$

with $0\le t\le\pi$ , and the line segment by

$\vec s(t)=(1-t)(-1,0)+t(2,-\pi)=(3t-1,-\pi t)$

with $0\le t\le1$ . Then

$\displaystyle\int_C(\sin x\,\mathrm dx+\cos y\,\mathrm dy)$

$=\displaystyle\int_0^\pi(-\sin t\sin(\cos t)+\cos t\cos(\sin t)\,\mathrm dt+\int_0^1(3\sin(3t-1)-\pi\cos(-\pi t))\,\mathrm dt$

$=0+(\cos1-\cos2)=\boxed{\cos1-\cos2}$

Using the fundamental theorem of calculus:

The integral can be written as

$\displaystyle\int_C(\sin x\,\mathrm dx+\cos y\,\mathrm dy)=\int_C\underbrace{(\sin x,\cos y)}_{\vec F}\cdot\underbrace{(\mathrm dx,\mathrm dy)}_{\vec r}$

If there happens to be a scalar function $f$ such that $\vec F=\nabla f$ , then $\vec F$ is conservative and the integral is path-independent, so we only need to worry about the value of $f$ at the path's endpoints.