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DanielleElmas [232]
3 years ago
7

Why does it take 10 copies of 1 sixth to make the same amount as five copies of 1 third explain your answer in words and picture

s?
Mathematics
1 answer:
vesna_86 [32]3 years ago
5 0
10 is double of 5
6 is double of 3

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Explain the steps on how u got the answer <br> ••••••••••••••••••
dem82 [27]

Answer:

volume of cyclinder=πr²h

=3.14×2²×3=37.68cm³

rectangular prism volume=6×5×7

=210cm³

total volume=37.68+210=247.68cm³

6 0
3 years ago
Read 2 more answers
Show that the line integral is independent of path by finding a function f such that ?f = f. c 2xe?ydx (2y ? x2e?ydy, c is any p
Juli2301 [7.4K]
I'm reading this as

\displaystyle\int_C2xe^{-y}\,\mathrm dx+(2y-x^2e^{-y})\,\mathrm dy

with \nabla f=(2xe^{-y},2y-x^2e^{-y}).

The value of the integral will be independent of the path if we can find a function f(x,y) that satisfies the gradient equation above.

You have

\begin{cases}\dfrac{\partial f}{\partial x}=2xe^{-y}\\\\\dfrac{\partial f}{\partial y}=2y-x^2e^{-y}\end{cases}

Integrate \dfrac{\partial f}{\partial x} with respect to x. You get

\displaystyle\int\dfrac{\partial f}{\partial x}\,\mathrm dx=\int2xe^{-y}\,\mathrm dx
f=x^2e^{-y}+g(y)

Differentiate with respect to y. You get

\dfrac{\partial f}{\partial y}=\dfrac{\partial}{\partial y}[x^2e^{-y}+g(y)]
2y-x^2e^{-y}=-x^2e^{-y}+g'(y)
2y=g'(y)

Integrate both sides with respect to y to arrive at

\displaystyle\int2y\,\mathrm dy=\int g'(y)\,\mathrm dy
y^2=g(y)+C
g(y)=y^2+C

So you have

f(x,y)=x^2e^{-y}+y^2+C

The gradient is continuous for all x,y, so the fundamental theorem of calculus applies, and so the value of the integral, regardless of the path taken, is

\displaystyle\int_C2xe^{-y}\,\mathrm dx+(2y-x^2e^{-y})\,\mathrm dy=f(4,1)-f(1,0)=\frac9e
8 0
3 years ago
What is a unit fraction
amid [387]
A unit fraction is a rational number written as a fraction where the numerator is one and the denominator is a positive integer. A unit fraction is therefore the reciprocal of a positive integer, 1/n. Examples are 1/1, 1/2, 1/3, 1/4 ,1/5, etc.
3 0
3 years ago
Read 2 more answers
6.<br> 1<br> 68<br> 61<br> 2<br> m21 =<br> 3<br> m22= <br> m23 -
Advocard [28]

1 = 51

2= 61

3= 29

Step-by-step explanation:

1) 61+68= 129

180-129= 51

2) 61 is across it so they have the same number

3) 61 +90= 151

180-151= 29

6 0
2 years ago
The length of a couch is 200 centimeters. This is 16 centimeters less than 3 times the width of a matching chair. How wide is th
Snowcat [4.5K]

Answer:

i think the answer is 72

Step-by-step explanation:

6 0
2 years ago
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