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Licemer1 [7]
3 years ago
5

How do you find the surface area of a cube

Mathematics
1 answer:
lianna [129]3 years ago
6 0
Find the surface area of one side and multiply it by 6
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Let c be the curve of intersection of the parabolic cylinder x2 = 2y, and the surface 3z = xy. find the exact length of c from t
Mandarinka [93]
Parameterize the intersection by setting x(t)=t, so that

x^2=2y\iff y=\dfrac{x^2}2\implies y(t)=\dfrac{t^2}2
3z=xy\iff z=\dfrac{xy}3\implies z(t)=\dfrac{t^3}6

The length of the path C is then given by the line integral along C,

\displaystyle\int_C\mathrm dS

where \mathrm dS=\sqrt{\left(\dfrac{\mathrm dx}{\mathrm dt}\right)^2+\left(\dfrac{\mathrm dy}{\mathrm dt}\right)^2+\left(\dfrac{\mathrm dz}{\mathrm dt}\right)^2}\,\mathrm dt. We have

\dfrac{\mathrm dx}{\mathrm dt}=1
\dfrac{\mathrm dy}{\mathrm dt}=t
\dfrac{\mathrm dz}{\mathrm dt}=\dfrac{t^2}2

and so the line integral is

\displaystyle\int_{t=0}^{t=2}\sqrt{1^2+t^2+\dfrac{t^4}4}\,\mathrm dt

This result is fortuitous, since we can write

1+t^2+\dfrac{t^4}4=\dfrac14(t^4+4t^2+4)=\dfrac{(t^2+2)^2}4=\left(\dfrac{t^2+2}2\right)^2

and so the integral reduces to

\displaystyle\int_{t=0}^{t=2}\frac{t^2+2}2\,\mathrm dt=\dfrac{10}3
3 0
3 years ago
What is the multiplicative inverse of -1/2
Alja [10]

In mathematics, the reciprocal, or multiplicative inverse, of a number x is the number which, when multiplied by x, yields 1. It is denoted 1/x or x-1.

6 0
3 years ago
In the past month, Abdul rented 7 video games and 3 DVDs. The rental price for each video game was $3.10. The rental price for e
kvv77 [185]

answer: Abdul spent $21.70 on video games and $12.60 on DVD's.

Step-by-step explanation:

7 0
4 years ago
Read 2 more answers
Chip and Dale have 42 marbles. chip has six more marbles than Dale .how many marbles does Chip have
yaroslaw [1]
47 marbles if they each have 42 marbles
3 0
4 years ago
Read 2 more answers
Please Help!! Will mark brainiest!!
Alex Ar [27]
B is the answer
It’s the one that shows 6 is greater than x. So that’s means x is less than 6 not equal to
5 0
3 years ago
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