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3 years ago

3. Combine like terms: 14 + 3 + 2c -20c Solve for x: x - 12= 20

Mathematics

1 answer:

Aneli [31]3 years ago

4 0

Answer:

-18c + 17

x = 32

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Lian has $1.00. She has only nickels and dimes. Lian has twice as many dimes as nickels. How many dimes does she have?

Anna11 [10]

Answer: 8

Step-by-step explanation:

Given

Lian has $\$1.00$ and she has twice as many dimes as nickels

Suppose she has $x$ nickels

So, the number of dimes is $2x$

Nickel is equivalent to 5 cents and dime is equivalent to 10 cent

$\therefore \ x(0.05)+2x(0.1)=1\\\Rightarrow 0.05x+0.2x=1\\\Rightarrow 0.25x=1\\\Rightarrow x=4$

Therefore she has 8 dimes with her.

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2 years ago

Integrate G(x,y,z)equalsz over the parabolic cylinder yequalszsquared, 0less than or equalsxless than or equals2, 0less than

yKpoI14uk [10]

I gather you're supposed to compute the integral of $G(x,y,z)=z$ over a surface $S$ that is the part of the parabolic cylinder $y=z^2$ with $0\le x\le2$ and $0\le z\le\frac{\sqrt{15}}2$ .

We can parameterize $S$ by

$\vec s(x,z)=x\,\vec\imath+z^2\,\vec\jmath+z\,\vec k$

with the given constraints on $x$ and $z$ . Take the normal vector to $S$ to be

$\vec s_x\times\vec s_z=-\vec\jmath+2z\,\vec k$

so that the surface element is

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Then in the integral, we have

$\displaystyle\iint_Sz\,\mathrm dS=\int_0^2\int_0^{\sqrt{15}/2}z\sqrt{1+4z^2}\,\mathrm dz\,\mathrm dx=\boxed{\frac{21}2}$

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The answer is 6 :), I hope this helps <33!3&9/&

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