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2 years ago

Denzel bought 3 sweatshirts for $21.99 each and 2 T-shirts for $18.50 each. How much did he spend?

Mathematics

2 answers:

alexdok [17]2 years ago

6 0

It cost a total of $102.97 without tax

Reika [66]2 years ago

3 0

Overall he spent $102.97

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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

$\mathrm dS=\|\vec s_x\times\vec s_z\|\,\mathrm dx\,\mathrm dz=\sqrt{1+4z^2}\,\mathrm dx\,\mathrm dz$

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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3 years ago

If f(x) = 5x-3, which expression represents its inverse function?

valentinak56 [21]

Answer:

Pretty sure it's C

Step-by-step explanation:

For inverse functions, I do the opposite operation

the only logical inverse function I see working in this expression would be C

divide the 5 from 5x and add the 3

Also, subtract the f(x) on both sides to get the "- y"

so, you get : 5/x + 3 = - y (f(x) is just "y")

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Mamont248 [21]

The pentagon has a sum of interior angles of 540 degrees.

Therefore,
(4x + 5) + (5x - 5) + (6x + 10) + (4x + 10) + 7x = 540;
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x = 20;

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