Suppose y = 2x +10. Find y if x = -2.

Mathematics

2 answers:

liubo4ka [24]3 years ago

5 0

If x = -2, y = 6.

To solve this quesiton, we need to find the value of y if x is equal to -2. We can do this by substiuting the value of x and then solving.

y = 2 (-2) + 10

y = -4 + 10

y = 6

PtichkaEL [24]3 years ago

3 0

Hi!

Plug in the value of x, and solve.

y = 2 * -2 + 10

Solve

y = -4 + 10

y = 6

The answer is y = 6

Hope this helps! :)

-Peredhel

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a) Estimate the volume of the solid that lies below the surface z = 7x + 5y2 and above the rectangle R = [0, 2]⨯[0, 4]. Use a Ri

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In the $x$ direction we consider the $m=2$ subintervals [0, 1] and [1, 2] (each with length 1), while in the $y$ direction we consider the $n=2$ subintervals [0, 2] and [2, 4] (with length 2). Then the lower right corners of the cells in the partition of $R$ are (1, 0), (2, 0), (1, 2), (2, 2).

Let $f(x,y)=7x+5y^2$ . The volume of the solid is approximately

$\displaystyle\iint_Rf(x,y)\,\mathrm dx\,\mathrm dy\approx f(1,0)\cdot1\cdot2+f(2,0)\cdot1\cdot2+f(1,2)\cdot1\cdot2+f(2,2)\cdot1\cdot2=\boxed{164}$

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More generally, the lower-right-corner Riemann sum over $m=\mu$ and $n=\nu$ subintervals would be

$\displaystyle\sum_{m=1}^\mu\sum_{n=1}^\nu\left(7\frac{2m}\mu+5\left(\frac{4n-4}\nu\right)^2\right)\frac{2-0}\mu\frac{4-0}\nu=\frac83\left(101+\frac{21}\mu+\frac{40}{\nu^2}-\frac{120}\nu\right)$