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GREYUIT [131]
1 year ago
5

A number increased by 5 and divided by 2 is equal to 75. What is the number?Solve and Show World!

Mathematics
1 answer:
Likurg_2 [28]1 year ago
3 0
\begin{gathered} \text{Let's the number is N.} \\ So, \\ \frac{N+5}{2}=75 \\ N=145(\text{Ans)} \end{gathered}

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The target function has partial derivatives (set equal to 0)

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\dfrac{\partial(x^2+3y^2+13x)}{\partial y}=6y=0\implies y=0

so there is only one critical point at \left(-\dfrac{13}2,0\right). But this point does not fall in the region x^2+y^2\le1. There are no extreme values in the region of interest, so we check the boundary.

Parameterize the boundary of x^2+y^2\le1 by

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t(x,y)=t(\cos u,\sin u)=T(u)

T(u)=\cos^2u+3\sin^2u+13\cos u

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T(u) has critical points where T'(u)=0:

T'(u)=-13\sin u+4\sin u\cos u=\sin u(4\cos u-13)=0

(1)\quad\sin u=0\implies u=0,u=\pi

(2)\quad4\cos u-13=0\implies\cos u=\dfrac{13}4

but |\cos u|\le1 for all u, so this case yields nothing important.

At these critical points, we have temperatures of

T(0)=14

T(\pi)=-12

so the plate is hottest at (1, 0) with a temperature of 14 (degrees?) and coldest at (-1, 0) with a temp of -12.

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C. About 32 times.....hope I be the Brainliest Answer

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Write the phrase as a numerical expression; the product of 5 and 7
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Step-by-step explanation:

12 = 7 + 5

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