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2 years ago

To subtract 250-105, Bea needs to regroup tens as ones. There are jelly beans left

Mathematics

1 answer:

mrs_skeptik [129]2 years ago

8 0

Answer:

250-105 = 145

Step-by-step explanation:

5 is greater than 0 so you must regroup:

Take 1 from 5, so 5 becomes 4.

Add 10 to 0, so 0 becomes 10.

10 minus 5 is 5

4 minus 0 is 4

2 minus 1 is 1

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The temperature at a point (x, y, z) is given by t(x, y, z) = 200e−x2 − 5y2 − 9z2 where t is measured in °c and x, y, z in meter

Olin [163]

Part A:

Given that

$T(x, y, z) = 200e^{-x^2-5y^2-9z^2} \\ \\ \nabla T=\left( \frac{\partial}{\partial x} +\frac{\partial}{\partial y}+\frac{\partial}{\partial z}\right)T=200e^{-x^2-5y^2-9z^2}\left\ \textless \ -2x,-10y,-18z\right\ \textgreater \ \\ \\ \nabla T(4,-1,4)=200e^{-(4)^2-5(-1)^2-9(4)^2}\left\ \textless \ -2(4),-10(-1),-18(4)\right\ \textgreater \ \\ \\ =200e^{-165}\left\ \textless \ -8,10,-72\right\ \textgreater \$

For the direction, let u be unit vector of point (6, -3, 6), then

$u= \frac{1}{||\left\ \textless \ 6,-3,6\right\ \textgreater \ ||} \left\ \textless \ 6,-3,6\right\ \textgreater \ \\ \\ = \frac{1}{\sqrt{6^2+(-3)^2+6^2}} \left\ \textless \ 6,-3,6\right\ \textgreater \ \\ \\ = \frac{1}{\sqrt{81}} \left\ \textless \ 6,-3,6\right\ \textgreater \ = \frac{1}{9} \left\ \textless \ 6,-3,6\right\ \textgreater \ \\ \\ =\frac{1}{3} \left\ \textless \ 2,-1,2\right\ \textgreater \$

Thus, the directional derivative is given by:

$D_u(4,-1,4)=200e^{-165}\left\ \textless \ -8,10,-72\right\ \textgreater \ \cdot\frac{1}{3} \left\ \textless \ 2,-1,2\right\ \textgreater \ \\ \\ = \frac{200}{3} e^{-165}(-16-10-144)=-\frac{170(200)}{3} e^{-165}\approx-2.49\times10^{-68}$

Part B:

The gradient direction is the direction of fastest increase. The direction that the temperature increase at the fastest rate is at the direction of the gradient vector.
From part A, the gradient vector is given by:
$\nabla T=200e^{-165}\left\ \textless \ -8,10,-72\right\ \textgreater \$
Thus, the direction with the fastest rate is given by:

$\frac{1}{||\left\ \textless \ -8,10,-72\right\ \textgreater \ ||} \left\ \textless \ -8,10,-72\right\ \textgreater \ \\ \\ =\frac{1}{\sqrt{(-8)^2+10^2+(-72)^2}}} \left\ \textless \ -8,10,-72\right\ \textgreater \ \\ \\ = \frac{1}{\sqrt{5348}} \left\ \textless \ -8,10,-72\right\ \textgreater \ = \frac{1}{2\sqrt{1337}} \left\ \textless \ -8,10,-72\right\ \textgreater \ \\ \\ =\frac{1}{\sqrt{1337}} \left\ \textless \ -4,5,-36\right\ \textgreater \$

Part C:

The magnitude of the maximum rate of increase is the length of the gradient vector. This is given by
$200e^{-165}\left(\sqrt{(-8)^2+10^2+(-72)^2}\right)=200\sqrt{5348}e^{-165} \\ \\ =100\sqrt{1337}e^{-165}$

8 0

3 years ago

What is the answer to this question?

lions [1.4K]

*Hint: The formula to solve this is SA = 2bs + b^2

Now that you know the formula, plug in and solve.

SA = 2(5)(8) + (5)^2
SA = 80 + 25
SA = 105

Now that you see that the question is asking for the answer in yards, you convert feet into yards.

3 feet = 1 yard.

105 is divided by 3 and you get 35.

The answer is 35 square yards.

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3 years ago

#8 Dylan, Mike and Jeremy had $171. Mike had twice as much money as Dylan. Jeremy had three times as much money as Mike. How muc

kkurt [141]

Answer:

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Step-by-step explanation

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3 years ago

Simplify hshwhebhsjsbshs

kipiarov [429]

Answer:

2k^5/k^-3

Step-by-step explanation:

1. Use Product Rule

2k^(3+2)/k^-3

2. Simplify you answer by adding 3+2

2k^5/k^-3

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Vsevolod [243]

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3 years ago