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3 years ago

7

There are 4 standard U.S. coins. If a person has one of each. How many different amounts of money can the person give someone us

ing 3 coins?
(e.g. 1¢ + 5¢ + 25¢ =31¢ OR 5¢ + 10¢ + 25¢ =40¢ )

1 answer:

AURORKA [14]3 years ago

8 0

Answer:

4

Explanation:

36, 31, 40, 16

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If f(x, y, z) = x sin(yz), (a) find the gradient of f and (b) find the directional derivative of f at (2, 4, 0) in the direction

valentina_108 [34]

Answer:

a) $\nabla f(x,y,z) = \sin{yz}\mathbf{i} + xz\cos{yz}\mathbf{j} + xy \cos{yz}\mathbf{k}$ .

b) $Du_{f}(2,4,0) = -\frac{8}{\sqrt{11}}$

Step-by-step explanation:

Given a function $f(x,y,z)$ , this function has the following gradient:

$\nabla f(x,y,z) = f_{x}(x,y,z)\mathbf{i} + f_{y}(x,y,z)\mathbf{j} + f_{z}(x,y,z)\mathbf{k}$ .

(a) find the gradient of f

We have that $f(x,y,z) = x\sin{yz}$ . So

$f_{x}(x,y,z) = \sin{yz}$

$f_{y}(x,y,z) = xz\cos{yz}$

$f_{z}(x,y,z) = xy \cos{yz}$ .

$\nabla f(x,y,z) = f_{x}(x,y,z)\mathbf{i} + f_{y}(x,y,z)\mathbf{j} + f_{z}(x,y,z)\mathbf{k}$ .

$\nabla f(x,y,z) = \sin{yz}\mathbf{i} + xz\cos{yz}\mathbf{j} + xy \cos{yz}\mathbf{k}$

(b) find the directional derivative of f at (2, 4, 0) in the direction of v = i + 3j − k.

The directional derivate is the scalar product between the gradient at (2,4,0) and the unit vector of v.

We have that:

$\nabla f(x,y,z) = \sin{yz}\mathbf{i} + xz\cos{yz}\mathbf{j} + xy \cos{yz}\mathbf{k}$

$\nabla f(2,4,0) = \sin{0}\mathbf{i} + 0\cos{0}\mathbf{j} + 8 \cos{0}\mathbf{k}$ .

$\nabla f(2,4,0) = 0i+0j+8k=(0,0,8)$

The vector is $v = i + 3j - k = (1,3,-1)$

To use v as an unitary vector, we divide each component of v by the norm of v.

$|v| = \sqrt{1^{2} + 3^{2} + (-1)^{2}} = \sqrt{11}$

So

$v_{u} = (\frac{1}{\sqrt{11}}, \frac{3}{\sqrt{11}}, \frac{-1}{\sqrt{11}})$

Now, we can calculate the scalar product that is the directional derivative.

$Du_{f}(2,4,0) = (0,0,8).(\frac{1}{\sqrt{11}}, \frac{3}{\sqrt{11}}, \frac{-1}{\sqrt{11}}) = -\frac{8}{\sqrt{11}}$

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3 years ago

What is the area of the drawing of the Jones' house? Round your answer to the nearest tenth

slega [8]

Wher is said drawing?

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3 years ago

Estimate by rounding each number to the nearest hundredth and then subtract 360.727 - 89.852

kykrilka [37]

Hi there!

The correct answer for you is 270.88.

To round to the hundreth's place (.0<u>1</u><u />), you need to take the number in the thousand's place (.00<u>1</u>), and determine if the number needs to go up or down.

If the number in the thousand's place is <u>greater</u> than 4, then the number goes up.

360.72<u>7</u> --> This means that the hundreth's number goes up to 3.

If the number in the thousand's place is <u>lesser</u> than 5, then that number stays the same.

89.85<u>2</u> --> This means that the hundreth's number stays the same.

After you round, then just subtract:

360.73 - 89.85 = 270.88.

I hope this helps!
Brady
<u />

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3 years ago

20. An amount of money was shared among five boys Ali, Juma, Musa, Khalid and Mustafa. Ali got /8 of the total amount while Juma

Nadusha1986 [10]

Answer:

$x=\frac{18000}{7}=2571\frac{3}{7}$

Step-by-step explanation:

Let the total amount be x

Then Ali got 1/8x With 7/8x left

Juma got 7/40x with 7/10x left

Musa, Khalid and Mustafa got 7/30x each

since $\frac{7}{30}x=600$

7x=18000

$x=\frac{18000}{7}=2571\frac{3}{7}$

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Help me i actually need this asap...Only right answer ..No spammer.No wrong answer.

Leona [35]

$\sqrt[3]{8} \: - \sqrt{3}$

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3 years ago

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