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2 years ago

NEED HELP ASAP!!! Which of the following shows the prime factorization of 72 using exponential notation?

Mathematics

1 answer:

elena-14-01-66 [18.8K]2 years ago

5 0

Answer:

D)2^3 x 3^2

Step-by-step explanation:

2 x 2 x 2 = 8

3 x 3 = 9

8 x 9 = 72

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Volume of a cylinder with a radius of 13 in and height of 30 in

Elodia [21]

Answer:

V≈15927.87 in³

Step-by-step explanation:

The volume of a cylinder is found by multiplying the area of its top or base by its height and is defined as: V = π*r²*· h

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2 years ago

Read 2 more answers

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.

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

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

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

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

6 0

3 years ago

To help give money to the homeless Alaska made an organization to spread awareness on homelessness and poverty for every new mem

dusya [7]

Answer:

5870

Step-by-step explanation:

587*10=5870

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3 years ago

30% of the 600 students at Mayberry Middle School have PE this semester. How many students have PE?

ella [17]

Answer:

180 students

Step-by-step explanation:

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2 years ago

Help me please please!!!!!!!!

vova2212 [387]

Answer:

Step-by-step explanation:

The circumference (C) of a circle is calculated as

C = 2πr ( r is the radius ) , then

C = 2π × 20 = 40π

6 0

2 years ago