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3 years ago

3^5 . write each power as a product of the same factor . then find the value

Mathematics

2 answers:

8090 [49]3 years ago

6 0

Answer:

3*3*3*3*3=243

Step-by-step explanation:

It is self explanatory

crimeas [40]3 years ago

4 0

3x3x3x3x3 will equal to 243

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Sophie has a doll collection with 36 dolls. She decides to sell s dolls to a museum and has r dolls remaining.

Natasha2012 [34]

Lol xd i jejuducyycya udhydggd 8737377 dhhdhxy

5 0

3 years ago

Determine the relative order of the metric prefixes of kilo-, micro-, centi-, and milli-.

nadya68 [22]

The relative order of the metric prefixes is micro-, milli-, centi- and kilo-,

<h3>What are metric units?</h3>

Metric units are units used to measure quantities

The units are given as:

kilo-, micro-, centi-, and milli-

In metric units, the value of each prefix is:

Kilo = 1000

Micro = 0.0001

Centi = 100

Milli = 0.1

In order of arrangement, we have:

Micro = 0.0001

Milli = 0.1

Centi = 100

Kilo = 1000

Hence, the relative order of the metric prefixes is micro-, milli-, centi- and kilo-,

Read more about metric units at:

brainly.com/question/2555957

8 0

2 years ago

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

Mr. mole left his burrow

pav-90 [236]

Answer:Did he ever come back?

Step-by-step explanation:

8 0

3 years ago

Rounded to the nearest inch , what is the appoxiomate circumference of a circle with a diameter of 40 inches (Use pi = 3.14

sweet-ann [11.9K]

С = πD
С = 3,14×40
С = 126 in ← <span>to the nearest inch </span>

3 0

3 years ago