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4 years ago

Alessandra tried to fill the prism with unit cubes but did not have enough.

Mathematics

2 answers:

Naya [18.7K]4 years ago

7 0

Answer:

It is A: 120

Step-by-step explanation:

She knows there are 30 unit cubes in the bottom layer. Since the height is 4, there are 4 layers of 30 cubes each. She should multiply 4 times 30 = 120. The volume is 120 cubic units.

Bas_tet [7]4 years ago

3 0

Answer

Answer is 120

Step-by-step explanation:

Multiply the length, width, and height to get the volume. Do 6x4x5 to get 120.

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PLEASE HELP!!!!!!!!!!!!

yanalaym [24]

This is your generic run-of-the-mill sinusoidal function:

f(x) = sin(x)

This is the same sine function but with a phase shift of 3 units to the right:

f(x) = sin(x-3)

This is the sine function but with an amplitude of 4 units:

f(x) = 4sin(x)

This is the sine function but flipped across the x-axis:

f(x) = -sin(x)

Combine all these transformations to get:

f(x) = -4sin(x-3)

6 0

4 years ago

Suppose that an individual has a body fat percentage of 14.1% and weighs 132 pounds. How many pounds of her weight is made up of

nadya68 [22]

18.6 pounds of her weight is made up of fat.

5 0

4 years ago

20 points

Elodia [21]

<h2>Answer:</h2>

A one solution because it's x=1

<h3>Step By Step explanation:</h3>

this is the original problem

8x-3=3x+2

we want to have x by itself so. . .

we add three on both sides. it cancels -3. And 2+3=5

8x=3x+5

we subtract 3x on both sides so 8x-3x=5x and 3x cancels on the other side

5x=5

we divide by 5 on both sides to get x by itself

x=1

if it was 1=1 or x=x (the same on both side) it would've been infinite solutions. if the numbers didn't match like 4=6 it would've been no solution

3 0

4 years ago

Use the method of "undetermined coefficients" to find a particular solution of the differential equation. (The solution found ma

Naddika [18.5K]

Answer:

The particular solution of the differential equation

= $\frac{-1,36,656cos5x+1,89,800 sin5x}{-1204}$ + $\frac{1}{37}185e^{6x})$

Step-by-step explanation:

Given differential equation y''(x) − 10y'(x) + 61y(x) = −3796 cos(5x) + 185e6x

The differential operator form $(D^{2} -10D+61)y(x) = −3796 cos(5x) + 185e^{6x}$

<u>Rules for finding particular integral in some special cases:-</u>

let f(D)y = $e^{ax}$ then

the particular integral $\frac{1}{f(D)} (e^{ax} ) = \frac{1}{f(a)} (e^{ax} ) if f(a)$ ≠ 0

let f(D)y = cos (ax ) then

the particular integral $\frac{1}{f(D)} (cosax ) = \frac{1}{f(D^2)} (cosax ) =\frac{cosax}{f(-a^2)}$ f(-a^2) ≠ 0

Given problem

$(D^{2} -10D+61)y(x) = −3796 cos(5x) + 185e^{6x}$

P<u>articular integral</u>:-

$P.I = \frac{1}{f(D)}( −3796 cos(5x) + 185e^{6x})$

$P.I = \frac{1}{D^2-10D+61}( −3796 cos(5x) + 185e^{6x})$

$P.I = \frac{1}{D^2-10D+61}( −3796 cos(5x) + \frac{1}{D^2-10D+61}185e^{6x})$

P.I = $I_{1} +I_{2}$

we will apply above two conditions, we get

$I_{1}$ =

$\frac{1}{D^2-10D+61}( −3796 cos(5x) = \frac{1}{(-25)-10D+61}( −3796 cos(5x) ( since D^2 = - 5^2)$ $= \frac{1}{(36-10D}( −3796 cos(5x) \\= \frac{1}{(36-10D}X\frac{36+10D}{36+10D} ( −3796 cos(5x)$

on simplification we get

= $\frac{1}{(36^2-(10D)^2}36+10D( −3796 cos(5x)$

= $\frac{-1,36,656cos5x+1,89,800 sin5x}{1296-100(-25)}$

= $\frac{-1,36,656cos5x+1,89,800 sin5x}{-1204}$

$I_{2}$ =

$\frac{1}{D^2-10D+61}185e^{6x}) = \frac{1}{6^2-10(6)+61}185e^{6x})$

$\frac{1}{37}185e^{6x})$

Now particular solution

P.I = $I_{1} +I_{2}$

P.I = $\frac{-1,36,656cos5x+1,89,800 sin5x}{-1204}$ + $\frac{1}{37}185e^{6x})$

8 0

3 years ago

Which of the following grids correctly graphs the points A (3, 1), B (0, 3), and C (1, 3)? A. A coordinate plane has an x-axis f

cricket20 [7]

Answer:

Step-by-step explanation:

B. A coordinate plane has an x axis from 0 to 5 in increments of 1 and a y axis from 0 to 5 in increments of 1. Point A (3,1) is plotted 3 units to the right and 1 unit above the origin. Point B (0,3) is plotted 3 units above the origin. Point C (1,3) is plotted 1 unit to the right and 3 units above the origin.

7 0

3 years ago