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2 years ago

Liam buys three identical plastic

Mathematics

1 answer:

liq [111]2 years ago

7 0

The number of rectangular prism container that would be set on the shelf is: 4.

<h3>What is the Volume of a Rectangular Prism?</h3>

Volume of rectangular prism = length × width ×height

Given the following:

Volume of three containers = 135 in.³
Volume of each rectangular prism container = 135/3 = 45 in.³
One face = width × height = 4.5 × 2 = 9 in.

Find the length of one rectangular prism using the volume formula since volume for one prism = 45 in.³

45 = length × 9

length = 5 in.

Each rectangular prism container is 5 in. long, therefore, the number of the containers that can be set on the shelf that is 24 in. long, if the 4.5 in by 2 in. face touches each other = 24/5 = 4.8.

The fifth container won't fit in. Therefore, the number of rectangular prism container that would be set on the shelf is: 4.

Learn more about rectangular prism on:

brainly.com/question/1015291

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3y''-6y'+6y=e*x sexcx

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From the homogeneous part of the ODE, we can get two fundamental solutions. The characteristic equation is

$3r^2-6r+6=0\iff r^2-2r+2=0$

which has roots at $r=1\pm i$ . This admits the two fundamental solutions

$y_1=e^x\cos x$
$y_2=e^x\sin x$

The particular solution is easiest to obtain via variation of parameters. We're looking for a solution of the form

$y_p=u_1y_1+u_2y_2$

where

$u_1=-\displaystyle\frac13\int\frac{y_2e^x\sec x}{W(y_1,y_2)}\,\mathrm dx$
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and $W(y_1,y_2)$ is the Wronskian of the fundamental solutions. We have

$W(e^x\cos x,e^x\sin x)=\begin{vmatrix}e^x\cos x&e^x\sin x\\e^x(\cos x-\sin x)&e^x(\cos x+\sin x)\end{vmatrix}=e^{2x}$

and so

$u_1=-\displaystyle\frac13\int\frac{e^{2x}\sin x\sec x}{e^{2x}}\,\mathrm dx=-\int\tan x\,\mathrm dx$
$u_1=\dfrac13\ln|\cos x|$

$u_2=\displaystyle\frac13\int\frac{e^{2x}\cos x\sec x}{e^{2x}}\,\mathrm dx=\int\mathrm dx$
$u_2=\dfrac13x$

Therefore the particular solution is

$y_p=\dfrac13e^x\cos x\ln|\cos x|+\dfrac13xe^x\sin x$

so that the general solution to the ODE is

$y=C_1e^x\cos x+C_2e^x\sin x+\dfrac13e^x\cos x\ln|\cos x|+\dfrac13xe^x\sin x$

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3 years ago

Combine like terms to create an equivalent expression. -3.6-1.9t+1.2+5.1t−3.6−1.9t+1.2+5.1t

Andreyy89

Question

Combine like terms to create an equivalent expression.

-3.6-1.9t+1.2+5.1t

Answer:

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Step-by-step explanation:

Given;

-3.6 - 1.9t + 1.2 + 5.1t

Combining like terms means bringing terms that have "t" together and separately, those that don't have "t" together. i.e

=> − 1.9t + 5.1t - 3.6 + 1.2

=> 3.2t - 2.4

Therefore, the equivalent expression is;

3.2t - 2.4

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