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3 years ago

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Hiking up a mountain, you notice that the air temperature drops 10°C for every 1,000 meters increase in elevation. Write a multi

plication expression to represent the decrease in temperature if you hike up the mountain 3,000 meters. Then evaluate the expression and explain its meaning.

1 answer:

den301095 [7]3 years ago

7 0

Answer:

30,000

Step-by-step explanation:

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In problem solve the given differential equation by underdetermined coefficients y''-2y+y=xe^x

Alexus [3.1K]

Answer:

Solution is $y(t)=C_1e^x+C_2xe^x+\frac{x^3e^x}{6}$

Step-by-step explanation:

Given Differential Equation,

$y"-2y'+y=xe^x$ ...............(1)

We need to solve the given differential equations using undetermined coefficients.

Let the solution of the given differential equation is made up of two parts. one complimentary solution and one is particular solution.

$\implies\:y(x)=y_c(x)+y_p(x)$

For Complimentary solution,

Auxiliary equation is as follows

m² - 2m + 1 = 0

( m - 1 )² = 0

m = 1 , 1

So,

$y_c(x)=C_1e^x+c_2xe^x$

Now for particular solution,

let $y_p(x)=Ax^3e^x$

$y'=Ax^3e^x+3Ax^2e^x$

$y"=Ax^3e^x+6Ax^2e^x+6Axe^x$

Now putting these values in (1), we get

$Ax^3e^x+6Ae^2e^x+6Axe^x-2(Ax^3e^x+3Ax^2e^x)+Ax^3e^x=xe^x$

$Ax^3e^x+6Ae^2e^x+6Axe^x-2Ax^3e^x-6Ax^2e^x+Ax^3e^x=xe^x$

$6Axe^x=xe^x$

$6A=1$

$A=\frac{1}{6}$

$\implies\:y_p(x)=\frac{x^3e^x}{6}$

Therefore, Solution is $y(t)=C_1e^x+C_2xe^x+\frac{x^3e^x}{6}$

8 0

4 years ago

Is this right if not can you show me what i did wrong?

aev [14]

Answer:eyyy thats pretty good

Step-by-step explanation:

3 0

4 years ago

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Part 2: Use congruency theorems to prove congruency

Evgesh-ka [11]

Answer: see proof below

<u>Step-by-step explanation:</u>

Statement Reason

1. YO = NZ 1. Given

2. OZ = OZ 2. Reflexive Property

3. YO + OZ = YZ 3. Segment Addition Property

NZ + OZ = NO

4. YO + OZ = NZ + OZ 4. Addition Property

5. YZ = NO 5. Substitution

6. ∠M ≅ ∠X 6. Given

7. ∠N ≅ ∠Y 7. Given

8. ΔMNO ≅ ΔXYZ 8. AAS Congruency Theorem

8 0

4 years ago

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The volume of a sphere is two-thirds of a cylinder. What is the volume of a cylinder that has the same diameter as a sphere with

sattari [20]

Answer:

$V_2= \frac{28}{3} u^3$

Step-by-step explanation:

Given

Represent the volume of the cylinder with V1 and the volume of the sphere with V2

So, from the first statement: we have:

$V_2 =\frac{2}{3}V_1$

and

$V_1 = 14u^3$

To solve for $V_2$ , we simply substitute $14u^3$ for $V_1$ in $V_2 =\frac{2}{3}V_1$

$V_2 =\frac{2}{3}V_1$

$V_2= \frac{2}{3} * 14u^3$

$V_2= \frac{2* 14}{3} u^3$

$V_2= \frac{28}{3} u^3$

Hence, the volume of the sphere is $\frac{28}{3} u^3$

5 0

3 years ago

PLEASE ONLY ANSWER IF YOU KNOW FOR SURE! THANK YOU!

bulgar [2K]

A. I know for sure, trust me.

4 0

4 years ago

Read 2 more answers