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3 years ago

14

Which expression represents "5 times the sum of 4 and y?"

1 answer:

Mkey [24]3 years ago

8 0

Answer:

5 x (4+y)

Step-by-step explanation:

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Ava has a jewelry box in the shape of a pentagonal prism.

olga55 [171]

Answer:

C. 460 square inches

Step-by-step explanation:

Side of the base = 8 in
Height of the prism = 6 in
Base area = 110 in²

<u>Total surface area (two bases and 5 faces):</u>

S = 2(110) + 5(6*8) = 460 in²

Correct choice is C

3 0

3 years ago

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3100 times 43 how much is this

Soloha48 [4]

Answer:

133,300

Step-by-step explanation:

3100 x 43 = 133,300

7 0

3 years ago

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Consider the following differential equation to be solved by undetermined coefficients. y(4) − 2y''' + y'' = ex + 1 Write the gi

kompoz [17]

Answer:

The general solution is

$y= (C_{1}+C_{1}x) e^0x+(C_{3}+C_{4}x) e^x +\frac{1}{2} (e^x(x^2-2x+2)-e^x(2(x-1)+e^x(2))$

+ $\frac{x^2}{2}$

Step-by-step explanation:

Step :1:-

Given differential equation y(4) − 2y''' + y'' = e^x + 1

The differential operator form of the given differential equation

$(D^4 -2D^3+D^2)y = e^x+1$

comparing f(D)y = e^ x+1

The auxiliary equation (A.E) f(m) = 0

$m^4 -2m^3+m^2 = 0$

$m^2(m^2 -2m+1) = 0$

$(m^2 -2m+1) this is the expansion of (a-b)^2$

$m^2 =0 and (m-1)^2 =0$

The roots are m=0,0 and m =1,1

complementary function is $y_{c} = (C_{1}+C_{1}x) e^0x+(C_{3}+C_{4}x) e^x$

<u>Step 2</u>:-

The particular equation is $\frac{1}{f(D)} Q$

P.I = $\frac{1}{D^2(D-1)^2} e^x+1$

P.I = $\frac{1}{D^2(D-1)^2} e^x+\frac{1}{D^2(D-1)^2}e^{0x}$

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

$\frac{1}{D^2} (\frac{x^2}{2!} )e^x + \frac{1}{D^{2} } e^{0x}$

$\frac{1}{D} means integration$

$\frac{1}{D^2} (\frac{x^2}{2!} )e^x = \frac{1}{2D} \int\limits {x^2e^x} \, dx$

applying in integration u v formula

$\int\limits {uv} \, dx = u\int\limits {v} \, dx - \int\limits ({u^{l}\int\limits{v} \, dx } )\, dx$

$I_{1}$ = $\frac{1}{D^2(D-1)^2} e^x$

$\frac{1}{2D} (e^x(x^2)-e^x(2x)+e^x(2))$

$\frac{1}{2} (e^x(x^2-2x+2)-e^x(2(x-1)+e^x(2))$

$I_{2}$ $= \frac{1}{D^2(D-1)^2}e^{0x}$

$\frac{1}{D} \int\limits {1} \, dx= \frac{1}{D} x$

again integration $\frac{1}{D} x = \frac{x^2}{2!}$

The general solution is $y = y_{C} +y_{P}$

$y= (C_{1}+C_{1}x) e^0x+(C_{3}+C_{4}x) e^x +\frac{1}{2} (e^x(x^2-2x+2)-e^x(2(x-1)+e^x(2))$

+ $\frac{x^2}{2!}$

3 0

3 years ago

Erica had 6 coins in her coin collection. She goes to a coin show and buys some more coins. How many coins does she have now?

goldfiish [28.3K]

Answer:

6+x with x equalling the amount of coins bought if that is what you were looking for

Step-by-step explanation:

if you want to make and equation out of this you don't know the amount of coins she bought so you use a variable (x) to replace that unknown number then since it says she bought more she is adding more to her collection which means it would be an addition problem, leaving you with 6+x for your final answer

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3 years ago

8. | 11 | 14 | 17 | 20<br> What’s the function

Murrr4er [49]

Answer:

What do you exactly need to do?

Step-by-step explanation:

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