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2 years ago

8

Container A is 13 inches by 19 inches by 25 inches. Container B is 13 inches by 13 inches by 31 inches. In cubic inches, how muc

h greater is the volume of Container A.

1 answer:

Ilia_Sergeevich [38]2 years ago

4 0

Answer:

936

Step-by-step explanation:

First calculate the volume of each container. to calculate volume, multiply the length * width * height.

For Container A, the volume is 13 * 19 * 25 = 6175 inches.

For Container B, the volume is 13 * 13 * 31 = 5239 inches.

6175 - 5239 = 936 so the volume Container A is 936 cubic inches greater than the volume of Container B.

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Find a homogeneous linear differential equation with constant coefficients whose general solution is given by

frez [133]

Answer:

$y" + 2y' + 2y = 0$

Step-by-step explanation:

Given

$y=c_1e^{-x}cosx+c_2e^{-x}sinx$

Required

Determine a homogeneous linear differential equation

Rewrite the expression as:

$y=c_1e^{\alpha x}cos(\beta x)+c_2e^{\alpha x}sin(\beta x)$

Where

$\alpha = -1$ and $\beta = 1$

For a homogeneous linear differential equation, the repeated value m is given as:

$m = \alpha \± \beta i$

Substitute values for $\alpha$ and $\beta$

$m = -1 \± 1*i$

$m = -1 \± i$

Add 1 to both sides

$m +1= 1 -1 \± i$

$m +1= \± i$

Square both sides

$(m +1)^2= (\± i)^2$

$m^2 + m + m + 1 = i^2$

$m^2 + 2m + 1 = i^2$

In complex numbers:

$i^2 = -1$

So, the expression becomes:

$m^2 + 2m + 1 = -1$

Add 1 to both sides

$m^2 + 2m + 1 +1= -1+1$

$m^2 + 2m + 2= 0$

This corresponds to the homogeneous linear differential equation

$y" + 2y' + 2y = 0$

6 0

3 years ago

Jimmy invests $2500 in an account with a 5% interest rate, making no other deposits or withdrawals. What will Jimmy’s account ba

Alik [6]

Answer:

We conclude that the total amount accrued, principal plus interest, from compound interest on an original principal of $2500 at a rate of 5% per year compounded 6 times per year over 8 years is $3723.38.

Step-by-step explanation:

Given

Principle P = $2500

Interest rate r = 5% = 0.05

Time period t = 8 years

To determine

Accrue Amount A = ?

Using the compound interest equation

$A\:=\:P\left(1\:+\:\frac{r}{n}\right)^{nt}$

where:

A represents the Accrue Amount

P represents the Principal Amount

r represents the interest rate

t represents the time period in years

n represents the number of compounding periods per unit t

Important tip:

Given that the interest is compounded 6 times each year, therefore, the value of n = 6.

now substituting P = 2500, r = 0.05, t = 8 and n = 6 in the equation

$A\:=\:P\left(1\:+\:\frac{r}{n}\right)^{nt}$

$A=2500\left(1+\frac{0.05}{6}\right)^{\left(6\right)\left(8\right)}$

$\:A=2500\left(1+\frac{0.05}{6}\right)^{48}$

$A=2500\times 1.48935$ ∵ $\left(1+\frac{0.05}{6}\right)^{48\:\:}=1.48935$

$A=\:3723.38$ $

Therefore, we conclude that the total amount accrued, principal plus interest, from compound interest on an original principal of $2500 at a rate of 5% per year compounded 6 times per year over 8 years is $3723.38.

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2 years ago

I need help finding the mean, median, and mode(s) I need help with number 7

natta225 [31]

Answer:

the mean is 57.5 the median is 44.5 and the mode is 47

Step-by-step explanation:

the mode is 47 cuz it appeared twice. the median is 57.5 bc 47+147+24+47+38+42=345 and 345/6 is 57.5

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Verizon [17]

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torisob [31]

9:60 is one hours
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47-15=32

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3 years ago