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3 years ago

If a+b=−2a + b = -2a+b=−2a+b= -2 and x+y =−2 what is 4x+5a+4y+5b?

1 answer:

7 0

$a + b = -2\ and\ x + y = -2\\\\4x + 5a + 4y + 5b = (4x + 4y) + (5a + 5b) = 4(\underbrace{x + y}_{=-2}) + 5(\underbrace{a + b}_{=-2})\\\\=4(-2)+5(-2)=-8+(-10)=-18$

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(15 pts) 4. Find the solution of the following initial value problem: y"-10y'+25y = 0 with y(0) = 3 and y'(0) = 13

jolli1 [7]

Answer:

$y(x)=3e^{5x}-2xe^{5x}$

Step-by-step explanation:

The given differential equation is $y''-10y'+25y=0$

The characteristics equation is given by

$r^2-10r+25=0$

Finding the values of r

$r^2-5r-5r+25=0\\\\r(r-5)-5(r-5)=0\\\\(r-5)(r-5)=0\\\\r_{1,2}=5$

We got a repeated roots. Hence, the solution of the differential equation is given by

$y(x)=c_1e^{5x}+c_2xe^{5x}...(i)$

On differentiating, we get

$y'(x)=5c_1e^{5x}+5c_2xe^{5x}+c_2e^{5x}...(ii)$

Apply the initial condition y (0)= 3 in equation (i)

$3=c_1e^{0}+0\\\\c_1=3$

Now, apply the initial condition y' (0)= 13 in equation (ii)

$13=5(3)e^{0}+0+c_2e^{0}\\\\13=15+c_2\\\\c_2=-2$

Therefore, the solution of the differential equation is

$y(x)=3e^{5x}-2xe^{5x}$

5 0

3 years ago

Equations and inequalities!<br> solve for w <br> 11=253-w

Annette [7]

Answer:

w = 242

Step-by-step explanation:

Step 1: Simplify both sides of the equation.

$11=-w + 253$
$-w + 253 = 11$

Step 2: Subtract 253 from both sides.

$-w + 253 - 253 = 11 - 253$
$-w = -242$

Step 3: Divide both sides by -1.

$\frac{-w}{-1}=\frac{-242}{-1}$
$w = 242$

Step 4: Check if solution is correct.

$11 = 253 - (242)$
$11 = 253 - 242$
$11 = 11$

Therefore, w = 242.

Have a lovely rest of your day/night.

8 0

2 years ago

Granger walks 2 1/5 miles in 2/3 an hour at a constant speed.

Lorico [155]

She walks 3 3/10 mph
In 1/3 an hour she walks 2 1/5 : 2 = 11/10

4 0

3 years ago

17. A grab bag contains 3 football cards and 7 basketball cards. An experiment consists of taking one card out

allochka39001 [22]

Answer:

I think it is B but I'm sorry if it's wrong.

6 0

3 years ago

Hakim saves money for one year to buy a computer.

elena55 [62]

Answer:

$111

Step-by-step explanation:

First we need to take a look at the bank account of Hakim. Hakim initially invested $700 in the bank with a 5% simple interest annually. Since Hakim waited for an entire year before buying the computer, he will then have the extra 5% interest from the bank.

Let's first compute for how much Hakim will have in total in the bank.

A = P(1 + rt)

P = 700 Initial Investment

r = 5% or 0.05 Interest

t = 1 Year

A = 700(1 + (0.05 x 1))

A = 700(1 + 0.05)

A = 700(1.05)

A = 735

So now we know that Hakim has a total of $735 in his bank account.

Now let's move on to calculating the total cost of the computer. We know that the sales tax is always computed after the discounted price.

So first we find the discounted price.

x = 750

d = 20% or 0.20

Discount = 750 x 0.20

Discount = 150

Now that we have the discount of the computer, we then simply subtract the discount to the initial price.

750 - 150 = 600.

The computer will then cost $600 with the discounted price.

Now we have to find the sales tax.

Sales Tax = 4% or 0.04

Total Discounted Price = 600

600 x 0.04 = $24

Now that we have the sales tax, we simply add the sales tax to the discounted price.

600 + 24 = 624.

Now that we know how much the total cost of the computer is with the discount and sales tax, we simply subtract the total cost of the computer to Hakim's current account balance.

735 - 624 = 111

Hakim will have a total of $111 in his bank account after purchasing the computer.

4 0

3 years ago