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musickatia [10]
3 years ago
10

A savings account compounds interest, at a rate of 25%, once a year. Eve puts $500 in the account as the principal. How can Eve

set up a function to track the amount of money she has? (1 point)
Select one:
a. A(x) = 500(25)x where 25 is the interest rate
b. A(x) = 500(.25)x where .25 is the interest rate
c. A(x) = 500(1 + 25)x where 25 is the interest rate
d. A(x) = 500(1 + .25)x where .25 is the interest rate
Mathematics
1 answer:
vladimir1956 [14]3 years ago
5 0
Year 1: 500 + 0.25*500 = 500 [1 + 0.25]

Year 2: 500*[ 1 + 0.25] * [1 + 0.25] = 500 [1 + 0.25]^2

Year x: 500 [1 + 0.25]^x

Option d: A(x) = 500[1 + .25]^x, where .25 is the interest rate
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3 years ago
if grant drove his car for 417 miles on 15 gallons of gas. how many miles per gallon does grants car get?
lara [203]

Answer:

27.8 per mile.

Step-by-step explanation:

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miles/ gallon

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2 years ago
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The indicated function y1(x is a solution of the given differential equation. use reduction of order or formula (5 in section 4.
Taya2010 [7]
Given a solution y_1(x)=\ln x, we can attempt to find a solution of the form y_2(x)=v(x)y_1(x). We have derivatives

y_2=v\ln x
{y_2}'=v'\ln x+\dfrac vx
{y_2}''=v''\ln x+\dfrac{v'}x+\dfrac{v'x-v}{x^2}=v''\ln x+\dfrac{2v'}x-\dfrac v{x^2}

Substituting into the ODE, we get

v''x\ln x+2v'-\dfrac vx+v'\ln x+\dfrac vx=0
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Setting w=v', we end up with the linear ODE

w'x\ln x+(2+\ln x)w=0

Multiplying both sides by \ln x, we have

w' x(\ln x)^2+(2\ln x+(\ln x)^2)w=0

and noting that

\dfrac{\mathrm d}{\mathrm dx}\left[x(\ln x)^2\right]=(\ln x)^2+\dfrac{2x\ln x}x=(\ln x)^2+2\ln x

we can write the ODE as

\dfrac{\mathrm d}{\mathrm dx}\left[wx(\ln x)^2\right]=0

Integrating both sides with respect to x, we get

wx(\ln x)^2=C_1
w=\dfrac{C_1}{x(\ln x)^2}

Now solve for v:

v'=\dfrac{C_1}{x(\ln x)^2}
v=-\dfrac{C_1}{\ln x}+C_2

So you have

y_2=v\ln x=-C_1+C_2\ln x

and given that y_1=\ln x, the second term in y_2 is already taken into account in the solution set, which means that y_2=1, i.e. any constant solution is in the solution set.
4 0
3 years ago
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Paraphin [41]

Answer:

The answer will turn out to be y= 5 or y= -5.

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