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Harman [31]
3 years ago
13

Lacy opened a savings account and deposited $100. The account earns 6% interest compounded monthly if she wants to use the money

to buy a new bicycle in two years how much will she be able to spend on the bike
Mathematics
1 answer:
Dafna11 [192]3 years ago
5 0

Answer:

Future Value= $112.72

Step-by-step explanation:

Giving the following information:

Initial deposit (PV)= $100

Number of periods (n)= 2*12= 24 months

Interest rate (i)= 0.06/12= 0.005

<u>To calculate the future value (FV), we need to use the following formula:</u>

FV= PV*(1 + i)^n

FV= 100*(1.005^24)

FV= $112.72

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Express the integral as a limit of Riemann sums. Do not evaluate the limit. (Use the right endpoints of each subinterval as your
Darina [25.2K]

Answer:

Given definite  integral as a limit of Riemann sums is:

\lim_{n \to \infty} \sum^{n} _{i=1}3[\frac{9}{n^{3}}i^{3}+\frac{36}{n^{2}}i^{2}+\frac{97}{2n}i+22]

Step-by-step explanation:

Given definite integral is:

\int\limits^7_4 {\frac{x}{2}+x^{3}} \, dx \\f(x)=\frac{x}{2}+x^{3}---(1)\\\Delta x=\frac{b-a}{n}\\\\\Delta x=\frac{7-4}{n}=\frac{3}{n}\\\\x_{i}=a+\Delta xi\\a= Lower Limit=4\\\implies x_{i}=4+\frac{3}{n}i---(2)\\\\then\\f(x_{i})=\frac{x_{i}}{2}+x_{i}^{3}

Substituting (2) in above

f(x_{i})=\frac{1}{2}(4+\frac{3}{n}i)+(4+\frac{3}{n}i)^{3}\\\\f(x_{i})=(2+\frac{3}{2n}i)+(64+\frac{27}{n^{3}}i^{3}+3(16)\frac{3}{n}i+3(4)\frac{9}{n^{2}}i^{2})\\\\f(x_{i})=\frac{27}{n^{3}}i^{3}+\frac{108}{n^{2}}i^{2}+\frac{3}{2n}i+\frac{144}{n}i+66\\\\f(x_{i})=\frac{27}{n^{3}}i^{3}+\frac{108}{n^{2}}i^{2}+\frac{291}{2n}i+66\\\\f(x_{i})=3[\frac{9}{n^{3}}i^{3}+\frac{36}{n^{2}}i^{2}+\frac{97}{2n}i+22]

Riemann sum is:

= \lim_{n \to \infty} \sum^{n} _{i=1}3[\frac{9}{n^{3}}i^{3}+\frac{36}{n^{2}}i^{2}+\frac{97}{2n}i+22]

4 0
3 years ago
A student solved 3/x−4=x/7 in six steps, as shown.
Stolb23 [73]

Answer:

Option A.

Step-by-step explanation:

The given equation is

\dfrac{3}{x-4}=\dfrac{x}{7}

Step 1: Multiply both sides by (x-4).

3=\dfrac{x(x-4)}{7}

Step 2: Multiply both sides by 7.

21=x(x-4)

Step 3: Using distributive property.

21=x^2-4x

Step 4: Isolate all terms on one side.

0=x^2-4x-21

Step 5: Find factors by splitting the middle term.

0=x^2-7x+3x-21

0=x(x-7)+3(x-7)

0=(x-7)(x+3)

Step 6: Using zero product property, we get

x=-3, x=7

It means student solved the equation correctly.

Therefore, the correct option is A.

5 0
3 years ago
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-3r +9 = -4r +5<br>what's r?​
-BARSIC- [3]

Answer:

-4

Step-by-step explanation:

-3r+9=-4r+5

-3r+4r=5-9

r=-4

8 0
3 years ago
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Show how you can make ten to find the sum 9 + 2 equal
Fudgin [204]
You can add 9+1 then make ten and add 10 +1
4 0
3 years ago
Plz answer everything i will do A B C D E F G and some other ones
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A= 4091

B=9303

C=4436

D=4460

E=4436

F=1455

G=1898

H=15275

I=181632

J=705.453045922

K=6.04166666667

3 0
3 years ago
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