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3 years ago

Kết quả của phép tính 3 mũ 6 nhân 3 mũ 4 là

Mathematics

1 answer:

tatiyna3 years ago

8 0

Answer:

n = the number

The words of the problem statement translate into algebra as

6n - 3 = 4n + 11

Solve for n.

2n = 14

n = 7

Step-by-step explanation:

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If Tanisha has $1000 to invest at 7% per annum compounded semiannually, how long will it be before she has $1600? If the co

Sphinxa [80]

Answer:

Using continuous interest 6.83 years before she has $1600.

Using continuous compounding, 6.71 years.

Step-by-step explanation:

Compound interest:

The compound interest formula is given by:

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

Where A(t) is the amount of money after t years, P is the principal(the initial sum of money), r is the interest rate(as a decimal value), n is the number of times that interest is compounded per unit year and t is the time in years for which the money is invested or borrowed.

Continuous compounding:

The amount of money earned after t years in continuous interest is given by:

$P(t) = P(0)e^{rt}$

In which P(0) is the initial investment and r is the interest rate, as a decimal.

If Tanisha has $1000 to invest at 7% per annum compounded semiannually, how long will it be before she has $1600?

We have to find t for which $A(t) = 1600$ when $P = 1000, r = 0.07, n = 2$

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

$1600 = 1000(1 + \frac{0.07}{2})^{2t}$

$(1.035)^{2t} = \frac{1600}{1000}$

$(1.035)^{2t} = 1.6$

$\log{1.035)^{2t}} = \log{1.6}$

$2t\log{1.035} = \log{1.6}$

$t = \frac{\log{1.6}}{2\log{1.035}}$

$t = 6.83$

Using continuous interest 6.83 years before she has $1600

If the compounding is continuous, how long will it be?

We have that $P(0) = 1000, r = 0.07$

Then

$P(t) = P(0)e^{rt}$

$1600 = 1000e^{0.07t}$

$e^{0.07t} = 1.6$

$\ln{e^{0.07t}} = \ln{1.6}$

$0.07t = \ln{1.6}$

$t = \frac{\ln{1.6}}{0.07}$

$t = 6.71$

Using continuous compounding, 6.71 years.

7 0

3 years ago

5.5 cm<br> What is the circumference of this circle?<br> cm

FromTheMoon [43]

Answer:

23.76

Step-by-step explanation:

5 0

3 years ago

Read 2 more answers

The work of a student to solve the equation 2(5y – 2) = 12 + 6y is shown below: Step 1: 2(5y – 2) = 12 + 6y Step 2: 7y – 4 = 12

kirza4 [7]

2(5y - 2) = 12 + 6y
7y - 4 = 12 + 6y ⇒ wrong, it has to be: 10y - 4 = 12 + 6y

so the correct answer is B

7 0

3 years ago

Read 2 more answers

Can you please help me solve for the area

ycow [4]

Answer:

area is equal to 198 cm^2

Step-by-step explanation:

the height h of the left triangle can be obtained by

Pytagoras theorem:

$5^2+h^2=13^2\\25+h^2=169\\h^2=169-25\\h^2=144\\h=\sqrt{144} \\h=12$

the, the area of the left triangle is

$A_1=\frac{5*12}{2} \\A_1=5*6\\A_1=30$

the area of the right triangle is

$A_2=\frac{2*12}{2} \\A_2=12$

and the area of the rectangle in the middle is

$A_3=(13)(12)\\A_3=156$

Por tanto, el area total sera

$A=A_1+A_2+A_3\\A=30+12+156\\A=198$

8 0

3 years ago

Please help! Thanks! (:

djyliett [7]

Ok this is simple. first, lets look at the 123 angle, so the entire line is 180. subtract 123 from 180 and you have 57. a triangle will always add up to 180 degress aswell. so add 58 and 57 and thats 115. so since a triangle will always add up to 180, subtract 115 from 180 and you have the missing angle:

65!

4 0

3 years ago