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3 years ago

Write as a sum, difference or multiple of logarithms. In(8x) = [ ? ]8+ [ ]x

Mathematics

1 answer:

deff fn [24]3 years ago

8 0

Answer:

In(8x)=[In]8 + [In]x

Step-by-step explanation:

By product rule:

$In(8x)=[In]8 + [In]x$

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Capital Value Find the capital value of an asset that generates $7200 yearly income if the interest rate is as follows.

olganol [36]

a. An asset that generates $7200 yearly income if the interest rate 5% compounded continuously, then its capital value is $140433.002

b. An asset that generates $7200 yearly income if the interest rate 10% compounded continuously, then its capital value is $68460.59

Step-by-step explanation:

For continuously compound interest

$A = P \times e^{r t}$ ---------------> eq.1

Where

P = principal amount (initial investment)

r = annual interest rate (as a decimal)

t = number of years

A = amount after time t.

Let’s solve the equation

Where,

P is unknown

A = P + 7200 (asset after 1 year) ---------------> eq. 2

Case A:

$r=\frac{\text {interest rate}}{100}=\frac{5}{100}=0.05$

t = 1 (1 year)

Substitute all values in the formula (2) using the formula (1),

$P \times e^{(0.05)(1)}=P+7200$

$P \times e^{0.05}-P=7200$

$P\left(e^{0.05}-1\right)=7200$

$P(1.05127-1)=7200$

$P(0.05127)=7200$

$P=\frac{7200}{0.05127}=\$140433.002$

Case B:

$r=\frac{\text {interest rate}}{100}=\frac{10}{100}=0.10$

t = 1 (1 year)

Substitute all values in the formula (2) using the formula (1),

$P \times e^{(0.10)(1)}=P+7200$

$P \times e^{0.10}-P=7200$

$P\left(e^{0.10}-1\right)=7200$

$P(1.10517-1)=7200$

$P(0.10517)=7200$

$P=\frac{7200}{0.10517}=\$68460.59$

7 0

3 years ago

Evaluate the expression for w= - 9 2(w+3)=

lara [203]

Answer:

2(-9+3) = -12

8 0

3 years ago

Read 2 more answers

An art store buys a painting for $210 and then sells it and makes a profit of 70%.

Hoochie [10]

Answer:

Step-by-step explanation:

I don't say you must have to mark my ans as brainliest but if you think it has really helped you plz don't forget to thank me my frnd...

3 0

3 years ago

Read 2 more answers

Help!!! Write and equation in point-slope form and slope-intercept for each line. Passes through (2,2) , slope =3

professor190 [17]

Okay here it is

Y- 2 = 3 (X- 2)

And do you have the Y intercept? Because so far your slope intercept equation is

Y = 3x + ____

6 0

3 years ago

A scale drawing of a building has the scale 0.5in : 6ft. A wall is 30 ft long. How long will the wall be on the drawing?

g100num [7]

The scale 0.5 in : 6 ft, means that

any distance of 0.5 in on paper, represents 6 ft in reality

for example:

0.5*2= 1(in) represents 6*2=12 (ft)

0.5*4= 2(in) represents 6*4=24 (ft)

0.5*10=5(in) represents 6*10=60 (ft) and so on...

Let the wall be x (in) in the drawing:

0.5 (in) represents 6 (ft),
x (in) represents 30 (ft)
----------------------------------------

thus x = (0.5*30)/6 = 15/6= 2.5 (in)

Answer: 2.5 in

8 0

4 years ago