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3 years ago

If e^5x = k, where k is any positive number, then what is the value of x?

Mathematics

1 answer:

Makovka662 [10]3 years ago

7 0

$e^{5x}=k\implies\ln(e^{5x})=\ln(k)\implies\boxed{x=\ln(k)/5}$

Hope this helps.

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The volume of a CONE-shaped hole is 75pi ft cubed. If the hole is 9 feet deep, what is the radius of the hole?

Arturiano [62]

Answer:

The radius of hole is 5 feet

Step-by-step explanation:

Depth of conical hole = 9 feet

Let the radius of hole be r

Volume of conical hole = $\frac{1}{3} \pi r^2 h$

So, Volume of conical hole = $\frac{1}{3} \pi \times r^2 \times 9$

We are given that volume of a CONE-shaped hole is 75pi ft cubed.

So, $\frac{1}{3} \pi \times r^2 \times 9=75 \pi$

$\frac{1}{3} \times r^2 \times 9=75$

$r^2=\frac{75 \times 3}{9}$

$r=\sqrt{\frac{75 \times 3}{9}}$

r=5

Hence The radius of hole is 5 feet

6 0

3 years ago

A bag has 9 marbles: 4 are green, 2 are red, and 3 are blue. Melissa chooses a marble at random, and without putting it back, ch

nika2105 [10]

Answer: pr (blue) = 1/3 or 0.33

Pr(green without replacement) = 1/2 = 0.5

Step-by-step explanation:

Probability = number of possible outcomes/ number of total outcomes

Total number of outcomes is the sum of all the marbles, given as 9

Pr ( first marble blue) = no of blue marbles/ total number of marbles

= 3/9 = 1/3 or 0.333

Second marble is chosen without replacement- this means that the total outcome has reduced by 1, total number of marbles has reduced to 8 because there was no replacement.

Pr (second marble is green) = number of green marble/ total number of marbles without replacing the first marble

= 4/8 = 1/2 = 0.5

I hope this helps.

7 0

3 years ago

16.

ss7ja [257]

The simplified polynomial that represents how many more economy cars are rented in w weeks than full-size cars is 53 - w.

<h3>Linear equation:</h3>

Linear equation is an equation in which the highest power of the variable is equals to one.

Therefore, the number of economy-size cars rented in w weeks is represented as follows:

152 + 3w

The number of full-size cars rented in w weeks is represented as follows:

99 + 2w

where

w = number of weeks

A simplified polynomial that represents how many more economy cars are rented in w weeks than full-size cars is as follows:

152 + 3w - (99 + 2w)
152 + 3w - 99 - 2w
53 - w

learn more on polynomial here: brainly.com/question/2566362

5 0

2 years ago

6 × 2 − 4 × 5 + 12 ÷ 4 insert parentheses

Varvara68 [4.7K]

Answer: (6 x 2) - (4 x 5) + (12 / 4)

6 0

3 years ago

Read 2 more answers

Which equation represents a population of 210 animals that decreases at an annual rate of 14%

soldi70 [24.7K]

Answer:

The equation i.e. used to denote the population after x years is:

P(x) = 490(1 + 0.200 to the power of x

Step-by-step explanation:

This problem could be modeled with the help of a exponential function.

The exponential function is given by:

P(x) = ab to the power of x

where a is the initial value.

and b=1+r where r is the rate of increase or decrease.

Here the initial population of the animals are given by: 490

i.e. a=490

Also, the rate of increase is: 20%

i.e. r=20%

i.e. r=0.20

Hence, the population function i.e. the population of the animals after x years is:

P(x) = 490(1 + 0.200 to the power of x

6 0

3 years ago