I need help immediately, you’ll receive brainlest if answered correctly!!!

Aneli [31]

Answer:

Logarithms are the "opposite" of exponentials, just as subtraction is the opposite of addition and division is the opposite of multiplication. Logs "undo" exponentials. Technically speaking, logs are the inverses of exponentials. On the left-hand side above is the exponential statement "y = bx

Step-by-step explanation:

3 0

3 years ago

The total sales of a company (in millions of dollars) t months from now are given by S(t) = 0.03t3 + 0.5t2 + 9t + 4. Find S'(t).

mars1129 [50]

Answer:

$S(2) = 24.24$ . This means that in the second month, the company will sell 24.24 millions of dollars in total.

$S'(2) = 11.36$ . This means that in the second month the total sales will increase in 11.36 millions of dollars from the previous month.

d. The total sales 11 months from now will be $203.43 million dollars.

Step-by-step explanation:

The total sales of the company, in millions of dollars is given by the following formula:

$S(t) = 0.03t^{3} + 0.5t^{2} + 9t + 4$

This function has the following derivative, which represents the variation in relation to the previous month.

$S'(t) = 0.09t^{2} + t + 9$

Find S(2) and S'(2)

$S(t) = 0.03t^{3} + 0.5t^{2} + 9t + 4$

$S(2) = 0.03*(2)^{3} + 0.5*(2)^{2} + 9*2 + 4 = 24.24$

$S(2) = 24.24$ . This means that in the second month, the company will sell 24.24 millions of dollars in total.

$S'(t) = 0.09t^{2} + t + 9$

$S'(2) = 0.09*2^{2} + 2 + 9 = 11.36$

$S'(2) = 11.36$ . This means that in the second month the total sales will increase in 11.36 millions of dollars from the previous month.

Choose the correct interpretation of S(11)=203.43.

S represents total sales, and S(11) is the total sales 11 months from now.

So the correct answer is:

d. The total sales 11 months from now will be $203.43 million dollars.

7 0

2 years ago

What is the equation of the axis of symmetry?

Aleksandr [31]

Answer:

Step-by-step explanation:

8 0

2 years ago

Eights rooks are placed randomly on a chess board. What is the probability that none of the rooks can capture any of the other r

erastova [34]

Answer:

The probability is $\frac{56!}{64!}$

Step-by-step explanation:

We can divide the amount of favourable cases by the total amount of cases.

The total amount of cases is the total amount of ways to put 8 rooks on a chessboard. Since a chessboard has 64 squares, this number is the combinatorial number of 64 with 8, $64 \choose 8 .$

For a favourable case, you need one rook on each column, and for each column the correspondent rook should be in a diferent row than the rest of the rooks. A favourable case can be represented by a bijective function $f : A \rightarrow A ,$ with A = {1,2,3,4,5,6,7,8}. f(i) = j represents that the rook located in the column i is located in the row j.

Thus, the total of favourable cases is equal to the total amount of bijective functions between a set of 8 elements. This amount is 8!, because we have 8 possibilities for the first column, 7 for the second one, 6 on the third one, and so on.

We can conclude that the probability for 8 rooks not being able to capture themselves is

$\frac{8!}{64 \choose 8} = \frac{8!}{\frac{64!}{8!56!}} = \frac{56!}{64!}$

7 0

2 years ago

Which of the following is the domain and range of the ellipse with equation x2 + 4y2 – 2x + 16y – 19 = 0?

Nata [24]

The option second D: [–5, 7]; R: [–5, 1] is correct the domain is D: [–5, 7], and the range is R: [–5, 1]

<h3>What is an ellipse?</h3>

An ellipse is a locus of a point that moves in a plane such that the sum of its distances from the two points called focus adds up to a constant. It is taken from the cone by cutting it at an angle.

We have an ellipse equation:

$\rm x^{2}+4y^{2}-2x+16y-19=0$