First to answer and is correct gets brainliest

Gemiola [76]

The answer is no question for you lol

7 0

2 years ago

convert the following logarithmic equation to the equivalent exponential equation. Use the caret (^) to enter exponents. y=ln x

GarryVolchara [31]

1. To solve this problem, you need to remember that an exponential function has the following form:

f(x)=a^x

"a" is the base and "x" is the exponent.

2. It is important to know that the logarithmic functions and the exponential functionsare inverse. Then, you have:

y=ln x
 e^y=e^(lnx)
 e^y=x

3. Therefore, the answer is:

x=e^y

5 0

3 years ago

The unit cost, in dollars, to produce tubs of ice cream is $18 and the fixed cost is $11610. The price-demand function, in dolla

Trava [24]

Answer:

Step-by-step explanation:

Let x represent the number of tubs of ice cream that was produced.

The unit cost, in dollars, to produce tubs of ice cream is $18 and the fixed cost is $11610. This means that the total cost of producing x tubs of ice cream would be

C(x) = 18x + 11610

The price-demand function, in dollars per tub, is p(x)=374-2x.

The revenue function is product of the output by the price function

R(x) = x × p(x) = xp(x)

R(x) = x(374 - 2x) = 374x - 2x²

The profit function P(x) = R(x) - C(x)

Therefore,

P(x) = 374x - 2x² - (18x + 11610)

P(x) = 374x - 2x² - 18x - 11610

P(x) = - 2x² + 374x - 18x - 11610

P(x) = - 2x² + 356x - 11610

At the break even point,

Revenue = total cost.

Therefore,

374x - 2x² = 18x + 11610

2x² + 18x - 374x + 11610 = 0

2x² - 356x + 11610 = 0

Dividing through by 2, it becomes

x² - 178x + 5805 = 0

Applying the general formula for quadratic equations,

x = [- b ±√(b² - 4ac)]/2a

x = [- - 178 ±√(-178² - 4 × 1 × 5805)]/2 × 1

x = [178 ±√(31684 - 23220)]/2

x = [178 ±92]/2

x = (178 + 92)/2 or (178 - 92)/2

x = 135 or x = 43

Therefore, the quantity for the smallest break-even point is 43.

4 0

3 years ago

Write the function in standard form f(x) = -4 (x - 6)^2 + 15

amid [387]

9514 1404 393

Answer:

f(x) = -4x^2 +48x -129

Step-by-step explanation:

It usually works well to compute the square first. That is, simplify according to the order of operations.

f(x) = -4(x^2 -12x +36) +15

f(x) = -4x^2 +48x -144 +15

f(x) = -4x^2 +48x -129

7 0

2 years ago

Read 2 more answers

An n × n matrix B has characteristic polynomial p(λ) = −λ(λ − 3) 3 (λ − 2) 2 (λ + 1). Which of the following statements is false

asambeis [7]

Answer:

Only d) is false.

Step-by-step explanation:

Let $p=p(\lambda)=\lambda(\lambda-3)^3 (\lambda-2)^2 (\lambda+1)$ be the characteristic polynomial of B.

a) We use the rank-nullity theorem. First, note that 0 is an eigenvalue of algebraic multiplicity 1. The null space of B is equal to the eigenspace generated by 0. The dimension of this space is the geometric multiplicity of 0, which can't exceed the algebraic multiplicity. Then Nul(B)≤1. It can't happen that Nul(B)=0, because eigenspaces have positive dimension, therfore Nul(B)=1 and by the rank-nullity theorem, rank(B)=7-nul(B)=6 (B has size 7, see part e)

b) Remember that $p(\lambda)=\det(B-\lambda I)$ . 0 is a root of p, so we have that $p(0)=\det(B-0 I)=\det B=0$ .

c) The matrix T must be a nxn matrix so that the product BTB is well defined. Therefore det(T) is defined and by part c) we have that det(BTB)=det(B)det(T)det(B)=0.

d) det(B)=0 by part c) so B is not invertible.

e) The degree of the characteristic polynomial p is equal to the size of the matrix B. Summing the multiplicities of each root, p has degree 7, therefore the size of B is n=7.

8 0

3 years ago