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Misha Larkins [42]
2 years ago
9

For the following function y = f(x) = 4x^3 - 5

Mathematics
1 answer:
goblinko [34]2 years ago
6 0

The answer for each of the differentiation are; f'(-6) = 432;  f⁻¹(y) = ∛((y + 5)/4); df⁻¹/dy = 1/432

<h3>How to differentiate functions?</h3>

1) f(x) = 4x³ - 5

We will differentiate it to get;

f'(x) = df/dx = 12x²

f'(-6) = 12(-6)²

f'(-6) = 432

2) We are given the formula;

x = f⁻¹(y)

Thus;

y = 4x³ - 5

4x³ = y + 5

x³ = (y + 5)/4

x = ∛((y + 5)/4)

f⁻¹(y) = ∛((y + 5)/4)

c)  f⁻¹(y) = ∛((y + 5)/4)

df⁻¹/dy = -1/12y²

At f(-6), we have;

df⁻¹/dy = 1/432

Read more about Differentiation at; brainly.com/question/5313449

#SPJ1

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Theo earns a base salary plus commission. At the end of September, he was paid $3,835.25 based on his monthly sales of $12,850.
hodyreva [135]

Theo's base salary  using a simultaneous equation approach is $2,996.22 .

In order to determine the base salary of Theo, we can express the two earnings and sales amounts using simultaneous equation, that we would solve to arrive at the base salary

Bear in mind that total earnings are determined as base salary plus commission

Let X be the base salary

Let R be the rate of commission

commission =sales*rate of commission

When earnings were $3,835.25 and sales is $12,850, we have the below equation:

X+(12,850*R)=3,835.25

X+12850R=3,835.25  .................... equation (1)

When earnings were $3,641 and sales is $9,875, we have the below equation:

X+(9,875*R)=3641

X+9875R=3641 .........................  equation (2)

subtract equation 2 from 1

2975R=194.25

R=194.25/2975

R=commission rate=6.52941176470588%

substitute for R in equation 1 to arrive at X(base salary)

X+(12850*6.52941176470588%)=3,835.25

X=3,835.25-(12850*6.52941176470588%)

X=base salary=$2,996.22

Find further guide on simultaneous equation in the link below:

brainly.com/question/6597041

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7 0
2 years ago
Paul lands a home mortgage of $58,200 at a
qwelly [4]

Answer:

$72,100

Step-by-step explanation:

To calculate the total principal+interest payment, you can use the formula to find the future value:

FV=PV(1+i)^n

FV= Future value

PV= Present value= $58,200

i= Interest rate= 7.40%

n= Number of periods of time= 3 years

Now, you can replace the values on the formula:

FV=58,200*(1+0.0740)^3

FV=58,200*(1.0740)^3

FV=72,100

According to this, the answer is that the  total principal + interest  payment will be $72,100.

8 0
2 years ago
Y = 230X + 100<br><br> What is the constant rate
Ad libitum [116K]

Answer: y 12 6 4 3. - 2 Y x 1 | 2 | 3 | 4 |. | y | 7 | 5| 3 1. 3.

Step-by-step explanation:

6 0
2 years ago
HELP PLEASE DUE IN 3 MINUTES
Anarel [89]

Answer:

101

Step-by-step explanation:

If you add up all of the answers, it equals 101 due to the fact of just adding all of the x's together in a row.

6 0
2 years ago
2\times 3x\times y\times 4z\times 2x\times y\times z​
Arturiano [62]

Step-by-step explanation:

48{x}^{2} {y}^{2} {z}^{2}

6 0
3 years ago
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