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2 years ago

If f(x) = x3 – 2x2, which expression is equivalent to f(i)?

Mathematics

2 answers:

Tasya [4]2 years ago

7 0

<span>f(i) = i³ - 2(i)²

Use the facts, i³ = -i and i² = -1

f(i) = 2 - i</span>

Illusion [34]2 years ago

4 0

Its letter D on 3dgenuity because i took the test.

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Babe Ruth's 1931 salary was $80,000, Government statistics show a consumer price index of 15.2 for 1931 and 237 for 2015. Ruth's

Lady_Fox [76]

Answer:

Ruth's 1931 salary was equivalent to a 2015 salary of $1,247,368.

Step-by-step explanation:

This question can be solved by a rule of three.

Government statistics show a consumer price index of 15.2 for 1931 and 237 for 2015.

This means that $15.2 in 1931 is equivalent to $237 in 2015. So

$15.2 in 1931 - $237 in 2015

$80,000 in 1931 - $x in 2015

$15.2x = 237*80,000$

$x = \frac{237*80,000}{15.2}$

$x = 1,247,368$

Ruth's 1931 salary was equivalent to a 2015 salary of $1,247,368.

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2 years ago

The table shows the number of grapes eaten over several minutes. What is the rate of change for the function on the table? 15 gr

Mkey [24]

Answer:

1. 15 grapes eaten per minute.

Step-by-step explanation:

We have been given a table that shows the number of grapes eaten over several minutes. We are asked to find the rate of change of our given function.

Since we know that rate of change of a function can be found by vertical change of the function divided by horizontal change of the function.

$\text{Rate of change of a function}=\frac{\text{Vertical change}}{\text{Horizontal change}}$

$\text{Rate of change of a function}=\frac{y_2-y_1}{x_2-x_1}$

$y_2-y_1$ =Difference between two y-coordinates.

$x_2-x_1$ =Difference between corresponding x-coordinates of y-coordinates.

Upon substituting coordinates of any two points in above formula we will get,

$\text{Rate of change of the function}=\frac{60-15}{4-1}$

$\text{Rate of change of the function}=\frac{45}{3}$

$\text{Rate of change of the function}=15$

We can see that rate of change of our given function is 15 grapes eaten per minute and 1st option is the correct choice.

7 0

2 years ago

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Mrs. Jones attended a Southern Living home party. She purchased a vase which cost $34.99. The shipping charge was $3.00, and 8.2

kipiarov [429]

Answer:

Step-by-step explanation:

1.0825×(34.99+3) = $41.124175, and the government always rounds up.

$41.13

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2 years ago

A rectangular tank that is 5324 ft cubed with a square base and open top is to be constructed of sheet steel of a given thicknes

marishachu [46]

Answer:

Side of 22 and height of 11

Step-by-step explanation:

Let s be the side of the square base and h be the height of the tank. Since the tank volume is restricted to 5324 ft cubed we have the following equation:

$V = s^2h = 5324$

$h = 5324 / s^2$

As the thickness is already defined, we can minimize the weight by minimizing the surface area of the tank

Base area with open top $s^2$

Side area 4sh

Total surface area $A = s^2 + 4sh$

We can substitute $h = 5324 / s^2$

$A = s^2 + 4s\frac{5324}{s^2}$

$A = s^2 + 21296/s$

To find the minimum of this function, we can take the first derivative, and set it to 0

$A' = 2s - 21296/s^2 = 0$

$2s = 21296/s^2$

$s^3 = 10648$

$s = \sqrt[3]{10648} = 22$

$h = 5324 / s^2 = 5324 / 22^2 = 11$

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2 years ago

A boat is traveling east across a river that is 112 meters wide at 8 meters per second. If the river has a northward current of

andreyandreev [35.5K]

This is the concept of application of the Pythagorean theorem. The resultant speed of the motorboat which is crossing the river that has a northward current of 5 m/s at a speed of 8 m/s will be given by:
c^2=a^2+b^2
c^2=8^2+5^2
c^2=64+25
c^2=89
c=sqrt89
c=9.4 m/s

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2 years ago

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