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3 years ago

Given f(x) = 7x^9, find f^-1 (x). Then state whether f^-1 (x) is a function

1 answer:

7 0

A though without graphing software it would appear to be C

Step-by-step explanation:
The inverse of a function is the function reflected across the line y=x. This results in the coordinate points (x,y) of the function becoming (y,x) for the inverse function. Algebraically to find the inverse, switch the x and y locations and solve for y.
y = 7x^9
x = 7y^9
x/7 = y^9
(9)√(x/7) = y
This is a ninth root of (x/7) also written in exponents as y = (x/7)^(1/9).
This is a function. While it appears not to be a function because the middle portion over the origin appears vertical, it is a function because the middle portion over the origin is changing and graphing software shows it has no input with more than one output. Without graphing software you would rule it is not a function.

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AlekseyPX

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3 years ago

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The Magic Dragon has 2013 heads. Leo the Brave is cutting off the Dragon's heads at a speed of 5 heads per minute. The Dragon's

aivan3 [116]

Answer: The answer is 1833 heads and 11 hours, 11 minutes.

Step-by-step explanation: Given that the Magic Dragon has 2013 heads. The brave Leo is cutting off the Dragon's heads at a speed of 5 heads per minute. But, the Dragon's heads are growing back at a speed of 2 heads per minute.

So, the number of heads of Dragon that are decreasing per minute = 3.

Therefore, after 1 hour, i.e., 60 minutes, The number of heads of the Dragon

= 2013 - 60 × 3 = 2013 - 180 = 1833 heads.

Now, the fight will last until all the heads of the Dragon are cut. Let the fight lasts for 'x' minutes, then

$2013-x\times 3=0\\\\\Rightarrow 3x=2013\\\\\Rightarrow x=\dfrac{2013}{3}=671.$

Hence the fight lasts for 671 minutes, i.e., 11 hours and 11 minutes.

Thus, the Dragon will have 1833 heads after 1 hour and the fight will last for 11 hour and 11 minutes.

3 0

3 years ago

Solve in attachment....

olga2289 [7]

Answer:

A)2

Step-by-step explanation:

we would like to integrate the following definite Integral:

$\displaystyle \int_{0} ^{1} 5x \sqrt{x} dx$

use constant integration rule which yields:

$\displaystyle 5\int_{0} ^{1} x \sqrt{x} dx$

notice that we can rewrite √x using Law of exponent therefore we obtain:

$\displaystyle 5\int_{0} ^{1} x \cdot {x}^{1/2} dx$

once again use law of exponent which yields:

$\displaystyle 5\int_{0} ^{1} {x}^{ \frac{3}{2} } dx$

use exponent integration rule which yields;

$\displaystyle 5 \left( \frac{{x}^{ \frac{3}{2} + 1 } }{ \frac{3}{2} + 1} \right) \bigg| _{0} ^{1}$

simplify which yields:

$\displaystyle 2 {x}^{2} \sqrt{x} \bigg| _{0} ^{1}$

recall fundamental theorem:

$\displaystyle 2 ( {1}^{2}) (\sqrt{1} ) - 2( {0}^{2} )( \sqrt{0)}$

simplify:

$\displaystyle 2$

hence

our answer is A

8 0

3 years ago

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A cylinder has a radius of 30 ft and a height of 19 ft. What is the exact surface area of the cylinder?

Ad libitum [116K]

$A=2\pi r(r+h)\\
A=2\pi\cdot30\cdot(30+19)\\
A=60\pi\cdot49\\
A=2940\pi\hbox{ ft}^2$

4 0

3 years ago

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Consider the equation: 3(–4n – 9) = 21

hram777 [196]

Answer: N=-4

Step-by-step explanation:

STEP

Pulling out like terms

2.1 Pull out like factors :

-4n - 9 = -1 • (4n + 9)

Equation at the end of step

-3 • (4n + 9) - 21 = 0

STEP

Pulling out like terms

4.1 Pull out like factors :

-12n - 48 = -12 • (n + 4)

Equation at the end of step

-12 • (n + 4) = 0

STEP

Equations which are never true:

5.1 Solve : -12 = 0

This equation has no solution.

A a non-zero constant never equals zero.

Solving a Single Variable Equation:

5.2 Solve : n+4 = 0

Subtract 4 from both sides of the equation :

n = -4

One solution was found :

n = -4

7 0

3 years ago

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