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3 years ago

Which function below is the inverse of f(x) = x2 − 25?

Mathematics

2 answers:

FrozenT [24]3 years ago

8 0

(x-5)(x+5) is the answer

IRINA_888 [86]3 years ago

3 0

$f(x) = x^{2} - 25
$ can be written as $y = x^{2} - 25$

when finding inverse the first step is to interchange x and y in the equation

∴ $(x) = (y)^{2} - 25$

then you simply solve for y

$x + 25 = y^{2}$

$y = \sqrt{ (x + 25)}$

Thus $f^{-1} (x) = \sqrt{(x + 25)}$

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Find an equation of the tangent to the curve x =5+lnt, y=t2+5 at the point (5,6) by both eliminating the parameter and without e

svet-max [94.6K]

ANSWER

$y = 2x -4$

EXPLANATION

Part a)

Eliminating the parameter:

The parametric equation is

$x = 5 + ln(t)$

$y = {t}^{2} + 5$

From the first equation we make t the subject to get;

$x - 5 = ln(t)$

$t = {e}^{x - 5}$

We put it into the second equation.

$y = { ({e}^{x - 5}) }^{2} + 5$

$y = { ({e}^{2(x - 5)}) } + 5$

We differentiate to get;

$\frac{dy}{dx} = 2 {e}^{2(x - 5)}$

At x=5,

$\frac{dy}{dx} = 2 {e}^{2(5 - 5)}$

$\frac{dy}{dx} = 2 {e}^{0} = 2$

The slope of the tangent is 2.

The equation of the tangent through

(5,6) is given by

$y-y_1=m(x-x_1)$

$y - 6 = 2(x - 5)$

$y = 2x - 10 + 6$

$y = 2x -4$

Without eliminating the parameter,

$\frac{dy}{dx} = \frac{ \frac{dy}{dt} }{ \frac{dx}{dt} }$

$\frac{dy}{dx} = \frac{ 2t}{ \frac{1}{t} }$

$\frac{dy}{dx} = 2 {t}^{2}$

At x=5,

$5 = 5 + ln(t)$

$ln(t) = 0$

$t = {e}^{0} = 1$

This implies that,

$\frac{dy}{dx} = 2 {(1)}^{2} = 2$

The slope of the tangent is 2.

The equation of the tangent through

(5,6) is given by

$y-y_1=m(x-x_1)$

$y - 6 = 2(x - 5) =$

$y = 2x -4$

5 0

3 years ago

Given that a triangle has two sides of lengths 5 inches and 7 inches, which is a possible length of the third side?

victus00 [196]

Answer:

big poop face looking butt with a massive forehead poopy duck dipers

Step-by-step explanation:

↑∴↔↔⇔⇔³∛÷≈≤≥≥β⇵⊕⊕¬⊕⊕⊕⊕⊕⊕¬∪∪⊥∡∠°∞㏒㏑∡Ф⇒⇒√³π∫↓∵∴∴ $\lim_{n \to \infty} a_n \lim_{n \to \infty} a_n \neq \sqrt{x} x^{2} x^{2} \geq \geq \pi \frac{x}{y}$ and thats why it is big poop face looking butt with a massive forehead poopy duck dipers

3 0

3 years ago

The domain of u(x) is the set of all real values except 0 and the domain of v(x) is the set of all real values except 2. What

Oksana_A [137]

Using the domain concept, the restrictions on the domain of (u.v)(x) are given by:

A. u(x) ≠ 0 and v(x) ≠ 2.

<h3>What is the domain of a data-set?</h3>

The domain of a data-set is the set that contains all possible input values for the data-set.

To calculate u(x) x v(x) = (u.v)(x), we calculate the values of u and v and then multiply them, hence the restrictions for each have to be considered, which means that statement A is correct.

Summarizing, u cannot be calculated at x = 0, v cannot be calculated at x = 2, hence uv cannot be calculated for either x = 0 and x = 2.

More can be learned about the domain of a data-set at brainly.com/question/24374080

#SPJ1

3 0

2 years ago

If a fire is burning a building and it takes 2 hours to put it out using 2000 gal./min., what minimum diameter cylindrical tank

strojnjashka [21]

Answer:

The minimum diameter of the cylindrical tank needed to store the quantity needed to put out the fire is approximately 58.415 feet.

Step-by-step explanation:

A gallon equals 0.134 cubic feet. First, we determine the amount of water ( $Q$ ), measured in cubic feet, needed to put out the fire under the assumption that water is consumed at constant rate: