After the 30% discount was applied, Patricia paid $45.50 for the ring. What was the original price of the ring

These prisms are similar. Find the surface

Bumek [7]

Answer:

823.7 m^2

Step-by-step explanation:

The ratio of the side lengths is 6/5.

The ratio of the areas is the square of the ratio of the side lengths, 36/25.

572 m^2 * 36/25 = 823.7 m^2

5 0

2 years ago

Write each expression as an algebraic (nontrigonometric) expression in u, u > 0.

max2010maxim [7]

Answer:

$\displaystyle \sin\left(2\sec^{-1}\left(\frac{u}{10}\right)\right)=\frac{20\sqrt{u^2-100}}{u^2}\text{ where } u>0$

Step-by-step explanation:

We want to write the trignometric expression:

$\displaystyle \sin\left(2\sec^{-1}\left(\frac{u}{10}\right)\right)\text{ where } u>0$

As an algebraic equation.

First, we can focus on the inner expression. Let θ equal the expression:

$\displaystyle \theta=\sec^{-1}\left(\frac{u}{10}\right)$

Take the secant of both sides:

$\displaystyle \sec(\theta)=\frac{u}{10}$

Since secant is the ratio of the hypotenuse side to the adjacent side, this means that the opposite side is:

$\displaystyle o=\sqrt{u^2-10^2}=\sqrt{u^2-100}$

By substitutition:

$\displaystyle= \sin(2\theta)$

Using an double-angle identity:

$=2\sin(\theta)\cos(\theta)$

We know that the opposite side is √(u² -100), the adjacent side is 10, and the hypotenuse is u. Therefore:

$\displaystyle =2\left(\frac{\sqrt{u^2-100}}{u}\right)\left(\frac{10}{u}\right)$

Simplify. Therefore:

$\displaystyle \sin\left(2\sec^{-1}\left(\frac{u}{10}\right)\right)=\frac{20\sqrt{u^2-100}}{u^2}\text{ where } u>0$

4 0

2 years ago

If p is inversely proportional to the square of q, and p is 18 when q is

aniked [119]

Answer:

P=648

Step-by-step explanation:

6 0

2 years ago

Estimate the limit A B C D

Lera25 [3.4K]

Answer:

C. $\lim_{x\rightarrow f(x)=2$

Step-by-step explanation:

Given problem is $\lim_{x\rightarrow \frac{\pi}{4}}\frac{tan(x)-1}{x-\frac{\pi}{4}}$ .

Now we need to evaluate the given limit.

If we plug $\x=\frac{\pi}{4}$ , into given problem then we will get 0/0 form which is an indeterminate form so we can apply L Hospitals rule

take derivative of numerator and denominator

$\lim_{x\rightarrow \frac{\pi}{4}}\frac{tan(x)-1}{x-\frac{\pi}{4}}$

$=\lim_{x\rightarrow \frac{\pi}{4}}\frac{sec^2(x)-0}{1-0}$

$=\frac{sec^2(\frac{\pi}{4})-0}{1-0}$

$=\frac{(\sqrt{2})^2}{1}$

$=\frac{2}{1}$

=2

Hence choice C is correct.

5 0

2 years ago

Write the equation of the line in point-slope form that has slope 3 and passes through (2, -5)

Fynjy0 [20]

Answer:

y = 3x - 11

Step-by-step explanation:

Step 1:

y = mx + b Slope Intercept Form

Step 2:

y = 3x + b Input Slope

Step 3:

- 5 = 3 ( 2 ) + b Input x and y values

Step 4:

- 5 = 6 + b Multiply

Step 5:

- 11 = b Subtract 6 on both sides

Answer:

y = 3x - 11

Hope This Helps :)

5 0

2 years ago