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3 years ago

7

What is the solution to the equation log(2x + 4) = 2? Round to the nearest thousandth, if necessary.

1 answer:

Kazeer [188]3 years ago

5 0

Answer: 48

Step-by-step explanation:

$log_{b}M=n--> M=b^{n} \\log(2x+4)=2\\b=10, M=2x+4, n= 2 \\\\2x+4=10^{2} \\2x+4=100\\2x=96\\x=48$

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i f N(-7,-1) is a point on the terminal side of ∅ in standard form, find the exact values of the trigonometric functions of ∅.

Natali [406]

Answer:

$sin\ \varnothing = \frac{-1}{10}\sqrt 2$

$cos\ \varnothing = \frac{-7}{10}\sqrt 2$

$tan\ \varnothing = \frac{1}{7}$

$cot\ \varnothing = 7$

$sec\ \varnothing = \frac{-5}{7}\sqrt 2$

$csc\ \varnothing = -5\sqrt 2$

Step-by-step explanation:

Given

$N = (-7,-1)$ --- terminal side of $\varnothing$

Required

Determine the values of trigonometric functions of $\varnothing$ .

For $\varnothing$ , the trigonometry ratios are:

$sin\ \varnothing = \frac{y}{r}$ $cos\ \varnothing = \frac{x}{r}$ $tan\ \varnothing = \frac{y}{x}$

$cot\ \varnothing = \frac{x}{y}$ $sec\ \varnothing = \frac{r}{x}$ $csc\ \varnothing = \frac{r}{y}$

Where:

$r^2 = x^2 + y^2$

$r = \sqrt{x^2 + y^2$

In $N = (-7,-1)$

$x = -7$ and $y = -1$

So:

$r = \sqrt{(-7)^2 + (-1)^2$

$r = \sqrt{50$

$r = \sqrt{25 * 2$

$r = \sqrt{25} * \sqrt 2$

$r = 5 * \sqrt 2$

$r = 5 \sqrt 2$

<u>Solving the trigonometry functions</u>

$sin\ \varnothing = \frac{y}{r}$

$sin\ \varnothing = \frac{-1}{5\sqrt 2}$

Rationalize:

$sin\ \varnothing = \frac{-1}{5\sqrt 2} * \frac{\sqrt 2}{\sqrt 2}$

$sin\ \varnothing = \frac{-\sqrt 2}{5*2}$

$sin\ \varnothing = \frac{-\sqrt 2}{10}$

$sin\ \varnothing = \frac{-1}{10}\sqrt 2$

$cos\ \varnothing = \frac{x}{r}$

$cos\ \varnothing = \frac{-7}{5\sqrt 2}$

Rationalize

$cos\ \varnothing = \frac{-7}{5\sqrt 2} * \frac{\sqrt 2}{\sqrt 2}$

$cos\ \varnothing = \frac{-7*\sqrt 2}{5*2}$

$cos\ \varnothing = \frac{-7\sqrt 2}{10}$

$cos\ \varnothing = \frac{-7}{10}\sqrt 2$

$tan\ \varnothing = \frac{y}{x}$

$tan\ \varnothing = \frac{-1}{-7}$

$tan\ \varnothing = \frac{1}{7}$

$cot\ \varnothing = \frac{x}{y}$

$cot\ \varnothing = \frac{-7}{-1}$

$cot\ \varnothing = 7$

$sec\ \varnothing = \frac{r}{x}$

$sec\ \varnothing = \frac{5\sqrt 2}{-7}$

$sec\ \varnothing = \frac{-5}{7}\sqrt 2$

$csc\ \varnothing = \frac{r}{y}$

$csc\ \varnothing = \frac{5\sqrt 2}{-1}$

$csc\ \varnothing = -5\sqrt 2$

3 0

3 years ago

At the amusement park, Laura paid $6.00 for small cotton candy. Her older brother works at the park, and he told her they mark u

Rudiy27

$2 because 6/%300= 2

3 0

3 years ago

Read 2 more answers

The store,s rectangular floor is 42 meters long and 39 meters wide. How many square meters of flooring do they need? Use estimat

uranmaximum [27]

First multiply, so 42 x 39, which equals 1,638, then estimate, round 42 to 40, and 39 to 40, and do 40 x 40 = 1,600 which is close to your answer, so good.

3 0

4 years ago

Fantom [35]

Hi Timothy,

1. Write a rule for the sequence.

8, -1, -10, -19...

A. Start with 8 and add -9 repeatedly

B. star with -9 and add 8 repeatedly

C. start with 8 and add 9 repeatedly

D. start with 8 and subtract -9 repeatedly---

Answer - So you have to start with -9 then keep subtracting 9. Thats what I think the answer is but the answer is not stated in the question. Let me know on what that is. The closest answer is probably either B or D.

2. find the next three terms of the sequence.

-6, -24, -96, -384

1) -768, -1536 , -3072

2) -768, -3072, -12288

3) -1536, -6144 , -24567

4) -1536, -9216, -36864

The rule is multiplying by 4!

So the correct answer is 3) -1536, -6144 , -24567

5 0

3 years ago

0.5 of what number is 3

Radda [10]

Answer:

6

Step-by-step explanation:

Half of 6 is 3

5 0

3 years ago

Read 2 more answers