All categories

3 years ago

Evaluate log3^8, given log3^2 is equivalent to 0.631

Mathematics

1 answer:

elixir [45]3 years ago

7 0

We will use the followin property of logarithms:

$log(a^b) = b log(a)$

So, we have

$log(3^2) = 2 log(3) = 0.631$

If you multiply both sides by 4, you get

$8log(3) = log(3^8) = 2.524$

You might be interested in

In a school egg drop challenge, 136 of the eggs broke out of 200 total. What percent of the eggs survived the drop?

SSSSS [86.1K]

136 divided by 200 is 0.68 which you then x100 which is 68%
=68%

6 0

3 years ago

This graph shows how the length of time a bicycle is rented is related to the rental cost. What is the rate of change shown in t

Romashka-Z-Leto [24]

Answer:

$4/ hour

Step-by-step explanation:

every hour you go you add 4 dollars

example: 1 hour is $2

2 hours is $6

8 0

3 years ago

Find exact values for sin θ, cos θ and tan θ if csc θ = 3/2 and cos θ < 0.

kumpel [21]

Answer:

Part 1) $sin(\theta)=\frac{2}{3}$

Par 2) $cos(\theta)=-\frac{\sqrt{5}}{3}$

Part 3) $tan(\theta)=-\frac{2\sqrt{5}}{5}$

Step-by-step explanation:

step 1

Find the $sin(\theta)$

we have

$csc(\theta)=\frac{3}{2}$

Remember that

$csc(\theta)=\frac{1}{sin(\theta)}$

therefore

$sin(\theta)=\frac{2}{3}$

step 2

Find the $cos(\theta)$

we know that

$sin^{2}(\theta) +cos^{2}(\theta)=1$

we have

$sin(\theta)=\frac{2}{3}$

substitute

$(\frac{2}{3})^{2} +cos^{2}(\theta)=1$

$\frac{4}{9} +cos^{2}(\theta)=1$

$cos^{2}(\theta)=1-\frac{4}{9}$

$cos^{2}(\theta)=\frac{5}{9}$

square root both sides

$cos(\theta)=\pm\frac{\sqrt{5}}{3}$

we have that

$cos(\theta) < 0$ ---> given problem

$cos(\theta)=-\frac{\sqrt{5}}{3}$

step 3

Find the $tan(\theta)$

we know that

$tan(\theta)=\frac{sin(\theta)}{cos(\theta)}$

we have

$sin(\theta)=\frac{2}{3}$

$cos(\theta)=-\frac{\sqrt{5}}{3}$

substitute

$tan(\theta)=\frac{2}{3}:-\frac{\sqrt{5}}{3}=-\frac{2}{\sqrt{5}}$

Simplify

$tan(\theta)=-\frac{2\sqrt{5}}{5}$

6 0

3 years ago

Use the given conditions to write an equation for the line in point-slope form and general form. Passing through (8 comma negat

miskamm [114]

Answer:

The answer to your question is y = -5x + 32 point-slope form

5x + y - 32 = 0 general form

Step-by-step explanation:

Data

(8, -8)

⊥ x - 5y - 6 = 0

Process

1.- Get the slope of the line given

x - 5y - 6 = 0

-5y = -x + 6

y = -x/-5 + 6/-5

y = x/5 - 6/5

slope = 1/5

slope of the new line -5, because the lines are perpendicular

2.- Get the equation of the new line

y - y1 = m(x - x1)

y + 8 = -5(x - 8)

y + 8 = -5x + 40

y = -5x + 40 - 8

y = -5x + 32 point-slope form

Equal to zero to find the general form

5x + y - 32 = 0 general form

5 0

3 years ago

Please help will give brainlist

RoseWind [281]

6(x²-4x+4-4)+1=0, 6(x-2)²-24+1=0, 6(x-2)²=23, x-2=±√(23/6), x=2±√(23/6)=2±1.95789, so x=3.95789 or 0.04211 approx. These are the zeroes.

6 0

3 years ago

Read 2 more answers