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2 years ago

Help please asap algebra 2

Mathematics

1 answer:

timurjin [86]2 years ago

4 0

X = approximately 633

Steps:
lnx + ln3x = 14

ln3x^2 = 14 : Use the log property of addition which is to multiply same log together so you multiply x and 3x because they have log in common

(ln3x^2) = (14) : take base of e on both sides to get rid of the log
e e

3x^2 = e^14 : e cancels out log on the left side and the right side is e^14

x^2 = e^14 / 3 : divide both sides by 3

√x^2 = √(e^14 / 3) : take square root on both sides to get rid of the square 2 on x

x = √(e^14) / √3 : square root cancels out square 2 leaving x by itself

x = e^7 / √3 : simplify the √(e^14) so 14 (e^14) divide by 2 (square root) = 7

x = 633.141449221 : solve

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Read 2 more answers

At a ski resort, 1/4 of the 300 skiers are beginners, and 1/4 of the 260 snowboarders are beginners. The resort staff used the d

Evgen [1.6K]

$\frac{1}{4}(300 + 260) = \frac{1}{4} \times 300 + \frac{1}{4} \times 260$ is the expression that demonstrates the distributive property

Solution:

Given that,

At a ski resort, $\frac{1}{4}$ of the 300 skiers are beginners

$\frac{1}{4}$ of the 260 snowboarders are beginners

The resort staff used the distributive property to make the calculation of the total number of beginners on the ski slopes

Beginners in skiers = $\frac{1}{4}$ of the 300

Beginners in snowboarders = $\frac{1}{4}$ of the 260

Total number of beginners = Beginners in skiers + Beginners in snowboarders

$\text{ Total number of beginners } = \frac{1}{4}(300) + \frac{1}{4}(260)$

We have to use distributive property

The distributive property of multiplication states that when a number is multiplied by the sum of two numbers, the first number can be distributed to both of those numbers and multiplied by each of them separately, then adding the two products together for the same result as multiplying the first number by the sum

Therefore, our expression is:

$\frac{1}{4}(300) + \frac{1}{4}(260)$

We have to take $\frac{1}{4}$ as common term to get distributive property

$\frac{1}{4}(300) + \frac{1}{4}(260) = \frac{1}{4}(300 + 260)\\\\\frac{1}{4} \times 300 + \frac{1}{4} \times 260 = \frac{1}{4}(300 + 260)$

Thus distributive property is applied

8 0

2 years ago

There is a balcony that forms part of a circle around a stage, and they need to put up a safety railing. How long of a railing d

alexandr1967 [171]

A sector is a part of a circle that is formed by two radii, and an arc. So that the length of the safety railing required is 31.4 feet.

A sector is a part of a circle that is formed by two radii, and an arc, thus forming a central angle.

Thus the required length of safety railing can be considered as the arc of the sector.

So that;

length of an arc = (θ / $360^{o}$ ) * 2 $\pi$ r

where θ is the measure of the central angle of the sector, and r is the radius of the sector.

From the given question, θ = 45°, and r = 40 feet.

So that,

length of the safety railing = (45° / $360^{o}$ ) * 2 * 3.14 * 40

= 0.125 * 2* 3.14* 40

length of safety railing = 31.4

Therefore, the length of the safety railing required is 31.4 feet.

For more clarifications on the length of an arc, visit: brainly.com/question/2005046

#SPJ1

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1 year ago