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3 years ago

Ln (3x+1)-ln (5+x) = ln 2

1 answer:

3 0

First you would simplify the left side to get,

ln( ( 3x+1 ) / ( 5+x ) ) = ln 2

Then raise both sides as the power of e, so it would basically cancel out the ln's.

3x+1 / 5+x = 2

3x+1 = 2( 5+x )

3x+1 = 10+2x

x = 9

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Part a which projectile spends more time in the air, the one fired from 30∘ or the one fired from 60∘? which projectile spends m

bearhunter [10]

The correct answer is the One fired from from 60° . This is because the projectile fired from 60° has a greater vertical velocity compared to the one fired from 30° and therefore spends more time on air. Vertical velocity is the velocity of a body as it moves upwards, it is normally affected by the gravitational acceleration, however it is not affected by the horizontal velocity.

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2 years ago

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Joe can cut and split a cord of firewood in 3 fewer hours than Dwight can. When they work together, it takes them 2 hours. How

aalyn [17]

Answer:

Dwight will take 6 hours to finish the job alone and Joe will take 3 hours to finish the job alone.

Step-by-step explanation:

Let us assume the time taken by Dwight to split a cord of firewood = K hrs

So, the per hour rate of Dwight = $(\frac{1}{K})$

As, Joe uses 3 LESS hours then Dwight.

So, the time taken by Joe to split a cord of firewood = (K- 3) hrs

So, the per hour rate of Joe = $(\frac{1}{K-3})$

Now, when both of them wok together, it takes them 2 hours.

So, the per hour rate of BOTH of them = $(\frac{1}{2})$

⇒ Per hour rate of ( Dwight + Joe) = $(\frac{1}{2} )$

$\implies (\frac{1}{K}) + (\frac{1}{K-3}) = (\frac{1}{2})$

Now, solving for the value of K , we get:

$(\frac{1}{K}) + (\frac{1}{K-3}) = (\frac{1}{2})\\\implies \frac{(K-3) + K}{K (K-3)} = (\frac{1}{2})\\\implies 2(2K -3) = K^2 - 3K\\\implies k^2 - 3K -4K +6 = 0\\\implies K^2 - 7K + 6= 0\\\implies K^2 - 6K - K + 6= 0\\\implies K(K-6) -1(K - 6)= 0\\\implies (K-6)(K-1) = 0$

Implies either K = 6 Or K = 1

But if K = 1, (K-3) = 1- 3 = -2 hours would be A CONTRADICTION.

⇒ K = 6 hours

Hence, Dwight will take 6 hours to finish the job alone and Joe will take (k-3) = (6-3) = 3 hours to finish the job alone.

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2 years ago

Ralph is 3 times as old as Sara. In 4 years, Ralph will be only twice as old as Sara will be then. Find Ralph's age now. Ralph's

IgorLugansk [536]

Let
R = Ralph's age
S = Sara's age

First statement is translated as:
S = 3R

Second statement is translated as:
S + 4 = 2(R + 4)

Use the first equation to be substituted into the second one in terms of R which is the one we are actually going to solve for Ralph's age.
Since S = 3R, then
3R + 4 = 2(R + 4)
3R + 4 = 2R + 8
3R - 2R = 8 - 4
R = 4 years old

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2 years ago

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Manny and Evan were flying paper airplanes. Manny’s airplane flew 36.5 centimeters and Evan’s airplane flew 18 centimeters. How

professor190 [17]

First subtract manny value 36.5 from Evan values 18 which will give u 18.5 cm which then u have to convert. Since 1 cm is about .4, we can multiply 18.5 by .4 to get the answer 7.4 inches

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3 years ago

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Your carry on bag can weigh at most 40 ponds. Write and solve an inequality to represent how much more weight you can add to the

Alborosie

Answer:

82ibs - 40ibs = 22ibs

Step-by-step explanation:

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3 years ago