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3 years ago

A ) If f(x) = x^3-7/2, find f^-1(x) b ) find f^-1(28.5)

Mathematics

1 answer:

Lina20 [59]3 years ago

7 0

Step-by-step explanation:

The solution is more detailed

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What is the solution to the system of equations

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Coach Rivas can spend up to $750 on 30 swimsuits for the swim team. The inequality shown can be used to find the maximum amount

777dan777 [17]

Answer:

$0 < p ≤ $25

Step-by-step explanation:

We know that coach Rivas can spend up to $750 on 30 swimsuits.

This means that the maximum cost that the coach can afford to pay is $750, then if the cost for the 30 swimsuits is C, we have the inequality:

C ≤ $750

Now, if each swimsuit costs p, then 30 of them costs 30 times p, then the cost of the swimsuits is:

C = 30*p

Then we have the inequality:

30*p ≤ $750.

To find the possible values of p, we just need to isolate p in one side of the inequality.

So we can divide both sides by 30 to get:

(30*p)/30 ≤ $750/30

p ≤ $25

And we also should add the restriction:

$0 < p ≤ $25

Because a swimsuit can not cost 0 dollars or less than that.

Then the inequality that represents the possible values of p is:

$0 < p ≤ $25

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3 years ago

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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3 years ago

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