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miv72 [106K]
3 years ago
9

A boat makes a 120-mile trip downstream in 3 hours but makes the return trip in 4 hours. If b = the rate of the boat in still wa

ter and c = the rate of the current, which of the following equations represents the trip downstream?
3(b - c) = 120
3(b + c) = 120
4(b + c) = 120
Mathematics
2 answers:
soldi70 [24.7K]3 years ago
8 0
I think C will be the answer
Snezhnost [94]3 years ago
7 0
The rate downstream = b + c because the water and boat are moving in same direction.

also time downstream = 3 hours

 time * rate = distance 

3 * (b + c)  = 120


so its the second choice.
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Answer:

B. 1 and D. 3.  

Step-by-step explanation:

The figure below shows the graphs of f(x) = 3x - 1 (red) and g(x) = 2^x (blue).

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The solutions are at x = 1 and x = 3.

Check:

3 × 1 - 1 = 2¹     3 × 3 -1 = 2³

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4 years ago
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pishuonlain [190]

Answer:

a) SA = 331.2 mi²

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Step-by-step explanation:

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V = (6 x 0.5 x 5.2 x 6) x 4 = 374.4 mi³

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3 years ago
What is the exact solution for the equation
Nostrana [21]

Answer:

Option C is correct.

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Step-by-step explanation:

Given the equation: 2^{x+2} = 5^{2x}

Using logarithmic rules:

  • a^x=b^y ⇒ x \ln a =y \ln b
  • \ln x^a = a\ln x

Given: 2^{x+2} = 5^{2x}

Taking logarithmic both sides:

\ln 2^{x+2} = \ln 5^{2x}

By logarithmic rules;

(x+2) \ln 2 = (2x) \ln 5

Using distributive property i.e a\cdot (b+c) = a\cdot b + a\cdot c

x \ln 2 +2 \ln 2 = 2x \ln 5

Subtract x \ln 2 from both sides we get;

x \ln 2 +2 \ln 2 - x \ln 2= 2x \ln 5 - x \ln 2

Simplify:

2 \ln 2= 2x \ln 5 - x \ln 2

or

2 \ln 2= x (2\ln 5 - \ln 2)

Divide both sides by (2\ln 5 - \ln 2) we get;

\frac{2\ln 2}{2\ln 5 - \ln 2} = x

Therefore, the exact solution of the given equation is \frac{2\ln 2}{2\ln 5 - \ln 2}


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