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julsineya [31]
3 years ago
12

A river is flowing at the rate of 2.4 miles an hour when a boy rows across it. If the boy rows at a still-water speed of 3.1 mil

es per hour and heads the boat perpendicular to the direction of the current. The ground speed of the boat is _____ miles per hour.

Mathematics
1 answer:
Xelga [282]3 years ago
7 0

Answer:

3.9 mi/h

Step-by-step explanation:

If the boy is rowing perpendicular to the current, the two vectors form a right triangle.

AB represents the downstream current, BC is the speed across the river, and AC is the ground speed of the boat

AC^2 = 2.4^2 + 3.1^2 =5.76 + 9.61 = 15.37

AC = sqrt(15.37) = 3.9 mi/h

The boat's speed over the ground is 3.9 mi/h.

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4 0
3 years ago
The function g(x) = 12,500(0.91)x represents the value of a piece of farm equipment after x years. Approximately when will its v
topjm [15]

Answer:

B. 7.3 years

Step-by-step explanation:

The question is wrong. The correct function is :

g(x)=12500(0.91)^{x}

We have the function g(x) that represents the value of a piece of farm equipment after x years.

This means that when x=0 its original value is :

g(0)=12500(0.91)^{0}=12500

Now we want to calculate approximately when will its value be half its original value. Then, we write :

\frac{12500}{2}=6250

6250 is half of its original value. We need to find x that satisfies the following equation :

g(x)=6250=12500(0.91)^{x}

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6250=12500(0.91)^{x} ⇒

0.5=(0.91)^{x}

Now we apply natural logarithm to each side of the equation :

ln(0.5)=ln[(0.91)^{x}]

Using logarithm properties :

ln(0.5)=ln[(0.91)^{x}] ⇒

ln(0.5)=x[ln(0.91)]

x=\frac{ln(0.5)}{ln(0.91)} ⇒

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