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amm1812
3 years ago
6

A collection of nickels and dimes is worth $6.10. There are 67 coins in all. how many nickels are there?

Mathematics
1 answer:
Dmitrij [34]3 years ago
7 0

 Question 1:

 For this case, the first thing we must do is define variables.
 We have then:
 x: number of nickels
 y: number of dimes
 We write the system of equations that adapts to the problem.
 We have then:
 0.05x + 0.10y = 6.10
 x + y = 67
 Solving the system we have:
 x = 12
 y = 55
 Answer:
 there are 12 nickels

 Question 2:

 For this case, the first thing we must do is define variables.
 We have then:
 x: Allan's score
 y: Dave's score
 We write the system of equations that adapts to the problem.
 We have then:
 x + y = 375
 x = 2y-60
 Solving the system we have:
 x = 230
 y = 145
 Answer:
 
Dave: 145 Allan: 230
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3 years ago
At 3pm, the length of the shadow of a thin vertical pole standing on level ground is the same as the height of the pole. A while
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Answer: The height of the pole is 175.97 ( approx )

Step-by-step explanation:

Let the height of the pole is x cm,

Also, let the angle of elevation of the sun to the pole at 3 pm is \theta

Thus, by the question,

tan\theta = \frac{\text{ The height of the pole}}{\text{ The height of the shadow}}

\implies tan\theta = \frac{x}{x}    ( at 3pm the height of shadow = height of the pole)

\implies tan\theta = 1

\implies \theta = 45^{\circ}

Again, according to the question,

When the angle of elevation is   (\theta - 12^{\circ}),

The height of shadow = x + 95,

\implies tan(45-12)^{\circ}=\frac{x}{x+95}

\implies tan 33^{\circ}=\frac{x}{x+95}

\implies tan 33^{\circ}x + 95\times tan33^{\circ}=x

\implies tan 33^{\circ}x - x = - 95\times tan33^{\circ}

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Read 2 more answers
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