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emmasim [6.3K]
3 years ago
15

(PLEASE ANSWER!!) a college student completed some courses worth 4 credits and some courses worth 3 credits. the student earned

a total of 59 credits after completing 18 courses. how many courses worth 3 credits did the student complete?
Mathematics
1 answer:
Ierofanga [76]3 years ago
5 0

The college student took 13 courses of 3 credit hours.

Step-by-step explanation:

Given,

Total credits = 59

Total courses = 18

Let,

Number of 3 credit hour courses = x

Number of 4 credit hour courses = y

According to given statement;

x+y=18     Eqn 1

3x+4y=59   Eqn 2

We will eliminate y to find the number of 3 credit hour courses, therefore,

Multiplying Eqn 1 by 4

4(x+y=18)\\4x+4y=72\ \ \ Eqn\ 3

Subtracting Eqn 2 from Eqn 3

(4x+4y)-(3x+4y)=72-59\\4x+4y-3x-4y=13\\x=13

The college student took 13 courses of 3 credit hours.

Keywords: linear equation, subtraction

Learn more about linear equations at:

  • brainly.com/question/10708697
  • brainly.com/question/10710410

#LearnwithBrainly

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shusha [124]

Question:

\frac{2tan30^{\circ}}{1 + tan^2(30^{\circ})}

Answer:

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Step-by-step explanation:

Given

\frac{2tan30^{\circ}}{1 + tan^2(30^{\circ})}

Required

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In trigonometry:

tan(30^{\circ}) = \frac{1}{\sqrt{3}}

So, the expression becomes:

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Simplify the denominator

\frac{2tan30^{\circ}}{1 + tan^2(30^{\circ})} = \frac{2 * \frac{1}{\sqrt{3}}}{1 + \frac{1}{3}}

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\frac{2tan30^{\circ}}{1 + tan^2(30^{\circ})} = \frac{\frac{2}{\sqrt{3}}}{ \frac{3+1}{3}}

\frac{2tan30^{\circ}}{1 + tan^2(30^{\circ})} = \frac{\frac{2}{\sqrt{3}}}{ \frac{4}{3}}

Express the fraction as:

\frac{2tan30^{\circ}}{1 + tan^2(30^{\circ})}= \frac{2}{\sqrt 3} / \frac{4}{3}

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Answer:

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This is an alternating series, and converges.

Therefore, the interval of convergence is:

0 < x ≤ 16

Or, in interval notation, (0, 16].

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