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Fed [463]
3 years ago
9

5000 is 1/10 of what

Mathematics
2 answers:
KatRina [158]3 years ago
8 0
<span>The correct answer is 50,000.

Explanation<span>:
We can set up the equation 5000=1/10x to represent this situation.

To solve, we will divide both sides by 1/10:
5000</span></span>÷<span><span>(1/10) = (1/10x)</span></span>÷<span><span>(1/10)
5000</span></span>÷<span><span>(1/10) = x.

To divide fractions, flip the second one and multiply; this gives us
5000*(10/1) = x
50000 = x.</span></span>
leva [86]3 years ago
7 0

\boxed{ \ 5,000 \ is \ \frac{1}{10} \ of \ 50,000 \ }  

<h3>Further explanation  </h3>

The question can be rewritten to \boxed{ \ 5,000 \ is \ \frac{1}{10} \ of \ P \ }  

This case about equations with one variable. We have to solve this calculation to obtain the value of P. Our task is to isolate the variable P alone at the end of the process on one side of the equation until the variable will be equal to a value on the opposing side.  

Let's arrange it into an equation, i.e., \boxed{ \ 5,000 \ = \ \frac{1}{10} \times \ P \ }  

Turn this equation over so that the position of variable P is on the left side.  

\boxed{ \ P \times \frac{1}{10} = 5,000 \ }  

Both sides are multiplied by 10 to isolate P on the left side. The fraction are eliminated.  

\boxed{ \ P \times \frac{1}{10} \times 10 = 5,000 \times 10 \ }  

P = 50,000  

Therefore, we have calculated the number that was asked.  

Hence \boxed{ \ 5,000 \ is \ \frac{1}{10} \ of \ 5,0000 \ }  

<u>Note:  </u>

The significant thing to carry out is how to manipulate both sides of the equation with the algebraic properties of equality such as:  

  • Adding  
  • Subtracting  
  • Multiplying, and/or  
  • Dividing both sides of the equation with a similar number

And the commutative property of multiplication, i.e., \boxed{ \ a \times b = b \times a \ }

<h3>Learn more  </h3>
  1. How do I solve \frac{2}{7}m - \frac{1}{7} = \frac{3}{14}? brainly.com/question/1682776  
  2. The similar case brainly.com/question/96882
  3. Investigating the stages of solving a word problem about one variable linear equations brainly.com/question/2038876  

Keywords: 5,000 is 1/10 of, solve, 50,000, variable, 2/7m - 1/7 = 3/14, algebraic properties of equality, one, linear equation, isolated, manipulate, operations, add, subtract, multiply, divide, fraction, equate, denominator, numerator, both sides, equal, the opposite, both sides are multiplied by, turn, calculation

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This is finding exact values of sin theta/2 and tan theta/2. I’m really confused and now don’t have a clue on how to do this, pl
Lostsunrise [7]

First,

tan(<em>θ</em>) = sin(<em>θ</em>) / cos(<em>θ</em>)

and given that 90° < <em>θ </em>< 180°, meaning <em>θ</em> lies in the second quadrant, we know that cos(<em>θ</em>) < 0. (We also then know the sign of sin(<em>θ</em>), but that won't be important.)

Dividing each part of the inequality by 2 tells us that 45° < <em>θ</em>/2 < 90°, so the half-angle falls in the first quadrant, which means both cos(<em>θ</em>/2) > 0 and sin(<em>θ</em>/2) > 0.

Now recall the half-angle identities,

cos²(<em>θ</em>/2) = (1 + cos(<em>θ</em>)) / 2

sin²(<em>θ</em>/2) = (1 - cos(<em>θ</em>)) / 2

and taking the positive square roots, we have

cos(<em>θ</em>/2) = √[(1 + cos(<em>θ</em>)) / 2]

sin(<em>θ</em>/2) = √[(1 - cos(<em>θ</em>)) / 2]

Then

tan(<em>θ</em>/2) = sin(<em>θ</em>/2) / cos(<em>θ</em>/2) = √[(1 - cos(<em>θ</em>)) / (1 + cos(<em>θ</em>))]

Notice how we don't need sin(<em>θ</em>) ?

Now, recall the Pythagorean identity:

cos²(<em>θ</em>) + sin²(<em>θ</em>) = 1

Dividing both sides by cos²(<em>θ</em>) gives

1 + tan²(<em>θ</em>) = 1/cos²(<em>θ</em>)

We know cos(<em>θ</em>) is negative, so solve for cos²(<em>θ</em>) and take the negative square root.

cos²(<em>θ</em>) = 1/(1 + tan²(<em>θ</em>))

cos(<em>θ</em>) = - 1/√[1 + tan²(<em>θ</em>)]

Plug in tan(<em>θ</em>) = - 12/5 and solve for cos(<em>θ</em>) :

cos(<em>θ</em>) = - 1/√[1 + (-12/5)²] = - 5/13

Finally, solve for sin(<em>θ</em>/2) and tan(<em>θ</em>/2) :

sin(<em>θ</em>/2) = √[(1 - (- 5/13)) / 2] = 3/√(13)

tan(<em>θ</em>/2) = √[(1 - (- 5/13)) / (1 + (- 5/13))] = 3/2

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2 years ago
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