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Nookie1986 [14]
3 years ago
5

The difference of two numbers is 90 and their quotient is 10

Mathematics
1 answer:
bija089 [108]3 years ago
3 0
To solve this, set up two equations using the information you're given. Let's call our two numbers a and b:
1) D<span>ifference of two numbers is 90
a - b (difference of two numbers) = 90

2) The quotient of these two numbers is 10
a/b (quotient of the two numbers) = 10


Now you can solve for the two numbers.
1) Solve the second equation for one of the variables. Let's solve for a:
a/b = 10
a = 10b

2) Plug a =10b into the first equation and solve for the value of b:
a - b = 90
10b - b = 90
9b = 90
b = 10

3) Using b = 10, plug it back into one of the equations to find the value of a. I'll plug it back into the first equation:
a - b = 90
a - 10 = 90
a = 100

-------

Answer: The numbers are 100 and 10</span>
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Answer:

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We can use the notabl angle \pi/4 and we know that :

sin (\pi/4) = cos(\pi/4) = \frac{\sqrt{2}}{2}

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tan (5\pi/4) = \frac{sin(5\pi/4)}{cos(5\pi/4)}= \frac{\frac{sqrt{2}}{2}}{\frac{\sqrt{2}}{2}} = 1

Step-by-step explanation:

For this case we can use the notable angls given on the picture attached.

Part a

For this case we can use the fact that sin (\pi/3) = \frac{\sqrt{3}}{2}

And for this case since we ar einterested on -\frac{\pi}{3} and we know that the if we are below the y axis the sine would be negative then:

sin (-\pi/3) = -\frac{\sqrt{3}}{2}

Part b

From definition we can use the fact that tan x= \frac{sin x}{cos x} and we got this:

tan (5\pi/4) = \frac{sin(5\pi/4)}{cos(5\pi/4)}

We can use the notabl angle \pi/4 and we know that :

sin (\pi/4) = cos(\pi/4) = \frac{\sqrt{2}}{2}

Then we know that 5\pi/4 correspond to 225 degrees and that correspond to the III quadrant, and we know that the sine and cosine are negative on this quadrant. So then we have this:

tan (5\pi/4) = \frac{sin(5\pi/4)}{cos(5\pi/4)}= \frac{\frac{\sqrt{2}}{2}}{\frac{\sqrt{2}}{2}} = 1

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Hope this helps!

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===============================================

Work Shown:

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Step-by-step explanation:

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