Answer:
Between 3 and 4
Step-by-step explanation:
The question is somewhat poorly posed because the equation doesn't involve <em>θ</em> at all. I assume the author meant to use <em>x</em>.
sec(<em>x</em>) = csc(<em>x</em>)
By definition of secant and cosecant,
1/cos(<em>x</em>) = 1/sin(<em>x</em>)
Multiply both sides by sin(<em>x</em>) :
sin(<em>x</em>)/cos(<em>x</em>) = sin(<em>x</em>)/sin(<em>x</em>)
As long as sin(<em>x</em>) ≠ 0, this reduces to
sin(<em>x</em>)/cos(<em>x</em>) = 1
By definition of tangent,
tan(<em>x</em>) = 1
Solve for <em>x</em> :
<em>x</em> = arctan(1) + <em>nπ</em>
<em>x</em> = <em>π</em>/4 + <em>nπ</em>
(where <em>n</em> is any integer)
In the interval 0 ≤ <em>x</em> ≤ 2<em>π</em>, you get 2 solutions when <em>n</em> = 0 and <em>n</em> = 1 of
<em>x</em> = <em>π</em>/4 <u>or</u> <em>x</em> = 5<em>π</em>/4
Answer:
105
Step-by-step explanation:
35 quarters ($8.75)
21 dimes ($2.10)
49 nickels ($2.45)
Answer:
61.25%
Step-by-step explanation:
How many ml of 20 percent acid should be added to pure acid
to make 70 ml of 30 percent acid?
:
let x = amt of 20% mixture
then
(70-x) = amt of pure acid
:
0.20x + (70-x) =0 .30(70)
0.20x + 70 - x = 21
= 21 - 70
-0.8x =-49
x = 61.25%
x = +61.25 ml of 20% stuff
You want to begin by changing your units to the same thing. The problem uses minutes and hours, and according to time 1 hour is 60 minutes.
Since we have 2 hours we want to multiply 60 by 2 to get 120. According to the problem, the biker to an extra 30 minutes and adding that to the time we already calculated we get 150.
We can say, the biker took 150 minutes to go through 45 miles. To find out how many miles he took per minute, we divide them (45/150) to get that he or she went through 0.3 miles per minute.
Again, we know 1 hour is 60 minutes, so to get how many miles per hour we want to multiply .3 by 60. This gets us 18.
Therefore, the biker travels 18 miles per hour
