Answer:
Step-by-step explanation:
Step 1 Answer: Yes, 3
Step 2 Answer: Yes, 5
Step 3 Answer: No
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
3/4 is .75. translate that to percentages, and you get 75%. This means that it is likely that 75% of the 340 students in total will vote for Nuncio.
write it out:
.75*340
solve:
255
about 255 students are likely to vote for Nuncio
Total surface area = 2 * circular base + circumference * height
= 2 * pi*(4)^2 + 8pi * 12
= 32pi + 96pi
= 128pi answer
-24°F
Step-by-step explanation:
-18°F + 13°F - 19°F
= -5°F - 19°F
= -24°F
