Problem 1
The formula to use is
s = r*theta
where,
s = arc length
r = radius
theta = angle in radians
Note: if the angle is not in radians, you have to convert it over to radians. However, in this case we are told the angle is "5pi/4 radians". So no conversion is needed.
In this case,
s = unknown (this is what we want to solve for)
r = 34
theta = 5pi/4
keep in mind that 5pi/4 is the same as (5/4)*pi
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Plug the value of r and theta into the formula to get...
s = r*theta
s = 34*(5pi/4)
s = (34*5/4)*pi
s = 42.5*pi
s = 42.5*3.14
s = 133.45
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Final Answer: 133.45
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Problem 2
sin(angle) = opposite/hypotenuse
sin(61.7) = 8/y
y*sin(61.7) = 8
y = 8/sin(61.7)
y = 9.08598042654456 ... use a calculator
y = 9 ... rounding to the nearest whole number
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Final Answer: 9
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Problem 3
We need to know the length of BC. Let's call this x for now. Use the pythagorean theorem to find x
x^2 + 14^2 = 50^2
x^2 + 196 = 2500
x^2 + 196-196 = 2500-196
x^2 = 2304
sqrt(x^2) = sqrt(2304)
x = 48
So BC = 48 units long
Now we can compute the tangent of angle B
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tan(angle) = opposite/adjacent
tan(B) = AC/BC
tan(B) = 14/48
tan(B) = 7/24
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Final Answer: 7/24
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Problem 4
In this current stage, I cannot answer this question because the image isn't showing up. On my end, all I see is a black rectangle with no triangle showing. It seems like some kind of glitch is happening. Please repost this image. Thank you.
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Problem 5
There are multiple answers here so it seems like there should be a restriction. Does it state what the restriction must be? Please let me know. Thank you.
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Problem 6
Rule:
sin(x) = cos(90-x)
where x is an angle in degrees
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Using that rule mentioned above, we can replace the "sin(x)" term with "cos(90-x)" then solve for x
cos(63) = sin(x)
cos(63) = cos(90-x)
both arguments must be equal, so 63 must be equal to 90-x
63 = 90-x
63+x = 90-x+x
x+63 = 90
x+63-63 = 90-63
x = 27
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Final Answer: 27
Kate: 1250 ≥ 525+25x
25x ≥1250 -525
25x ≥ 725
x ≥ 725 / 25
x≥ 29 weeks
Rebecca: 1350 ≥ 510 + 30x
30x ≥ 1350 - 510
30x≥ 840
x≥ 840 / 30
x≥28 weeks
Katie needs 1 more week than Rebecca
Estimate
<span>35.78 = 36
</span><span>12.31 = 12
so
36/12 = 3
answer
3</span>
so, start floor = x
x + 7 - 9 - 4 + 8 - 2 = 14
x = 14
the elevator started on the 14th floor.
to verify: 14 + 7 = 21 - 9 = 12 - 4 = 8 + 8 = 16 - 2 = 14
-3/2 , -3/7 , 0.75 , 2 i'm pretty sure this is right!
