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
Hypotenuse^2 = leg1^2 + leg2^2
3^2 = 2^2 + leg2^2
leg2^2 = 3^2 -2^2
leg2^2 =9 -4
leg2^2 = 5
leg2 = square root (5)
What do you mean by "relative growth rate?"
You need to specify whether this situation involves compounding, and, if it does, whether it's continuous compounding, monthly, annual or what.
Just supposing that it's semi-annual compounding:
A = $35000 (1 + 0.051/2)^(5*2)
= $35000(1.0255)^10 = $35000 (1.2863) = $45021.99 (answer)
Answer:
Step-by-step explanation:
1. JK ∥ LM, KL ∥ MN Given
2. ∠KJL ≅ ∠MLN; ∠KLJ ≅ ∠MNL c. Corresponding Angles
3. JK ≅ LM Given
4. ∆JKL ≅ ∆LMN e. AAS
