11. Describe and correct the error in evaluating the expression. –21-7)= -14
1 answer:
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48. The surface area of a cylinder is given by
... A = 2πr² + 2πrh = 2πr(r+h)
For r = 13 mi and h = 7 mi, this becomes
... A = 2π(13 mi)(13 mi + 7 mi) = 520π mi²
The surface area of the cylinder is 520π mi² ≈ 1634 mi².
49. The surface area of a rectangular prism is
... A = 2(LW + H(L+W))
For L = 20 m, W = 10 m, H = 7 m, this becomes
... A = 2((20 m)(10 m) + (7 m)(20 m + 10 m)) = 2(200 m² + 210 m²) = 820 m²
The surface area of the prism is 820 m².
50. The formula is the same as for problem 48.
For r = 10 m and h = 13 m, this becomes
... A = 2π(10 m)(10 m + 13 m) = 460π m² ≈ 1445 m²
The surface area of the cylinder is 460π m² ≈ 1445 m².
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When calculations are repetitive, it is convenient to let a calculator or spreadsheet do them.
Answer:
and
Step-by-step explanation:
Let's first isolate the trig function.
Add 1 one on both sides:
Divide both sides by :
Now recall .
or
The first ratio I have can be found using in the first rotation of the unit circle.
The second ratio I have can be found using you can see this is on the same line as the
so you could write
as
.
So this means the following:
is true when
where is integer.
Integers are the set containing {..,-3,-2,-1,0,1,2,3,...}.
So now we have a linear equation to solve:
Add on both sides:
Find common denominator between the first two terms on the right.
That is 24.
(So this is for all the solutions.)
Now I just notice that it said find all the solutions in the interval .
So if and we let
, then solving for
gives us:
( I just added
on both sides.)
So recall .
Then .
Subtract on both sides:
Simplify:
So we want to find solutions to:
with the condition:
That's just at and
So now adding to both gives us the solutions to:
in the interval:
.
The solutions we are looking for are:
and
Let's simplifying:
and
and
and
<u>Part A</u>
Using the Pythagorean on the right triangle PQR, with PQ and QR as the legs and PR as the hypotenuse,
<u>Part B</u>
