is a right triangle with base length 1 and height 8, so the area of
is
.
The average value of
over
is given by the ratio
The denominator is just the area of
, which we already know. The average value is then simplified to
In the
-plane, we can describe the region
as all points
that lie between the lines
and
(the lines which coincide with the triangle's base and hypotenuse, respectively), taking
. So, the integral is given by, and evaluates to,
Answer:
Step-by-step explanation:
Z = (x-µ)/(s/√n)=(98.5-98.2)/(0.62/√19) = 2.11
left tail p-value = 0.9826
so 98.26% are lower.
Answer: 2 units left and 3 units up
Step-by-step explanation:
Answer:
Part 1)
Bob's mistake was to have used the cosine instead of the sine
The measure of the missing angle is 
Part 2) The surface area of the pyramid is 
Step-by-step explanation:
Part 1)
Let
x----> the missing angle
we know that
In the right triangle o the figure
The sine of angle x is equal to divide the opposite side angle x to the hypotenuse of the right triangle
Bob's mistake was to have used the cosine instead of the sine
Part 2) we know that
The surface area of the square pyramid is equal to the area of the square base plus the area of its four lateral triangular faces
so
![SA=b^{2}+4[\frac{1}{2}(b)(h)]](https://tex.z-dn.net/?f=SA%3Db%5E%7B2%7D%2B4%5B%5Cfrac%7B1%7D%7B2%7D%28b%29%28h%29%5D)
where
b is the length side of the square
h is the height of the triangular lateral face
In this problem
-------> by an 45° angle
so
Find the value of b
Find the surface area
![SA=12^{2}+4[\frac{1}{2}(12)(6)]=288\ cm^{2}](https://tex.z-dn.net/?f=SA%3D12%5E%7B2%7D%2B4%5B%5Cfrac%7B1%7D%7B2%7D%2812%29%286%29%5D%3D288%5C%20cm%5E%7B2%7D)
Answer:
3. 43.96 cm
4. 81.64 ft
Step-by-step explanation:
3. The formula for the circumference of a circle in terms of radius is ...
C = 2πr
When π is approximated by 3.14, this becomes ...
C ≈ 6.28r
The only answer choice even close to 6.28×(7 cm) is the one shown above.
___
4. The formula for the circumference of a circle in terms of diameter is ...
C = πd
When π is approximated by 3.14, this becomes ...
C ≈ 3.14d
The only answer choice anywhere close to 3.14×(26 ft) is the one shown above.
_____
<em>Comment on the solution</em>
For questions like these, you only need to be able to estimate the answer to 1 or 2 significant digits. The answer choices are not so close together as to cause any confusion.
6×7 = 42, so the answer will be a few more than 42.
3×26 = 78, so the answer will be within a few numbers larger than that.
In each case, the answer is the largest value on the list. The other choices differ by a factor of 2, so aren't even close.
