Answer:
12
Step-by-step explanation:
Answer: 94.5
Step-by-step explanation:
9/2 × 21/4
Get common denominator
9 × 2 =18
2 × 2 = 4
18/4 × 21/4
21 × 18 = 378
378/4 = 94.5
Answer:
51 m^2
Step-by-step explanation:
The shaded area is the difference between the area of the overall figure and that of the rectangular cutout.
The applicable formulas are ...
area of a triangle:
A = (1/2)bh
area of a rectangle:
A = bh
area of a trapezoid:
A = (1/2)(b1 +b2)h
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We note that the area of a triangle depends only on the length of its base and its height. The actual shape does not matter. Thus, we can shift the peak of the triangular portion of the shape (that portion above the top horizontal line) so that it lines up with one vertical side or the other of the figure. That makes the overall shape a trapezoid with bases 16 m and 10 m. The area of that trapezoid is then ...
A = (1/2)(16 m + 10 m)(5 m) = 65 m^2
The area of the white internal rectangle is ...
A = (2 m)(7 m) = 14 m^2
So, the shaded area is the difference:
65 m^2 -14 m^2 = 51 m^2 . . . . shaded area of the composite figure
_____
<em>Alternate approach</em>
Of course, you can also figure the area by adding the area of the triangular "roof" to the area of the larger rectangle, then subtracting the area of the smaller rectangle. Using the above formulas, that approach gives ...
(1/2)(5 m)(16 m - 10 m) + (5 m)(10 m) - (2 m)(7 m) = 15 m^2 + 50 m^2 -14 m^2
= 51 m^2
Answer:
or 
.
Step-by-step explanation:
How are tangents and secants related to sines and cosines?
.
.
Sticking to either cosine or sine might help simplify the calculation. By the Pythagorean Theorem, 
. Therefore, for the square of tangents,
.
This equation will thus become:
.
To simplify the calculations, replace all 
with another variable. For example, let 
. Keep in mind that 
.
.
.
Solve this equation for 
:
.
.
.
Given that 
, 
is the only possible solution.
,
, where 
(i.e., 
is an integer.)
Given that 
,
.
or 
. Accordingly,
or .
