7^2 - x^2 = 4^2 + 4^2
49 - x^2 = 32
x^2 = 49 - 32
x^2 = 17
x = sqrt (17) ≈ 4.1
Yep....hope I didn't miss any !!!!
Mmmm....good question ....here's my best attempt ....
a b n a b n a b n
1 3 1
2 3 8 2 5 32 2 7 128
3 3 27 3 5 243
4 3 64 4 5 1024
5 3 125
6 3 216
7 3 343
8 3 512
9 3 729
10 3 1000
11 3 1331
12 3 1728
Impressive, Math Whiz, that you know all the Prezzes !!!
I can name them from about Hoover on , but before his time I'd need Wikipedia ( or you !!! )
Area of rectangle = 7 x 4 = 28 cm^2
Area of trapezoid with height of 8 and bases of 7 and 19 =
(1/2) ( 8) ( 7 + 19 ) = 104 cm^2
Total area = ( 28 + 104) = 132 cm^2
Second one
Angle E = 180 - 50 - 66 = 64°
Law of Sines :
8 / sin 64° = EF /sin 50°
EF = 8 sin 50° / sin 64 ° = 6.8
Area = (1/2) ( 6.8 * 8) sin 66° = 24.8 cm^2
First one
sin F / 5 = sin 35 / 9
sin F = 5 sin 35 /9
arcsin ( 5 sin 35 / 9) = F ≈ 18.58°
Angle E =180 - 35 -18.58 = 126.42°
Area = (1/2) (5 * 9) sin 126.42 ≈ 18.1 cm^2
We have two inequalities to solve
(1/3)t - 5 < t - 2 and t - 2 ≤ -3t + 7
add 2 to both sides, add 2, 3t to both sides
subtract 1/3t from both sides
-3 < t - (1/3)t 4t ≤ 9
-3 < (2/3)t t ≤ 9/4
(-3)(3/2) < t
-9/2 < t
So t = ( -9/2 , 9/4 ]
Area =
2 * side^2 ( 1 + sqrt 2 ) =
2 * (20)^2 ( 1 + sqrt 2) =
800 ( 1 + sqrt 2) ≈ 1931.37 cm^2
The altitude, A, can be found as
cos 58° = A / 44
A = 44 * cos 58°
And x can be found as
tan 48° = A / x
x = A / tan 48° = 44 *cos 58° / tan 48° = 21
