9:
-q^2 - r^2 + 3s
-9^2 - -6^2 + 3(-20)
-9^2 = -9 * -9 = 81
81 - -6^2 + 3(-20)
-6^2 = -6 * -6 = 36
81 - 36 + 3(-20)
3(-20) = -60
81 - 36 + -60
81 + 36 = 117
117 + (-60)
117 - 60= 57
57
10:
3| x + y |^2 - (xy)^2
3| 3 + -5 |^2 - (3-5)^2
(3-5) = 2
3| 3 + -5 |^2 - 2^2
|3 + -5| = 8
3|8|^2 - 2^2
8 * 8 = 64
3(64) - 2^2
2^2 = 2*2 = 4
3(64) - 4
3*64 = 192
192 - 4 = 188
188
11:
2x^2 - 5xy - y^3
2(-3)^2 - 5(-3-2) - -2^3
(-3-2) = -5
2(-3)^2 - 5(-5) - -2^3
-3^2 = -3 * -3 = -9
2(-9) - 5(-5) - -2^3
2^3 = 2 * 2 * 2 = 8
2(-9) - 5(-5) - 8
18 - 5(-5) - 8
5(-5) = -25
18 - (-25) - 8
18 + 25 - 8
18 + 25 = 43
43 - 8 = 35
35
12: -a^2 + 7b^4 -2c^3
—4^2 + 7(-2)^4 - 2(-3)^3
4^2 + 7(-2)^4 - 2(-3)^3
4 * 4 = 16
16 + 7(-2)^4 - 2(-3)^3
-2 * -2 * -2 * -2 = 16
16 + 7(16) - 2(-3)^3
-3 * -3 * -3 = -27
16 + 7(16) - 2(-27)
7 * 16 = 112
16 + 112 - 2(-27)
2 * -27 = -54
16 + 112 - -54
16 + 112 + 54
112 + 16 = 128
128 + 54 = 182
182
Answer:
Step-by-step explanation:
c. Look for a common factor in each term.
Answer:
33.18
Step-by-step explanation:
Use law of sines.
x / sin(65°) = 21 / sin(35°)
x = 21 sin(65°) / sin(35°)
x ≈ 33.18
We assume the composite figure is a cone of radius 10 inches and slant height 15 inches set atop a hemisphere of radius 10 inches.
The formula for the volume of a cone makes use of the height of the apex above the base, so we need to use the Pythagorean theorem to find that.
h = √((15 in)² - (10 in)²) = √115 in
The volume of the conical part of the figure is then
V = (1/3)Bh = (1/3)(π×(10 in)²×(√115 in) = (100π√115)/3 in³ ≈ 1122.994 in³
The volume of the hemispherical part of the figure is given by
V = (2/3)π×r³ = (2/3)π×(10 in)³ = 2000π/3 in³ ≈ 2094.395 in³
Then the total volume of the figure is
V = (volume of conical part) + (volume of hemispherical part)
V = (100π√115)/3 in³ + 2000π/3 in³
V = (100π/3)(20 + √115) in³
V ≈ 3217.39 in³
I think it is - 1/2
Or it could be 1/2 I am not that sure
Someone correct me if I am wrong
But I think it is - 1/2
