Answer:
78, 1275
Step-by-step explanation:
a) 12th= 78
b) 50th=1275
Simplifying
8 + 6t = 3t + t
Combine like terms: 3t + t = 4t
8 + 6t = 4t
Solving
8 + 6t = 4t
Solving for variable 't'.
Move all terms containing t to the left, all other terms to the right.
Add '-4t' to each side of the equation.
8 + 6t + -4t = 4t + -4t
Combine like terms: 6t + -4t = 2t
8 + 2t = 4t + -4t
Combine like terms: 4t + -4t = 0
8 + 2t = 0
Add '-8' to each side of the equation.
8 + -8 + 2t = 0 + -8
Combine like terms: 8 + -8 = 0
0 + 2t = 0 + -8
2t = 0 + -8
Combine like terms: 0 + -8 = -8
2t = -8
Divide each side by '2'.
t = -4
Simplifying
t = -4
Answer: Choice C) 10.5
The distance from A to C is 7 units (count out the spaces between the two points, or subtract y coordinates 4-(-3) = 4+3 = 7)
Let AC = 7 be the base of the triangle. You might want to rotate the image so that AC is laying horizontally rather than being vertical.
Now move to point P. Walk 3 spaces to the right until you land on segment AC. This shows that the height of the triangle is 3 when the base is AC = 7.
base = 7, height = 3
area of triangle = (1/2)*base*height
area of triangle = 0.5*7*3
area of triangle = 10.5 square units
Answer:
25.133 units
Step-by-step explanation:
Since the density ρ = r, our mass is
m = ∫∫∫r³sinθdΦdrdθ. We integrate from θ = 0 to π (since it is a hemisphere), Φ = 0 to 2π and r = 0 to 2 and the maximum values of r = 2 in those directions. So
m =∫∫[∫r³sinθdΦ]drdθ
m = ∫[∫2πr³sinθdθ]dr ∫dФ = 2π
m = ∫2πr³∫sinθdθ]dr
m = 2π∫r³dr ∫sinθdθ = 1
m = 2π × 4 ∫r³dr = 4
m = 8π units
m = 25.133 units
