Answer:
y = 7
Step-by-step explanation:
Mathematically, according to the Pythagoras’ theorem;
The square of the length of the hypotenuse of a right triangle is equal to the sum of the squares of the two other sides
The hypotenuse is the side that faces the right angle and it is represented by the square root of 85 here
Thus, we have it that;
(√85 )^2= 6^2 + y^2
85 = 36 + y^2
y^2 = 85-36
y^2 = 49
y = √49
y = 7
Answer:
792
Step-by-step explanation:
₁₂C₅ = (12!) / (5! (12-5)!)
₁₂C₅ = (12!) / (5! 7!)
₁₂C₅ = 792
Answer:Rolling a odd number is 3/6 and rolling a number less than five is 4/6
Step-by-step explanation:
Answer:
π − 2
Step-by-step explanation:
Graph of the region:
desmos.com/calculator/pcascl0frf
If we integrate with respect to x:
∫₀² (y − 0) dx
∫₀² sin⁻¹(x/2) dx
But we want to integrate with respect to y. Let's start by finding the new limits of integration.
y = sin⁻¹(x/2), so when x = 0, y = 0. When x = 2, y = π/2.
Next, we need to find x in terms of y.
sin y = x/2
x = 2 sin y
So the integral with respect to y is:
∫₀ᵖⁱ² (2 − x) dy
∫₀ᵖⁱ² (2 − 2 sin y) dy
Integrating:
(2y + 2 cos y + C) |₀ᵖⁱ²
(π + 2 cos (π/2) + C) − (0 + 2 cos 0 + C)
(π + 0 + C) − (0 + 2 + C)
π − 2