Volume of a sphere: (4/3)πr³
r=radius=9 in
Volume=(4/3)*π*(9 in)³=972π cubic inches≈3053.63 in³
answer: D) 972π cubic inches (3053.63 in³ is correct)
I'm guessing the diagram shows a ladder leaning against a wall, making a right angle triangle with respect to the ground and the wall.
So, the wall's height is going to be the 'h', which will also be the 'opposite side' from the angle <span>ϴ which is made from the ladder and the ground.
</span>The ladder's length (18 foot) is going to be the 'hypotenuse' side and the other remaining side will be the 'adjacent'.
Now, once you've sorted out which side is which, we have to find the h (opp), and according to SOH CAH TOA, we will choose Sin<span>ϴ = opp/hyp.
</span>so Sinϴ = h/18....now we gotta find h, so 'cross multiply' the equation to get h = 18 x sin<span>ϴ.
</span>
To find angle ϴ, simply take the inverse of Sinϴ= h/18... and you'll get ϴ = sin-1 (sin inverse) h/18
Hope this helps
Answer:
The average rate of change is 8
Step-by-step explanation:
Mathematically, we have the average rate of change over a given interval as;
f(b) - f(a)/b-a
Where the interval is [a,b]
With respect to this question, a = 3 and b = 5
f(a) = f(3) = 3^2 - 4 = 9-4 = 5
f(b) = f(5) = 5^2 - 4 = 25-4 = 21
Thus, the average rate of change over the intervals will be;
(21-5)/(5-3) = 16/2 = 8
To solve for the other leg, you need to use Pythagorean theory.
The theory states that C^2 = A^2 + B^2
In your case, you have to solve for B.
C = 40 (hypotenuse) A = 24 (leg 1)
The formula rewritten for B is
Now, you can solve.
Therefore, B = 32.
So the second leg is 32 feet.
