Answer:
He confused the height and the diameter
Step-by-step explanation:
the formula should have looked like this
V= 3.14 (2.5)^2 (24)
the reason why it is 2.5 and not 5 is because 5 is the diameter so divide 5 by 2 and you get 2.5
V= 3.14 (6.25) (24)
V= 3.14 (150)
V= 471
2). (x² - 5x) (2x - 3) = 2x³ -13x² + 15x
Actually, the point-slope form is
.. y -1 = (1/4)(x -12)
.. 4y -4 = x -12 . . . . multiply by 4
.. x -4y = -4 +12 . . . add 12-4y
.. x -4y = 8 . . . . . . . the equation in standard form
The y-intercept is -2 and the x-intercept is 2 (you can tell by where the line passes through the x and y)
Answer:
A) 6.32 in.
B) 71.56°
C) 36.88°
Step-by-step explanation:
To solve each part of the problem, let's pay attention to the triangle ABC shown in the figure.
A) The slant height (l) of the cone is the hypotenuse of the right triangle ABC, then, to calculate it you can apply the Pythagorean Theorem:
![l=\sqrt{(AB)^{2}+(BC)^{2}}=\sqrt{(2in)^{2}+(6in)^{2}}=6.32in](https://tex.z-dn.net/?f=l%3D%5Csqrt%7B%28AB%29%5E%7B2%7D%2B%28BC%29%5E%7B2%7D%7D%3D%5Csqrt%7B%282in%29%5E%7B2%7D%2B%286in%29%5E%7B2%7D%7D%3D6.32in)
B) The angle asked is the angle ∠A, then, you have:
![tan^{-1}(A)=\frac{opposite}{adjacent}\tan^{-1}(A)=\frac{6}{2}](https://tex.z-dn.net/?f=tan%5E%7B-1%7D%28A%29%3D%5Cfrac%7Bopposite%7D%7Badjacent%7D%5Ctan%5E%7B-1%7D%28A%29%3D%5Cfrac%7B6%7D%7B2%7D)
∠
°
C) The angle formed between the segments (which you can call α) that represent the slant heights is twice the angle ∠C.
By definition, the sum of the interior angles of a triangle is 180°,so you can calculate the angle ∠C as following:
∠![C=180-90-71.56=18.44](https://tex.z-dn.net/?f=C%3D180-90-71.56%3D18.44)
Then:
![\alpha=2*18.44](https://tex.z-dn.net/?f=%5Calpha%3D2%2A18.44)
°