Answer:
A. The volume of the prism = 204.7 cm³
Step-by-step explanation:
The difficult part is finding the hight x in the triangle with sides 6 6 and 7.
The half of the base of this triangle = 3,5
So we have the right sided triangle with a hypothenusa of 6, one right side of 3,5 and one right side which is x (and is unknown).
Use Pythagoras to find the value of x.
x² + (3,5)² = 6²
x² = 6² - (3,5)²
x² = 36 - 12,25
x² = 23.75
x = +- SQRT(23.75)
{Only the positive part has a meaning.}
x = 4.873
So now it is easy.
The area of the triangle = 3.5 * x
with x = 4.873
The area of the triangle = 3.5 * 4.873
The area of the triangle = 17.06 cm²
The volume of the prism = 12 * the area of the triangle
The volume of the prism = 12 * 17.06
The volume of the prism = 204.67
rounded on 1 decimal.
The volume of the prism = 204.7 cm³
Answer: x = 8.4
Work: So, the goal of this equation is to get x by itself, and the first thing we need to do is get 22 out of that current side. To do that, we are going to add 22 on both sides, cancelling it on the side it's currently on. So, the new equation is 5x = 42. Now, we need to divide 5 on both sides, and like I said, I'll cancel on the side it's currently on. So, the answer is x = 8.4
<em>I hope this helps, and Happy Holidays! :)</em>
9514 1404 393
Answer:
c = -3; d = 5
Step-by-step explanation:
The function is differentiable if it is continuous and the derivative is continuous.
This function will be continuous if the limit as x approaches 3 from either side is the same. From the left, the limit is ...
5(3^2) +c = 45 +c
From the right, the limit is ...
d(3^2) -3 = 9d -3
__
The derivative will be continuous if the limit as x approaches 3 from either side is the same. From the left, the limit is ...
f'(x) = 10x
= 10(3) = 30
From the right, the limit is ...
f'(x) = 2dx
= 2d(3) = 6d
__
This gives us a pair of simultaneous equations in 'c' and 'd':
45 +c = 9d -3
6d = 30
The latter tells us d = 5. Then the former tells us ...
45 +c = 9(5) -3 ⇒ c = -3
The function is differentiable if c = -3 and d = 5.
_____
<em>Additional comment</em>
With these values, the function becomes ...
3/5
Since 3 is also 3/1 and 3/1 × 1/5 = 3/5
Answer:
287
Step-by-step explanation:
The lateral surface area of a cone is r*pi*l, where l is the slant height. This is much like the formula of a square pyramid, which is a good way to understand this formula. But that aside, Lets plug in some values:
We know the diameter is 12 so r = 6.
Now lets find the slant height. We can draw a right triangle using the height, radius, and slant height. So we get, sqrt(6^2 + 14^2 ) = l, by Pythagorean's theorem. Therefore, l = sqrt(232) which is roughly 15.23
So we have 6*pi*15.23 which is roughly 287