This problem involves the uses of the Pythagorean Theorem as well as the use of Sine.
To start we need to identify what we know and what we don't know. We know that there are two triangles. We are given 2 sides lengths and an angle in one and only an angle in the other. They share one side meaning when we are given 2 sides in one triangle it will be easy to get the third side. What we don't know is the side length of CB DB or CD. We need to find CB in order to find CD.
<em>Pythagorean Theorem for side length CB:</em>
12^2-6^2=√108
√108=10.4 (average)
So CB is equal to 10.4
<em>Sine Calculation for side length CD:</em>
Since we have angle 56* we will use the length we found which will be the opposite side from the angle and then input x for our hypotenuse CD in order to solve.
sin 56* = 10.4/x
sin 56* × x = 10.4/x × x
sin 56*x = 10.4
/sin 56* /sin 56*
x = 12.544....
or 12.6 (average)
So, to conclude, our answer for CD is 12.6cm.
Hope I helped!
Answer:
The answer is below
Step-by-step explanation:
The volume of the cylinder with radius (r) and height (h) is given as:
Volume = πr²h
17 = πr²h
h = 17 / πr²
Let k represent the cost of the side and 2k the cost of the bottom.
The area of the side = 2πrh, hence the cost of the side = k(2πrh)
The area of the top and bottom = 2πr², hence the cost of the top and bottom = 2k(2πr²)
The total cost (T) = cost of side + cost of the top and bottom
T = k(2πrh) + 2k(2πr²)
T = 2kπ(rh + 2r²)
Put h = 17/πr²
T = 2kπ (r×17/πr² + 2r²)
T = 2kπ(17/πr + 2r²)
The minimal cost is at dT/dr = 0
![\frac{dT}{dr} =0=\frac{d}{dr} [2k\pi(\frac{17}{\pi r} +2r^2)]\\\\4r-\frac{17}{\pi r^2} =0\\\\4r=\frac{17}{\pi r^2}\\\\r^3=\frac{17}{4\pi }=1.35\\\\r=\sqrt[3]{1.35}\\\\r=1.1\ m\\\\h=\frac{17}{\pi r^2} =\frac{17}{\pi (1.1)^2} \\\\h=4.42\ m](https://tex.z-dn.net/?f=%5Cfrac%7BdT%7D%7Bdr%7D%20%3D0%3D%5Cfrac%7Bd%7D%7Bdr%7D%20%5B2k%5Cpi%28%5Cfrac%7B17%7D%7B%5Cpi%20r%7D%20%2B2r%5E2%29%5D%5C%5C%5C%5C4r-%5Cfrac%7B17%7D%7B%5Cpi%20r%5E2%7D%20%3D0%5C%5C%5C%5C4r%3D%5Cfrac%7B17%7D%7B%5Cpi%20r%5E2%7D%5C%5C%5C%5Cr%5E3%3D%5Cfrac%7B17%7D%7B4%5Cpi%20%7D%3D1.35%5C%5C%5C%5Cr%3D%5Csqrt%5B3%5D%7B1.35%7D%5C%5C%5C%5Cr%3D1.1%5C%20m%5C%5C%5C%5Ch%3D%5Cfrac%7B17%7D%7B%5Cpi%20r%5E2%7D%20%20%3D%5Cfrac%7B17%7D%7B%5Cpi%20%281.1%29%5E2%7D%20%5C%5C%5C%5Ch%3D4.42%5C%20m)
recalculate 3/7 to have the same denominator as 8/14 ( 14)
so multiply both top and bottom by 2. 3/7 becomes 6/14
8/14 - 6/14 = 2/14 reduces to 1/7
Hobbes made more snowballs by 1/7
24+x=14
you can get it by subtracting 24 from 14
therefor the answer issa
x=-10
Answer:
Recursive sequence
Step-by-step explanation:
<u>Explanation</u>:-
- Each next term was gotten by adding a previous two terms .This sort of sequence is called the recursive sequence.
- Example:- 1, 1, 2,3,5,8.........
The first two terms are adding and we get the third term
In above example first term is '1' and second term also '1'
adding these two terms we get the third term is '2'
and same as adding second term and third term we get the fourth is "3"
- This sequence is called the Fibonacci sequence and also it is called the recursive sequence.
