Answer: 53.13
Explanation of answer: since theta is the unknown, then you must use the inverse of sin. (Which is sin with -1 subscript) I used a calculator and used inverse of sin and put 4/5 in parenthesis
Answer:
3,6),(−1,−2)
x=3,y=6
x=−1,y=−2
Step-by-step explanation:
It took a while for me to make sense of the diagram at first also, but once you look a little closer this is what it would look like if you took a right triangular prism and cut up all the edges so that it lay flat. In order to calculate the surface area, all we have to do is find the area of every polygon created by the edges.
Giant Rectangle: Across the diagram is a rectangle with a width of 8 cm and a length of 15 cm. It is composed of three other individual rectangles created by the edges. Instead of calculating the area for each individual rectangle and adding it up, we can just take the area of the whole rectangle.
area of rectangle = length x width = 15 x 8 = 120cm squared
Two Congruent Right Triangles: if you haven't noticed, the two triangles are actually congruent by SAS.
area of a triangle = 1/2 x height x base
= 1/2 x 5 x 4
= 2 x 5
= 10 cm squared
Don't forget to double this because there are TWO triangles.
Total Triangle Area = 20 cm squared
Total Area = 20 + 120 = 140 cm squared
Answers:
The series converges
The sum is -8/3
-----------------------------------------------------
a = -4 is the first term
r = -1/2 is the common ratio
the reason why is because the expression -4(-1/2)^(n-1) is in the form a(r)^(n-1). Notice how -4 matches with the 'a'; the -1/2 matches with the r
The common ratio will determine if the infinite series converges or not.
r = -1/2 leads to |r| = |-1/2| = 1/2 = 0.5
Since |r| < 1 (in this case 0.5 < 1) is true, this means the series does converge.
Put another way, because r = -1/2 = -0.5 makes -1 < r < 1 true, the series converges.
Use the formula below to find the converging value S
S = a/(1-r)
S = -4/(1-(-1/2))
S = -4/(1+1/2)
S = -4/(2/2+1/2)
S = -4/(3/2)
S = (-4/1)/(3/2)
S = (-4/1)*(2/3)
S = (-4*2)/(1*3)
S = -8/3
The infinite series converges to -8/3
So the sum is -8/3
