Calculate the length of each path using the law of cosines:
AB = √(8^2 + 8^2 - 2*8*8*cos(36)
AB = 4.94 ft.
XY = √(8^2 + 8^2 - 2*8*8*cos(79)
XY = 10.18 ft.
ZY = √(8^2 + 8^2 - 2*8*8*cos(65)
ZY = 8.60 ft.
XY is longer than ZY and ZY is longer than AB
The first choice is correct.
Given data:
The given cube .
The expression for the volume of the sphere is,
Thus, the volume of the sphere is 261 cubic-m.
Answer:
sorry I don't remember bye I will try to remember
Answer <u>(assuming it can be in slope-intercept form)</u>:
Step-by-step explanation:
1) First, find the slope of the line by using the slope formula, 
. Substitute the x and y values of the given points into the formula and solve:
So, the slope is 
.
2) Now, use the point-slope formula 
to write the equation of the line in point-slope form. Substitute real values for the 
, 
, and 
in the formula.
Since represents the slope, substitute in its place. Since and represent the x and y values of one point the line intersects, choose any one of the given points (either one is fine, it will equal the same thing at the end) and substitute its x and y values into the formula as well. (I chose (0, -7), as seen below.) Then, isolate y to put the equation in slope-intercept form and find the following answer:
The original functions are: f(n) = 500 and g(n) = [9/10]^(n-1)
A geometric sequence combining them is: An = f(n)*g(n) = 500*[9/10]^(n-1):
Some terms are:
A1= 500
A2 = 500*[9/10]
A3 = 500*[9/10]^2
A4 = 500*[9/10]^3
....
A11 = 500*[9/10]^10 ≈ 174.339
Answer: the third option, An = 500[9/10]^(n-1); A11 = 174.339
