Calculate the lengths of the sides of the triangle:
The triangle has three different sides, so it's a scalene triangle.
Now if c is the longest side of the triangle, and a and b are the shorter sides, then:
- if , the triangle is right
- if , the triangle is acute
- if , the triangle is obtuse
The longest side is 5.
The square of the longest side is equal to the sum of the squares of the shorter sides, so it's a right triangle.
The triangle is a right scalene triangle.
The balloon has a volume 
dependent on its radius 
:
Differentiating with respect to time 
gives
If the volume is increasing at a rate of 10 cubic m/s, then at the moment the radius is 3 m, it is increasing at a rate of
The surface area of the balloon is
and differentiating gives
so that at the moment the radius is 3 m, its area is increasing at a rate of
Answer:
A: W = 8x
B: 12y + 320
C: 44
Step-by-step explanation:
A: Lana can make $8 an hour.
W = 8x
B: She makes $12 per hour for every hour of overtime. This means that she already worked 40 hours with regular pay. She has already made $320.
40 × $8 = $320
S = 12y + 320
C: Plug in the amount Lana earned into the second equation. The second equation will account for pay from both regular and overtime hours.
S = 12y + 320
368 = 12y + 320
368 - 320 = (12y + 320) - 320
48 = 12y
48/12 = (12y)/12
4 = y
y = 4
Lana worked 4 hours of overtime and 40 hours of regular hours. In total, she worked 44 hours.
4 + 40 = 44
Answer:
P = 2000 * (1.00325)^(t*4)
(With t in years)
Step-by-step explanation:
The formula that can be used to calculated a compounded interest is:
P = Po * (1 + r/n) ^ (t*n)
Where P is the final value after t years, Po is the inicial value (Po = 2000), r is the annual interest (r = 1.3% = 0.013) and n is a value adjusted with the compound rate (in this case, it is compounded quarterly, so n = 4)
Then, we can write the equation:
P = 2000 * (1 + 0.013/4)^(t*4)
P = 2000 * (1.00325)^(t*4)
