Answer:
The slope is -1/3 and the y-intercept is (0, 2).
Step-by-step explanation:
2x+6y=12
6y=12-2x
6y=-2x+12
y=-2/6x+12/6
y=-1/3x+2
y=mx+b where m=slope and b=y-intercept
Answer:
Step-by-step explanation:
Represent the length of one side of the base be s and the height by h. Then the volume of the box is V = s^2*h; this is to be maximized.
The constraints are as follows: 2s + h = 114 in. Solving for h, we get 114 - 2s = h.
Substituting 114 - 2s for h in the volume formula, we obtain:
V = s^2*(114 - 2s), or V = 114s^2 - 2s^3, or V = 2*(s^2)(57 - s)
This is to be maximized. To accomplish this, find the first derivative of this formula for V, set the result equal to 0 and solve for s:
dV
----- = 2[(s^2)(-1) + (57 - s)(2s)] = 0 = 2s^2(-1) + 114s - 2s^2
ds
Simplifying this, we get dV/ds = -4s^2 + 114s = 0. Then either s = 28.5 or s = 0.
Then the area of the base is 28.5^2 in^2 and the height is 114 - 2(28.5) = 57 in
and the volume is V = s^2(h) = 46,298.25 in^3
Answer:
5 years and 5 months
Step-by-step explanation:
<u />
<u>Compound Interest Formula</u>
where:
- A = final amount
- P = principal amount
- r = interest rate (in decimal form)
- n = number of times interest applied per time period
- t = number of time periods elapsed
Given:
- A = $17,474.00
- P = $7,790.00
- r = 15% = 0.15
- n = 12
- t = number of years
Substitute the given values into the formula and solve for t:
Therefore, the money was in the account for 5 years and 5 months (to the nearest month).
It doesn’t have an inverse because it doesn’t pass the horizontal line test
