Answer:
-1/11
Step-by-step explanation:
add 1/6 to both sides
make the same denominator 12 on the right side
solve
multiply by 12 both sides
11x= -1 divide by 11
x= -1/11
Given: C(N) = 15,000 + 8000N <span>
In the above equation simply substitute:
N(t) = 100t - 5t^2
for N
</span>
<span>Therefore:
C(t) = 15,000 + 8000{ 100t-5t^2 }
C(t) =15,000 + 800,000t - 40,000t^2.</span>
at t = 5
C(5) = 15,000 + 800,000*5
- 40,000*(5)^2
<span>C(5) = 3,015,000</span>
Answer: She would need 206 paper cups.
Step-by-step explanation: First of all, Monica has a 10-gallon container full of lemonade and this translates into 37850 cubic centimetres volume of lemonade. The conversion rate has been provided as one gallon equals 3785 cubic centimetres, therefore ten gallons would be 3785 times ten which gives you 37,850 cubic centimetres of lemonade.
Each cone shaped paper cup has a diameter measuring 8 centimetres and 11 centimetres in height. The radius of the cone shaped cup therefore is 4 centimetres (radius equals diameter divided by two). The volume of each cup therefore is given as;
Volume of a cone = (πr²h)/3
Volume of a cone = (3.14 * 4² * 11)/3
Volume of a cone = 552.64/3
Volume of a cone = 184.2
If each cone could hold 184 cubic centimetres of lemonade, then the entire ten gallons would require the following number of cone shaped cups;
Number of cups = Total volume/Volume of a cup
Number of cups = 37850/184.2
Number of cups = 205.48
Rounded to the nearest whole number, this becomes
Number of cups ≈ 206
Therefore Monica would need 206 cone shaped paper cups to empty the entire 10 gallons of lemonade.
