Answer:
A) x = 0 and x = 3π∕4
Step-by-step explanation:
cot 0° = oo (infinite)
4/3 x = 0
=> x = 0
cot 180° = oo (infinite)
4/3 x= 180
x = 3/4 × 180
= 135°
= ¾π
Answer:
a) The 95% confidence interval for the mean waste recycled per person per day for the population of Maine is between 1.19 and 1.61 pounds.
b) 
Step-by-step explanation:
We have the standard deviation for the sample, which means that the t-distribution is used to solve this question.
The first step to solve this problem is finding how many degrees of freedom, we have. This is the sample size subtracted by 1. So
df = 7 - 1 = 6
95% confidence interval
Now, we have to find a value of T, which is found looking at the t table, with 6 degrees of freedom(y-axis) and a confidence level of
. So we have T = 2.4469, and the answer to question b is 
The margin of error is:
In which s is the standard deviation of the sample and n is the size of the sample.
The lower end of the interval is the sample mean subtracted by M. So it is 1.4 - 0.21 = 1.19 pounds.
The upper end of the interval is the sample mean added to M. So it is 1.4 + 0.21 = 1.61 pounds.
The 95% confidence interval for the mean waste recycled per person per day for the population of Maine is between 1.19 and 1.61 pounds.
This question is the application of differential eqns in order to derive a model for the temperature dependence with time. Actually, a general equation has already been derived for this type of cases. This equation is known as the Newton's Law of Cooling. The equation is
(T - Ts) / (To -Ts) = e^(-kt)
where T is the the temperature at any time t
Ts is the surrounding temperature
To is the initial temperature
k is the constant
t is the time
several assumptions have been made to arrive at this form, i suggest you trace the derivation of the general formula.
First we need to look for k using the initial conditions that is @t = 1.5 min, T = 50 F
substituting we get a k = 0.2703
therefore @ t = 1 min, T = 55.79 F
@ T = 15 F the time required is 9.193 min.
Answer:
The answer to your question is 10 units
Step-by-step explanation:
Data
A (-3, -1)
B (-3 , 5)
length of a side = 8 units
Process
1.- Calculate the distance between A and B
dAB = 
x1 = -3 y1 = -1
x2 = -3 y2 = 5
-Substitution
dAB = 
dAB = 
dAB = 
dAB = 6 u
2.- Calculate the diagonal using the Pythagorean theorem.
c² = a² + b²
c² = 6² + 8²
c² = 36 + 64
c² = 100
c = 10 units
- Conclusion
The diagonal of the rectangle measures 10 units