Use following substitutions:
<span>r cosθ = x </span>
<span>r sinθ = u </span>
<span>r² = x² + y² </span>
<span>r = 8 cosθ + 4 sinθ </span>
<span>Multiply both sides by r </span>
<span>r² = 8 r cosθ + 4 r sinθ </span>
<span>x² + y² = 8x + 4y </span>
<span>This is equation of circle. We can put in standard form: </span>
<span>x² − 8x + y² − 4y = 0 </span>
<span>x² − 8x + 16 + y² − 4y + 4 = 16 + 4 </span>
<span>(x − 4)² + (y − 2)² = 20 </span>
<span>Circle centered at point (4, 2) with radius = √20</span><span />
y=2x+3 (the 3 can be changed)
Answer:
41
Step-by-step explanation: 11 coookies per cup of flour. 4 cups of flour. 11 x 4 = 41
Answer:Your left hand side evaluates to:
m+(−1)mn+(−1)m+(−1)mnp
and your right hand side evaluates to:
m+(−1)mn+(−1)m+np
After eliminating the common terms:
m+(−1)mn from both sides, we are left with showing:
(−1)m+(−1)mnp=(−1)m+np
If p=0, both sides are clearly equal, so assume p≠0, and we can (by cancellation) simply prove:
(−1)(−1)mn=(−1)n.
It should be clear that if m is even, we have equality (both sides are (−1)n), so we are down to the case where m is odd. In this case:
(−1)(−1)mn=(−1)−n=1(−1)n
Multiplying both sides by (−1)n then yields:
1=(−1)2n=[(−1)n]2 which is always true, no matter what n is
Answer:
The average rate of change in the balance over the interval t = 0 to t = 5 is of $20.82 a year. This means that the balance increased by $20.82 a year over the interval t = 0 to t = 5.
Step-by-step explanation:
Given a function y, the average rate of change S of y=f(x) in an interval
will be given by the following equation:
![S = \frac{f(x_{f}) - f(x_{s})}{x_{f} - x_{s}}](https://tex.z-dn.net/?f=S%20%3D%20%5Cfrac%7Bf%28x_%7Bf%7D%29%20-%20f%28x_%7Bs%7D%29%7D%7Bx_%7Bf%7D%20-%20x_%7Bs%7D%7D)
In this problem, we have that:
![B(t) = 1000(1.02)^{t}](https://tex.z-dn.net/?f=B%28t%29%20%3D%201000%281.02%29%5E%7Bt%7D)
Find the average rate of change in the balance over the interval t = 0 to t = 5.
![B(0) = 1000(1.02)^{0} = 1000](https://tex.z-dn.net/?f=B%280%29%20%3D%201000%281.02%29%5E%7B0%7D%20%3D%201000)
![B(5) = 1000(1.02)^{5} = 1104.08](https://tex.z-dn.net/?f=B%285%29%20%3D%201000%281.02%29%5E%7B5%7D%20%3D%201104.08)
Then
![S = \frac{1104.08 - 1000}{5-0} = 20.82](https://tex.z-dn.net/?f=S%20%3D%20%5Cfrac%7B1104.08%20-%201000%7D%7B5-0%7D%20%3D%2020.82)
The average rate of change in the balance over the interval t = 0 to t = 5 is of $20.82 a year. This means that the balance increased by $20.82 a year over the interval t = 0 to t = 5.