Answer:153.9 cm
Step-by-step explanation:
The area of a circle is found by pi × radius squared and pi is aprox 3.14 so 3.15×7² = 153.86 then round off to the nearest tenth you get 153.9
Answer:
651.
Step-by-step explanation:
Note: In the given series it should be -29 instead of 29 because 29 cannot be a term of AP whose first term is 91 and common difference is -6.
Consider the given series is
It is the sum of an AP. Here,
First term = 91
Common difference = 85 - 91 = -6
Last term = -29
nth term of an AP is
where, a is first term and d is common difference.
Sum of AP is
![Sum=\dfrac{n}{2}[\text{First term + Last term}]](https://tex.z-dn.net/?f=Sum%3D%5Cdfrac%7Bn%7D%7B2%7D%5B%5Ctext%7BFirst%20term%20%2B%20Last%20term%7D%5D)
![Sum=\dfrac{21}{2}[91+(-29)]](https://tex.z-dn.net/?f=Sum%3D%5Cdfrac%7B21%7D%7B2%7D%5B91%2B%28-29%29%5D)
![Sum=\dfrac{21}{2}[62]](https://tex.z-dn.net/?f=Sum%3D%5Cdfrac%7B21%7D%7B2%7D%5B62%5D)
Therefore, the sum of given series is 651.
Answer:
Equation: x + 16 + 13 + x = 21 ; x = -4
Step-by-step explanation:
x + 16 + 13 + x = 21 (Given)
2x + 29 = 21 (Added like terms)
2x = -8 (Subtracted 29 on both sides)
x = -4 (Divided 2 on both sides)
Answer:
y_c = 2 + 10*x
Step-by-step explanation:
Given:
y'' = 0
Find:
- The solution to ODE such that y(0) = 2, y'(0) = 10
Solution:
- Assuming a solution y = Ce^(mt)
So, y' = C*me^(mt)
y'' = C*m^2e^(mt)
- Back substitute into given ODE, we get:
y'' = C*m^2e^(mt) = 0
e^(mt) can not be equal to zero
- Hence, m^2 = 0
m = 0 , 0 - (repeated roots)
- The complimentary function for repeated roots is:
y_c = (C1 + C2*x)*e^(m*t)
y_c = C1 + C2*x
- Evaluate @ y(0) = 2
2 = C1 + C2*0
C1 = 2
-Evaluate @ y'(0) = 10
y'(t) = C2 = 10
Hence, y_c = 2 + 10*x
