Answer: 26 in.
Step-by-step explanation:
Given
Heights of Poles are ![12\ in., 22\ in.](https://tex.z-dn.net/?f=12%5C%20in.%2C%2022%5C%20in.)
distance between them is ![x=24\ in.](https://tex.z-dn.net/?f=x%3D24%5C%20in.)
the difference in heights of the pole is
From the figure, using Pythagoras theorem, distance L is given by
![\Rightarrow L^2=y^2+x^2\\\Rightarrow L^2=10^2+24^2\\\Rightarrow L^2=100+576=676\\\Rightarrow L=\sqrt{676}=26\ in.](https://tex.z-dn.net/?f=%5CRightarrow%20L%5E2%3Dy%5E2%2Bx%5E2%5C%5C%5CRightarrow%20L%5E2%3D10%5E2%2B24%5E2%5C%5C%5CRightarrow%20L%5E2%3D100%2B576%3D676%5C%5C%5CRightarrow%20L%3D%5Csqrt%7B676%7D%3D26%5C%20in.)
The distance between tops is 26 in.
Answer:
a) The sequence converges to 0
b) The lenght of the curve is ![\frac{1}{54}(217^{3/2}-37^{3/2})](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B54%7D%28217%5E%7B3%2F2%7D-37%5E%7B3%2F2%7D%29)
Step-by-step explanation:
Consider the sequence ![a_n = \frac{-6n^6 + \sin^2(7n)}{n^7+11}](https://tex.z-dn.net/?f=a_n%20%3D%20%5Cfrac%7B-6n%5E6%20%2B%20%5Csin%5E2%287n%29%7D%7Bn%5E7%2B11%7D)
a) We will prove it using the sandwich lemma. Note that for all n
, then
![\frac{-6n^6 -1}{n^7+11}\leq\frac{-6n^6 + \sin^2(7n)}{n^7+11}\leq \frac{-6n^6 + 1}{n^7+11}](https://tex.z-dn.net/?f=%20%5Cfrac%7B-6n%5E6%20-1%7D%7Bn%5E7%2B11%7D%5Cleq%5Cfrac%7B-6n%5E6%20%2B%20%5Csin%5E2%287n%29%7D%7Bn%5E7%2B11%7D%5Cleq%20%5Cfrac%7B-6n%5E6%20%2B%201%7D%7Bn%5E7%2B11%7D)
Note that the expressions on the left and the right hand side have a greater degree on the denominator than the one on the numerator. Then, by takint the limit n goes to infinty on both sides, we have that
![0 \leq\frac{-6n^6 + \sin^2(7n)}{n^7+11} \leq 0](https://tex.z-dn.net/?f=0%20%5Cleq%5Cfrac%7B-6n%5E6%20%2B%20%5Csin%5E2%287n%29%7D%7Bn%5E7%2B11%7D%20%5Cleq%200)
So, the sequence converges to 0.
b) The function
the formula of curve lenght is given by
![s = \int_a^b \sqrt[]{1+(f'(x))^2}dx](https://tex.z-dn.net/?f=s%20%3D%20%5Cint_a%5Eb%20%5Csqrt%5B%5D%7B1%2B%28f%27%28x%29%29%5E2%7Ddx)
in this case, a=1, b=6
Note that
. Then
. Take u = 1+36x. Then du= 36dx (i.e du/36 = dx). If x = 1, then u = 37 and if x = 6 then u = 217. So,
4. is proportional because it is 30x
Answer:
8^3 i think
Step-by-step explanation:
Answer:
Company one charges $11 + $0.16 per min.
Then if you talk for x minutes, the cost will be:
C₁(x) = $11 + ($0.16 per min)*x
For company two, the prize is $20 + $0.11 per min, and if yo talk for x minutes, the cost will be:
C₂(x) = $20 + ($0.11 per min)*x
Now we want to find the value of x, the number of minutes, such that the cost is the same with both companies.
C₁(x) = C₂(x)
$11 + ($0.16 per min)*x = $20 + ($0.11 per min)*x
($0.16 per min)*x - ($0.11 per min)*x = $20 - $11
($0.05 per min)*x = $9
x = $9/($0.05 per min) = 180 mins
If you speak for 180 minutes, the cost is the same in both companies.