Answer:
28.7 meters
Step-by-step explanation:
Draw a diagram. Let's say d is the distance between the anchor and the bottom of the tower, h is the height of the tower, and x is the length of the wire.
Using trigonometry, we can write two equations for the height of the tower:
h = d tan 65°
h = (d + 25) tan 35°
Setting these equal, we can solve for d.
d tan 65° = (d + 25) tan 35°
d tan 65° = d tan 35° + 25 tan 35°
d (tan 65° − tan 35°) = 25 tan 35°
d = 25 tan 35° / (tan 65° − tan 35°)
d ≈ 12.12
Now we can find x:
cos 65° = d / x
x = d / cos 65°
x ≈ 28.7
The wire is approximately 28.7 meters long.
6+5(x) < 1+(x) this is the correct form
It'd go down 6 and right 4
Answer: About 16 years
Step-by-step explanation:
The formula to find the compound amount if compounded continuously is given by :-
, where P is Principal amount, r is the rate of interest ( in decimal) and t is time ( in years).
Given : P= $1000 ; r= 4.6%=0.046
let t be the time it will take to double the amount, the we have
![2(1000)=(1000)e^{0.046\times t}](https://tex.z-dn.net/?f=2%281000%29%3D%281000%29e%5E%7B0.046%5Ctimes%20t%7D)
Dividing 1000 both sides, we get
![2=e^{0.046 t}](https://tex.z-dn.net/?f=2%3De%5E%7B0.046%20t%7D)
Taking natural log on each side, we get
![\ln2=\ln(0.046\times t)\\\\\Rightarrow\ 0.6931=0.046t\\\\\Rightarrow\ t=\dfrac{0.6931}{0.046}=15.0673913043\approx16\text{ years}](https://tex.z-dn.net/?f=%5Cln2%3D%5Cln%280.046%5Ctimes%20t%29%5C%5C%5C%5C%5CRightarrow%5C%200.6931%3D0.046t%5C%5C%5C%5C%5CRightarrow%5C%20t%3D%5Cdfrac%7B0.6931%7D%7B0.046%7D%3D15.0673913043%5Capprox16%5Ctext%7B%20years%7D)
Hence, it will take about 16 years to double the amount.
Answer:
Step-by-step explanation:
The surface area of a sphere with radius r is given by
S = 4 pi r^2
for a radius of 11 units,
S = 4 pi 11^2 = 484 pi = 1520.5 sq. units
This does not correspond to any of the answers.
Please check question.