Answer:
7.7 km
Explanation:
Use cosine rule as here given two sides and one angle.
Cosine rule states:
a² = b² + c² - 2bc cos(A)
While solving, treat a = 7.5 km as to that opposite angle is given of 68°
then b = missing side, c = 5.2 km, A = 68°
Applying rule:
7.5² = b² + 5.2² - 2(b)(5.2) cos(68)
56.25 = b² + 27.04 - 3.8959b
56.25 - 27.04 = b² - 3.8959b
b² - 3.8959b = 29.21
b² - 3.8959b - 29.21 = 0
apply quadratic equation, Here [a = 1, b = - 3.8959, c = -29.21]
As length cannot be negative. Hence the value of b is only 7.7 km
To solve for the solution of this system of linear equation, it is best to use substitution. From the first equation, x = 3y
Substituting the expression on the right for the value of x on the second equation,
-2(3y) + 3y = 16
Solving for the value of y gives y = -5 1/3
With this value of y, solving for x gives x = -16
Thus, the solution for this system of linear equation is (-16, -5 1/3)
Assuming no border or waste, 9m by 16 m translates to 29.52' x 52.49'.
use 32/8=4 sheets of plywood to cover the width on the 8' side.
For the length, use 52/4=13 pieces on the 4' side.
This gives a total of 4*13=52 sheets.
The extra 0.49' x 29.52 can be covered using the extra from the last four sheets for the width.
Check:
Area to be covered: 29.52*52.49=1550 sq. ft.
Area of plywood supplied = 52*4'x8'= 1664 sq. ft, > 1550 sq.ft.
Answer:
18 ft* (1 piece/ 1 1/3 ft)= 13.5 pieces.
Step-by-step explanation:
Answer:
Step-by-step explanation:
For this case we are interested on the region shaded on the figure attached.
And we can find the volume with the method of rings.
The area on this case is given by:
![A(x) = \pi [f(x)]^2 = \pi r^2 = \pi [3x]^2 = 9\pi x^2](https://tex.z-dn.net/?f=%20A%28x%29%20%3D%20%5Cpi%20%5Bf%28x%29%5D%5E2%20%3D%20%5Cpi%20r%5E2%20%3D%20%5Cpi%20%5B3x%5D%5E2%20%3D%209%5Cpi%20x%5E2)
And the volume is given by the following formula:
For our case our limits are x=0 and x=2 so we have this:
And if we solve the integral we got this:
![V= \pi [\frac{x^3}{3}]\Big|_0^{2}](https://tex.z-dn.net/?f=%20V%3D%20%5Cpi%20%5B%5Cfrac%7Bx%5E3%7D%7B3%7D%5D%5CBig%7C_0%5E%7B2%7D)
And after evaluate we got this:
![V=\pi [(\frac{8}{3} )-(\frac{0}{3} )]](https://tex.z-dn.net/?f=%20V%3D%5Cpi%20%5B%28%5Cfrac%7B8%7D%7B3%7D%20%29-%28%5Cfrac%7B0%7D%7B3%7D%20%29%5D)
