Given:
In triangle OPQ, o = 700 cm, p = 840 cm and q=620 cm.
To find:
The measure of angle P.
Solution:
According to the Law of Cosines:
Using Law of Cosines in triangle OPQ, we get
On further simplification, we get
Therefore, the measure of angle P is 79 degrees.
Let the side of the square base be x, and the height of the box be h.
<span>The material of the base is x^2, and the material of the four sides is 4xh. </span>
<span>4000 = hx^2 </span>
<span>h = 4000/x^2 </span>
<span>The total material is </span>
<span>M = x^2 + 4x(4000/x^2) = x^2 + 16000/x </span>
<span>Take the first derivative of M and set equal to 0. </span>
<span>M' = 2x - 16000/x^2 = 0 </span>
<span>Multiply by x^2: </span>
<span>2x^3 = 16000 </span>
<span>x^3 = 8000 </span>
<span>x = 20; h = 10; M = 1200</span>
Answer:
Step-by-step explanation:
First step plug the numbers into the equation.
-10/(5+2) = (-10/5) + (-10/2)
Solve both sides of the equation separately.
-10/(5+2) Use distributive property, multiply both 5 and 2 by -10.
= -50 + (-20) = -70
-10/5 + -10/2 Multiply the fractions so they can be added together.
-10/5*2 = -20/10 -10/2*5 = -50/10
-20/10 + -50/10 = -70
Now you have solved both equations and they are both equal to -70, so you have verified that the equations are equal to each other because they both equal -70.
Answer:
Try 4/6
Step-by-step explanation:
Answer:
The area of the pentagon is 193.45 square inches.
Step-by-step explanation:
In order to solve this question we need to use the appropriate formula for the pentagon's area shown below:
area = (p*a)/2
Where p is the perimeter for the pentagon and a is it's apothem.
area = (53*7.3)/2 square inches
area = 386.9/2 square inches
area = 193.45 square inches
The area of the pentagon is 193.45 square inches.
