Answer:
31.6 feet by 15.8 feet.
Step-by-step explanation:
Area of a Rectangle = Length X Breadth = LB
The area of the playground is to be 500 square feet
Therefore:
LB=500
Perimeter of the Rectangle = 2(L+B)
The Chain link fence that costs $2 per linear foot on three sides and a fancier wooden fence that costs $6 per linear foot on the fourth side.
Cost = ${2(L+2B)+6L}=2L+4B+6L=8L+4B
Cost= $(8L+4B)
From: LB=500, B=500/L
Substitute B into 8L+4B
C(L) = ![8L+4(\frac{500}{L} )=8L+\frac{2000}{L} =\frac{8L^2+2000}{L}](https://tex.z-dn.net/?f=8L%2B4%28%5Cfrac%7B500%7D%7BL%7D%20%29%3D8L%2B%5Cfrac%7B2000%7D%7BL%7D%20%3D%5Cfrac%7B8L%5E2%2B2000%7D%7BL%7D)
C(L)=![\frac{8L^2+2000}{L}](https://tex.z-dn.net/?f=%5Cfrac%7B8L%5E2%2B2000%7D%7BL%7D)
The minimum cost of the fencing occurs when the dimensions are minimum.
If we take the derivative of C(L)
![C^{'}(L)=\frac{8L^2-2000}{L^2}](https://tex.z-dn.net/?f=C%5E%7B%27%7D%28L%29%3D%5Cfrac%7B8L%5E2-2000%7D%7BL%5E2%7D)
At ![C^{'}(L)=0](https://tex.z-dn.net/?f=C%5E%7B%27%7D%28L%29%3D0)
![\frac{8L^2-2000}{L^2}=0\\8L^2-2000=0\\8L^2=2000\\L^2=250\\L=15.8 ft](https://tex.z-dn.net/?f=%5Cfrac%7B8L%5E2-2000%7D%7BL%5E2%7D%3D0%5C%5C8L%5E2-2000%3D0%5C%5C8L%5E2%3D2000%5C%5CL%5E2%3D250%5C%5CL%3D15.8%20ft)
Recall: B=500/L
![B=\frac{500}{15.8}=31.6 ft](https://tex.z-dn.net/?f=B%3D%5Cfrac%7B500%7D%7B15.8%7D%3D31.6%20ft)
The dimensions that minimizes the total cost of the fencing are 31.6 feet by 15.8 feet.
Let the ∠C be : θ
From the figure, We can see that the Side which is opposite to angle θ is measuring 7 units
Also, We can notice that Hypotenuse is 11 units
As we are dealing with opposite and hypotenuse, we can clearly use Sinθ to find out the angle θ
We know that :
![\bigstar \ \ \boxed{\sf{Sin\theta = \dfrac{Opposite \ Side}{Hypotenuse}}}](https://tex.z-dn.net/?f=%5Cbigstar%20%5C%20%5C%20%5Cboxed%7B%5Csf%7BSin%5Ctheta%20%3D%20%5Cdfrac%7BOpposite%20%5C%20Side%7D%7BHypotenuse%7D%7D%7D)
![\implies \sf{Sin\theta = \dfrac{7}{11}}](https://tex.z-dn.net/?f=%5Cimplies%20%5Csf%7BSin%5Ctheta%20%3D%20%5Cdfrac%7B7%7D%7B11%7D%7D)
![\implies \sf{\theta = Sin^{-1}\bigg(\dfrac{7}{11}\bigg)}](https://tex.z-dn.net/?f=%5Cimplies%20%5Csf%7B%5Ctheta%20%3D%20Sin%5E%7B-1%7D%5Cbigg%28%5Cdfrac%7B7%7D%7B11%7D%5Cbigg%29%7D)
![\implies \sf{\theta = 39.52^{\circ}}](https://tex.z-dn.net/?f=%5Cimplies%20%5Csf%7B%5Ctheta%20%3D%2039.52%5E%7B%5Ccirc%7D%7D)
<u>Answer</u> : The measure of ∠C to the nearest degree is 38°
Knowing base angles theorem, we know that if the triangle is isosceles, then the bottom base angles and congruent. That means that, we must subtract 80 from 180 and then divide the number by 2, since we must find 1 base angle. This brings us to the answer, 50 degrees.
Hope this helps! <3
Answer:
3x2+2x+2
Step-by-step explanation:
(2x2+3x+4)+(x2-x-2)
2x2+3x+4+x2-x-2
Like terms
1) numbers without variables: +4 and -2
2) numbers with a single x variable: +3x and -x
3) numbers with a x2 variable: +2x2 and +x2
Combine like terms
1) +4-2=2
2) +3x-x=2x
3) +2x2+x2=3x2
Add the combined terms together to get your answer
3x2+2x+2
The first part is addition.
45+m
If she spend a third of it, you could multiply by 1/3 or divide by 3.
Multiply: 45+m x 1/3
Divide: 45+m/3