Answer:
Area: 6a^2
Perimeter: 12a^2
Step-by-step explanation:
To find the area of a triangle, use the formula A=1/2 b*h. The base is 3a^2 and the height is 4a^2.
A= 1/2 (3a^2)(4a^2)
A = 1/2 (12a^4)
A = 6a^4
To find the perimeter of the triangle, add each of the sides of the triangle. The third side, the hypotenuse, can be found using Pythagorean theorem.
![a^2+b^2=c^2\\(3a^2)^2+(4a^2)^2 = c^2\\(9a^4)+(16a^4)=c^2\\25a^4=c^2\\5a^2=c](https://tex.z-dn.net/?f=a%5E2%2Bb%5E2%3Dc%5E2%5C%5C%283a%5E2%29%5E2%2B%284a%5E2%29%5E2%20%3D%20c%5E2%5C%5C%289a%5E4%29%2B%2816a%5E4%29%3Dc%5E2%5C%5C25a%5E4%3Dc%5E2%5C%5C5a%5E2%3Dc)
Now add each of the sides: 3a^2 + 4a^2 +5a^2 = 12a^2
Answer:
![\frac{dy}{dx} = \frac{13}{8}](https://tex.z-dn.net/?f=%5Cfrac%7Bdy%7D%7Bdx%7D%20%20%3D%20%20%5Cfrac%7B13%7D%7B8%7D%20)
Step-by-step explanation:
![y = 2x + 6 {x}^{ - \frac{1}{2} } \\ \frac{dy}{dx} = 2 + 6( - \frac{1}{2}) {x}^{ - \frac{1}{2} - 1 } \\ \frac{dy}{dx} = 2 - 3 {x}^{ - \frac{3}{2} } \\ \frac{dy}{dx} = 2 - \frac{3}{ \sqrt{ {x}^{3} } }](https://tex.z-dn.net/?f=%20y%20%3D%202x%20%2B%206%20%7Bx%7D%5E%7B%20-%20%20%5Cfrac%7B1%7D%7B2%7D%20%7D%20%20%5C%5C%20%20%5Cfrac%7Bdy%7D%7Bdx%7D%20%3D%202%20%2B%206%28%20-%20%20%5Cfrac%7B1%7D%7B2%7D%29%20%7Bx%7D%5E%7B%20-%20%20%5Cfrac%7B1%7D%7B2%7D%20-%201%20%7D%20%20%20%5C%5C%20%20%5Cfrac%7Bdy%7D%7Bdx%7D%20%20%3D%202%20-%203%20%7Bx%7D%5E%7B%20-%20%20%5Cfrac%7B3%7D%7B2%7D%20%7D%20%20%5C%5C%20%5Cfrac%7Bdy%7D%7Bdx%7D%20%20%3D%202%20-%20%20%5Cfrac%7B3%7D%7B%20%5Csqrt%7B%20%7Bx%7D%5E%7B3%7D%20%7D%20%7D%20)
When x = 4,
![\frac{dy}{dx} = 2 - \frac{3}{ \sqrt{ {4}^{3} } } \\ = \frac{13}{8}](https://tex.z-dn.net/?f=%5Cfrac%7Bdy%7D%7Bdx%7D%20%20%3D%202%20-%20%20%5Cfrac%7B3%7D%7B%20%5Csqrt%7B%20%7B4%7D%5E%7B3%7D%20%7D%20%7D%20%20%5C%5C%20%20%3D%20%20%5Cfrac%7B13%7D%7B8%7D%20)
Answer:
The function operation is 0
The composite function is -1
Step-by-step explanation:
Answer:
The dimension are 20 ft by 15 ft
Step-by-step explanation:
A = l*w
P = 2(l+w)
we know the area = 300
and the perimeter = 70
300 = lw
70 = 2 (l+w)
divide by 2
70/2 = 2/2 (l+w)
35 = l+w
subtract w
35-w = l+w-w
35 -w =l
substitute this into 300 = lw
300 = (35-w) * w
distribute
300 = 35w - w^2
subtract 300 from each side
0 = -w^2 +35w - 300
divide by -1
0 = w^2 - 35w + 300
factor
0= (w-15) (w-20)
using the zero product property
w-15 = 0 w-20 =0
so w=15, w=20
if w=15 then l=35 -w l = 35-15 l=20
if w=20 then l=35-w l= 35-20 = 15
The dimension are 20 ft by 15 ft