32^2 + x^2 = 38^2
1024 + x^2 = 1444
-1024 -1024
x^2= 420
x=20.493901532
Steps to solve:
f(x) = 3x³ – 2x² + x; x = -3
~Substitute
f(-3) = 3(-3)³ - 2(-3)² + (-3)
~Solve the exponents
f(-3) = 3(-27) - 2(9) + (-3)
~Multiply
f(-3) = -81 - 18 - 3
~Subtract
f(-3) = -102
Best of Luck!
Answer:
3.
Step-by-step explanation:
Implicit differentiation:
x^2 y + (xy)^3 + 3x = 0
x^2 y + x^3y^3 + 3x = 0
Using the product rule:
2x* y + x^2*dy/dx + 3x^2 y^3 + x^3* (d(y^3)/dx) + 3 = 0
2xy + x^2 dy/dx + 3x^2 y^3 + x^3* 3y^2 dy/dx + 3 = 0
dy/dx(x^2 + 3y^2x^3) = (-2xy - 3x^2y^3 - 3)
dy/dx= (-2xy - 3x^2y^3 - 3) / (x^2 + 3y^2x^3)
At the point (-1, 3).
the derivative = (6 - 81 - 3)/(1 -27)
= -78/-26
= 3.
Ok so if we call the width x then the length is 2x-7
Now by adding a 5 foot brick border around the edge the new dimensions are:
x+10 and 2x+3
Now we can form an equation to solve:
(x+10)(2x+3)=195
2x²+23x+30=195
2x²+23x-165=0
Now we can solve this for x
(2x+33)(x-5)=0
So x=-33/2 or x=5
As x cannot be less than 0 x must be equal to 5
So the dimensions of the garden are 5 feet by 3 feet