Answer:
a) dy/dx = 4/(2y+1)^2.
(b) y = 4/9 x - 14/9
(c) d2y/dx2 = -64/243
Step-by-step explanation:
You have the following equation
(1)
(a) You first derivative implicitly the equation (1) respect to x:
next, you solve the last result for dy/dx:
(2)
(b) The equation for the tangent line is given by:
(3)
with yo = -2 and xo = -1
To find the slope m you use the result of the equation (2), because dy/dx evaluated in (-1,-2) is the slope at such point:
m =
Hence, by replacing in the equation (3) you obtain:
hence, the equation for the tangent line is y = 4/9 x - 14/9
(c) To find d2y/dx2 you derivative the result obtain in the equation (2):
(4)
the second derivative for the point (-1,-2) is obtained by replacing y=-2 and dy/dx=m=4/9 in the equation (4):
hence, d2y/dx2 evaluated in (-1,-2) is -64/243
Step-by-step explanation:
Answer:
60 ft²
Step-by-step explanation:
You can divide the figure into 2 parts.
First, solve for the rectangle: Area of a rectangle = b*h = 4ft x 10ft = 40ft²
Then, solve for the triangle:
Height = 10ft - 5ft = 5ft
Base = 12ft - 4ft = 8ft
Area of a triangle = (b*h)/2 = (5ft x 8ft)/2 = 20ft²
Just add them together: 20ft² + 40ft² = 60ft²
:)
<h3>
Answer: 9</h3>
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Work Shown:
Apply the pythagorean theorem
a^2 + b^2 = c^2
12^2 + b^2 = 15^2
144 + b^2 = 225
b^2 = 225-144
b^2 = 81
b = sqrt(81)
b = 9
We want to determine the domain of

any function of the form

is called an "exponential function",
the only condition is that b is positive and different from 1, and a is a nonzero real number.
The domain of such functions is all real numbers.
That is for any x, the expression <span>3(2^-x) "makes sense".
Answer: </span><span>The domain is all real numbers</span>
Answer: The answer would be the one going a slope downwards
Step-by-step explanation: