a)
To find: The type of the
The graph of equation
Given information:
The equation is
Calculation:
Draw the graph of equation
Therefore, the graph represents an ellipse.
b)
To find: The equation in terms of
The required equation in terms of
Given information:
The equation is
Formula used:
Formula used to find the rotation angle
Here, A , B , and C are the values obtain by comparing given equation with equation
The equations for the axis of rotation are,
Calculation:
Comparing the given equation with the general equation,
Calculate the angle of rotation.
Further, simplify.
Substitute value of
And,
Substituting the values of x and y in given equation.
Dividing both sides by 10.
The equation
c)
To find: The vertex or vertices of equation
The vertices of equation
Given information:
The equation is
The equation in
Formula used:
The standard formula for an ellipse is,
Vertices of ellipse are:
Calculation:
Comparing this equation with standard equation of ellipse.
Therefore, the vertices of ellipse are
d)
To find: The vertices of ellipse in
The vertices of equation
Given information:
The equation is
The equations for the rotation of axis are,
The vertices of equation
Calculation:
Write the equation of the rotation of axis in terms of x and y .
Substitute the values
Similarly,
Substitute the values
Similarly,
The vertices of equation
Chapter 8 Solutions
PRECALCULUS:GRAPHICAL,...-NASTA ED.
- Perform long division on the integrand, write the proper fraction as a sum of partial fractions, and then evaluate the integral. 30x³-60x²+8 dx 2 x-2x After performing the long division, write the resulting proper fraction as a sum of partial fractions. Evaluate the integral. 30x³-60x²+8 2 x² -2x dx=arrow_forwardEvaluate the following integral. x/6 S tan 2x dx x/12arrow_forwardEvaluate the integral by using a substitution prior to integration by parts. 7) sin (In (6x)) dxarrow_forward
- Evaluate the integral using any appropriate algebraic method or trigonometric identity. S- dy 18 √2 (1+y2/3) yarrow_forward4. Suppose the demand for a certain item is given by D(p)=-2 p² - 4p+350, where p represents the price of the item in dollars. a) Find the rate of change of demand with respect to price. b) Find and interpret the rate of change of demand when the price is $11.arrow_forward√3-x, x≤3, 2. For f(x) = 1 find each of the following. x > 3, x-3' 1. f(-6) 2. f(3) 3. f(7) 3. Find the domain of each of the following functions.arrow_forward
- 1. Using the definition of the derivative, find f'(x). Then find f'(2), f'(0) and f'(3) when the derivative exists. a) f(x)=5x²-6x-1arrow_forward2. f(x)=√7-x 4. A manufacturer has a monthly fixed cost of $40,000 and a production cost of $8 for each unit produced. The product sells for $12 per unit. 1. What is the cost function? 2. What is the revenue function? 3. Compute the profit corresponding to 12,000 units. 5. A rectangular box is to have a square base and a volume of 20 ft3. The material for the base costs $0.30 per ft2, the material for the sides cost $0.10 per ft2, and the material for the top costs $0.20 per ft2. Letting x denote the length of one side of the base,arrow_forwardSolve using superposition principlearrow_forward
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