Explain in your own words how you approach solving any quadratic equation by factoring. What are the key things you keep in mind as you’re working towards finding the answer(s)? Your explanation must be at least a few sentences long. Remember to outline your specific, step-by-step process.

Solve the following initial-value problem:

(ye^2xy + x)dx − (y² − xe^2xy)dy = 0, y(2) = 0

Find the equation of the osculating circle at the local minimum of

3x^3 -7x^2 +(11/3)x+4

Revenue, cost, and profit. The price–demand equation and the cost function for the production of table saws are given, respectively, by

x=6,000−30pandC(x)=72,000+60xx=6,000−30pandC(x)=72,000+60x

where x is the number of saws that can be sold at a price of $p per saw and C(x) is the total cost (in dollars) of producing x saws.

• (F) Graph the cost function and the revenue function on the same coordinate system for 0≤x≤6,000. Find the break-even points, and indicate regions of loss and profit.

• (G) Find the profit function in terms of x.

• (H) Find the marginal profit.

• (I) Find P'(1,500) and P′(3,000) and interpret these quantities.

• Please write the answer clear Thank you!!

Consider the function f(x)= tan 1/x

Use the following table to guess the limit f(x) as x goes to 0+

Find the velocity, acceleration, and speed of a particle with the given position function. r(t) = 2 cos(t), 2t, 2 sin(t)

Question 5

Find all solutions of this system.

4x + 2y + 3z = 0 3x y + 2z = 0 x + 2y − z = 0

Compare the value of the determinant of the coefficient matrix to zero using the nature of the solution.

if you a square that is 3' 5" in width, length and height. How many five point stars (2" in size) filled with air will fit into the square? Please show all work.

For each statement, determine whether the statement is true or false. Give a sentence justifying your answer.

a. If tan(t)=0, then cos(t)=1 .

b. The function f(x)=sin(x)cos(x) has period 2π.

c. The graph of r = 1 is the unit circle.

d. Two angles with the same cosine value must have the same sine value.

e. The point (0, -3) in Cartesean coordinates can also be described by the ordered pair (-3, π/2) in polar coordinates

What other application's can we think of related to this topic leasing.

For each of the following integrals find an appropriate trigonometric substitution of the form x=f(t)x=f(t) to simplify the integral.

the inteagral

a) ∫x(3x^2+30x+73)^(1/2)dx

b)∫x/(−25−3x^2+18x)^(1/2)dx

1) Find the maximum and minimum values of the function y = 13x³ + 13x² − 13x on the interval [−2, 2].

2) Find the minimum and maximum values of the function f(x) = 4 sin(x) cos(x) + 8 on the interval [0, pi/2].

3)  Find the maximum and minimum values of the function y = 5 tan(x) − 10x on the interval [0, 1]

4) Find the maximum and minimum values of the function f(x) =ln(x)/x  on the interval [1,4]

5)  Find the maximum and minimum values of the function y = |x − 16| on the interval [0, 17] by comparing values at the critical points and endpoints.

A linear system of equations Ax=b is known, where A is a matrix of m by n size, and the column vectors of A are linearly independent of each other. Please answer the following questions based on this assumption, please explain all questions, thank you~.

(1) Please explain why this system has at most one solution.

(2) To give an example, Ax=b is no solution.

(3) According to the previous question, what kind of inference can be made to the size of A at this time? (What is the size of m and n,please explain also it thanks.)

Joanne sells​ silk-screened T-shirts at community festivals and craft fairs. Her marginal cost to produce one​ T-shirt is $ 2.50 . Her total cost to produce 60 ​T-shirts is  $ 220 comma and she sells them for ​$8 each. a. Find the linear cost function for​ Joanne's T-shirt production. b. How many​ T-shirts must she produce and sell in order to break​ even? c. How many​ T-shirts must she produce and sell to make a profit of ​$500​?