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The plane 2y+4z = 5 meets the cone z^2 = 4(x^2+y^2) in a curve. Use the method of Lagrange multipliers to find the point on this curve nearest to the origin.
Solving Systems of Linear Equations in Study Time.Jill, Karen, and Betsy studied a total of 93 hours last week
If the ratio of a to b is equal to the ratio of b to a, what can you say about the two numbers a and b?
Coordinate system to find slope of a line.Find the slope of the line passing through the points (-8, -3) and (-2, 2).
Factor the polynomial 7 a ^6 b ^7 c^ 5 - 35 a ^7 b ^5 c ^6, if possible. Find the GCF of the set of monomials of 252, 468.
Which method of solving a quadratic equation seems simplest to you? Which method should you try first?
Show the similarities between dividing two fractions and dividing two rational expressions using examples of each; explain your steps.
Twice the difference of seven times a number and four yields the same result as the same number increased by six.
A currency trader observes that in the spot exchange market, 1 U.S. dollar can be exchanged for 9 Mexican pesos or for 111.23 Japanese yen.
Give an example of a single polynomial with degree 3, whose value is 4 when the variable is equal to 1.
Show all stages of factoring separately (i.e., show the result of factoring out a GCF before taking the resulting polynomial and factoring it again).
Following are different algebraic expressions of the production function. Decide whether each one has constant, increasing, or decreasing returns to scale.
Factor the trinomial. factor out all common monomials first (including -1 if the lead coefficient is negative).
When converting from Fahrenheit degrees to Celsius degrees, a well known formula is used:
Venture capital. Henry invested $12,000 in a new restaurant. When the restaurant was sold two years later, he received $27,000.
Suppose you are at a gas station filling your tank with gas. The function C(g) represents the cost C of filling up the gas tank with g gallons.
Find k if the following system of equations has a unique solution
Do the multiplication and simplify if possible: 3√5(4√5) . Choose the correct answer from the following: 12, 300, or 60.
Find an equation of the line containing the given pair of points.
We have learned to solve quadratic equations using a variety of methods including completing the square and the quadratic formula.
Marginal revenue: A defense attorney charges her client $4000 plus $120 per hr. Formula R=120n+4000 gives her revenue in dollars for n hrs of work.
Find the value of 18, 19, and 110. What can you say about the value of any power of 1? Explain the reasoning.
A rectangle is 2 feet longer than it is wide, and its area is 8 square feet. Find its dimensions.
Solving Systems of Linear Equations by Graphing.Solve the system of equations graphically. Then classify the system as consistent or inconsistent
According to Einstein’s theory of relativity, time passes more quickly for bodies that travel very close to the speed of light.