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Basic Algebra

Gradient of Temperature in a Nebula

Suppose that distances are measured in light-years and that the temperature T of a gaseous nebula is inversely proportional to the distance from a fixed point, which we take to be the origin (0,0,0). Suppose that the temperature 1 light-year from the origin is 200 degrees Celsius. Find the gradient of T at (x,y,z). f = __

Cachy's Inequality

Let f be an entire function such that |f(z)|&#8804;A|z| for all z, where A is a fixed positive number. Sow that f(z) = az where a is a complex constant. Please see the attached file for the fully formatted problem.

Inequalities and Quadratic Formula - 5 Math Problems

1. Solve the inequality...State the interval(s) where the inequality is valid using the symbols <, >. 3. Solve problems with the quadratic formula. 3. 4x2 - 12x - 7 = 0 (See attachment for full questions)

Financial Math

Please explain to me where the .5675 in the following formula came from: v_0 = .5675(110-E) This is from the solution to problem 6, lecture 6. I don't understand where .5675 came from, but I understand the solution. I'ved attached lectures 5, 6, and the solution to lecture 6. The formula for a state price vector i

Banach Space and Hamel Dimension

Suppose that &#61541; is a Banach space. Prove that the Hamel dimension of &#61541; is not Please see the attached file for the fully formatted problem.

Sample Point Of Intersection Calculation: Quadratic With Line

Find the points of intersection algebraically of the graphs of the equations y=x^2-3x+4, and 2x-2y= -8 need to see the algebra got a bit lost as to how to get from Solve equations: Take y=x^2-3x+4 into 2x-2y=-8, we got: Here x-x^2+3x-4=-4 to here We got: x1=0,

Slope-intercept form

Write the slope-intercept form of the equation of the line that passes though point (6,-9) and is perpendicular to the line y+3x=9

Find the equation of the tangent plane to a surface at a given point.

Find the equation of the tangent plane to the surface at the point . Please see the attached file for the fully formatted problems.

When I work the problem square root of 4x^2 + 15 - 2x = 0, by using the quadratic equation, my answer is a real number because I end up with the square root of 256 which is 16. Should I square both sides 1st or how do I solve the equation?

Find the difference quotient.

Find the difference quotient f(x+deltax)-fx)/deltax for the function f(x)=2x^2-4x-3.

Unit multiplies converted

Use two unit mulipliers to convert 100CM2 to square millimeters

Solving Rational Expressions

I'm having a difficult time figuring out some of these! For some reason the -1 in this problem is throwing me off - I think! Here's what I came up with last time, I keep getting a different answer each time I work it. 3/(y+5) -1 = (4-y)/(2y+10) 3/(y+5)-1 = (4-y)/2(y+5) y is not equal to -5 LCD is 2(y+5) 2(y+5)*3/(y+5) =

10 Algebra Problems : Solve Equations and Quadratics

Please see the attached file for the fully formatted problems. #1 Solve a2 - 9a = -14 #2 Solve 2e(e +1) = 12 #3 Solve #4 Solve #5 Solve for z #6 Solve the equation and check for extraneous solutions. #7 Solve #8 Solve by completing the square. s2 + 8s -

Solve for a square root

Solve for a 54 4√a-4 = 3 4√a + 2

Solve for a

Solve for a 2a³ = 54

Calculate the Value

Calculate the value of 27²/³.

Sum of Integers as Related to the Sum of Squares

Prove or Disprove that the sum of two integers each representable as the sum of three squares of integers is also thus representable.

Principal Value (3 Problems)

Find the principal value of... Please see the attached file for the fully formatted problems.

Logarithm Proofs Components

Verify log(z1/z2) = log z1 - log z2 by a) using the fact that arg(z1/z2) = arg z1 - arg z2 b) showing that log(1/z) = -log z... Please see the attached file for the fully formatted problems.

Algebraic Simplification Functions

The expression (a²b³c-²/a³)/(c/a) simplifies to ( b/c )³. Justify that this statement is true.

Algebraic Simplification Function

Show steps on how 64(y^6)(x^9) may be written as (4y²x³)³.

Complex Logarithms

Please see the attached file for full problem description. --- 3. Show that (a) Log (1 + i)2 = 2 Log (1 + i) (b) Log (-1 + i)2 ≠ 2 Log (-1 + i).

Cauchy-Riemann Equations in Polar Form

Please see the attached file for the fully formatted problems. 8. Let a function f (z) = u + i v be differentiable at a nonzero point z0 = r0 e(i&#952;0). Use the expressions for ux and vx found in Exercise 7, together with the polar form (6) of Cauchy-Riemann equations, to rewrite the expression f &#900;(z0) = ux + i vx

Simplify using Synthetic Division

(3x3 -4x + 5)/(x+4)

Synthetic Division

See attachment: SIMPLIFY USING SYNTHETIC DIVISION

See attachment.

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Exponential and Logarithmic Functions : Capacitance

If a capacitor with a capacitance of 0.000005 farads is wired in a circuit with a total resistance of 5000 ohms (the standard unit of electrical resistance), how long must the capacitor be wired to a source voltage to reach 50% of its maximum charge? (The Hint was: Begin by expressing q as 0.5Q)

Prove Bonferroni's Inequality

21. If P(E) = 0.9 and P(F) = 0.8, show that P(EF) &#8805; 0.7. In general, prove Bonferroni's inequality, namely, P(EF) &#8805; P(E) + P(F) - 1.

Inequalities, Graphs and Maximizing Profit

Please see the attached file for the fully formatted problems. Solve each inequality state the solution set using interval notation and graph the solution. Solve rational inequality state and graph the solution set. A chain store manager has been told by the main office that daily profit P is related to the number of