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Rearranging and Solving Formulae

1. In a circuit containing a resistor and a capacitor, the instantaneous voltage V volts across the capacitor is given by the formula Where R is the resistance in Ohms V is the initial voltage, C the capacitance in Farads and t is the time in seconds. Determine the time at which the instantaneous voltage is 35 volts given

SQ Root

For the equation x-the sq root of x=0, how do I solve for all values of x to satisfy the equation?

Square roots

Can you show me how to solve the following equations? Square roots confuse me. Sq Root of X-1=3? Sq Root of X^3=8? and ^3sq root of x^2=4? Is the sq root of x^2=x an identity?

Prove that equation1 = equation2

This is a question from a past exam paper for entrance onto a degree course. Whilst I am sure that the question is not that difficult, I do have real problems with this type of question. I am not sure how to get started with part (a) so could you please list every step as simply as possible when solving the problem. On part (

Simple and Compound Interest

You have $380,000 in your bank account. The interest rate in your account is 5%. Solve for the following: a. How much interest will you accumulate if interest is compounded annually over the next five years? b. How much interest will you earn in your account over the next five years with continuous compounding?

Converging sequence

I would like help on the following problem: Suppose {a_n} is a sequence that satisfies the condition lim n-> oo (a_n+1 - a_n)=0. Prove that the sequence {a_n / n} converges to 0.

Fibonacci sequence

The problem is Take any of the generalizations about the Fibonacci Numbers that we have considered, and investigate what happens if the sequence is formed by two different starting numbers but continues in the same way by adding successive pairs of terms. For example, you might form a new pseudo-Fibonacci sequence in this w

Real and Non-Real Affine Intersection Points and Their Multiplicities

For the first 5 questions, consider the set of intersection points of two equations, and let a1 be the number of distinct affine real intersections with multiplicity one, let a2 be the number of distinct affine real intersections with multiplicity two, let b be the numberof distint complex non-real affine intersections and let

Solving a Word Problem Subject to Constraints

Joe has to take a test which consists of short-answer questions worth 9 points each and essay questions worth 25 points each. He must do at least 9 short-answer questions, but won't have time to do more than 10. He has to answer at least 3 essay questions, but can't spend time to do more than 10. If no more than 19 questions can

Hyperbolas and Completing the Square : Vertices, Foci and Asymptotes

Completing the square problems: HYPERBOLAS- Find the center, vertices, foci, and asymptotes of the hyperbola. Please give the equation in standard form, i.e. (x-h)^2/a^2 - (y-k)^2/b^2=1 or other way around. 15) ? 9x^2-y^2-36x-6y+18=0 Answer: Center (2,-3) Vertices (3,-3), (1,-3) Foci: (2+ or √10, -3)

Word Problems

1st one: A family has a rectangular kitchen which measures 12 by 18 feet. They want to put diagonal heating coils in the floor of the room. How much will it cost them to put in the coils if they cost $25 foot? 12 x18 =216= Area 216x25= 5400 but since they want to put diagonals would I take half of this? 2nd one: A wi

Word Problems

1st one- One leg of an isosceles right triangle measures 12 meters long. Find the length of the hypotenuse of the triangle.? Would it be 12 over the sq rt of 2 2nd one A wire is needed to support a vertical pole 18ft tall. A cable will be anchored to a stake and it forms a 30 degree with the ground. nearest tenth... How fa

Word Problem

The 42 kilometer drive from Oakdale to Ridgemont usually takes 28 minutes. Because highway construction requires reduced speed limit, the trip now takes 14 minutes longer. Find the reduced speed limit in km/hr.

Square roots in a system of equations.

An explanation of the steps to use in a problem involving square roots in a system of equations using the sample problem given. Thank You. Please see attached.


What are the inflection points? (a) f(x) = 12x^5 +15x^4 -240x^3+19 (One of the inflections is 0. Find the rest. Results cannot be -2.82 and 2.07) (b) f(x) = (x^2 - 8x + 32)(x-4)