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    Algebra

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    Solve: Slope of a Tangent

    Please solve for the following: Find the slope of a tangent to the curve of y = ln (25x + 3) at x = 2. a. 0.47 b. 0.50 c. 1.2 d. 2.5

    Estimating with e

    Which of the following expressions would help estimate Please see attachment

    Equation of a straight line.

    1. Tom planted a bamboo on June 1st that was eight feet tall. In June it grew at the rate of five inches per day. Find the equation of the line that shows how tall the bamboo was each day in June. 2. Find the equation of the line that passes through the points (4,-2) and (2,4). 3. Find the equation of the line that passes thr

    Probability of Rain as a Linear Function

    Can you please help me with these two word problem-examples? (Rental Charge) 1) The charge C for renting an air hammer from Taylor Rentals is a linear function of the number n of days in the rental period. The charge is $113 for two days and $209 for for five -days. Write C as a linear function of n. What would the ch

    Find the Integers

    The sum of two consecutive odd integers is 1472. Find the two integers.

    Equations: Find the Number

    A number is composed of x and y and its sum is 9 if the order of x and Y is inverted the result is equal to the given number plus 9 more units - find the number.

    Convert Two Variables

    Please show me how to convert 2 equations: ab + cd + ef = 0 bg + dh + fj = 0 into 3 equations: b / (cj - eh) = d / (eg - aj) = f / (ah - cg)

    Cryptography : Diffie Helman Key Exchange

    Alice and Bob want to do a Diffie-Helman Key Exhange. The public base is 5 and the public modulus is 11. Suppose Alice chooses a = 2 and Bob Chooses b=3. What common key did they calculate? What does the security of the Diffie Helman Key exhange depend upon?

    Congruency : Solve for a and b

    Solve for a and b 4a + b = 1 (mod 5) a + b = 2 (mod 5) check answers for a and b by substituting into the original equations

    Applications of Linear Equations : Word Problem

    A professor started a project with a group of students, 60% of whom were boys. Due to some unavoidable reason, six girls couldn't turn up, so the professor had to make some changes in the group. He admitted six boys. In doing so, the percentage of boys in the project increased to 75%. Find the number of boys and girls involved i

    Expressing in New and Old Coordinate Systems

    Sketch the following quadratic surface, showing the old and new coordinate systems, and identify it: Please see attachment for fully formatted equation. 3(x1)^2 + 2x1x2 + 2x1x3 + 4x2x3 = 12. See the attached file.

    Skolem Sequences

    Please see the attached file for the fully formatted problem. A Skolem sequence of order n is a sequence (s1, s2,...,s2n) of 2n integers satisfying the conditions: i) for every k in {1,2,3...,n} there exist exactly two elements si and sj with si = sj = k and ii) if si = sj = k with i<j then j - i = k. Find all Skolem seq

    Isolating variables in an equation

    Given the formula below, make (i) h and (ii) a the subject of the formula A = 1/2*h*(a+b) Given the formula below, change the subject of the formula to P A = [P(1+r)^n-1]/r

    Subject of equation

    Rearrange the following expression such that b is on the left hand side of the equality: d = 1.3[(ab)^0.625)/(a+b)^0.25]

    Decibels and intensity

    The level (Loudness) of sound is measured in decibels which is related to the intensity if sound (I) which is measured in watts per cm^2. One can convert from one measure to the other using the following formula d=10 log (I/10^-16) Due to the installation of acoustical tiles in an auditorium, the noise level was reduced from

    How far a raft will sink in water using hydraulics

    Given: raft consists of 4 sealed barrels laying on their sides with demensions of 21 in. diameter, 3 ft. in length, and weighing 30 lbs. each. The barrels are attached by a wooden deck weighing 179 lbs. find: how far does the raft sink below the waters surface with a specific weight of the water being 62.38 lb./cubic foot.

    Simultaneous Equations

    State whether the following system of equations is solvable or unsolvable. If it is solvable, find the solution. 3(y-1) = 2(x-3) 3> y-2x = -3

    Word problem (airports)

    1998 airports are each connected in both directions to exactly three other airports. Any airport can be reached from any other airport by a sequence of flights. It is decided to close down 200 of the airports, no two of which are connected by a single flight. Show that this can be done in such a way that any remaining airport ca