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# Basic Algebra

Consider the quadratic equation m(x)=0.20x^2-1.6x-1. Write the equation in standard form m(x)=a(x-h)^2+k, then find each of the following (to four decimal places): (A) Intercepts (B) Vertex (C) Maximum or minimum (D) Range

### Function/algebra

1.SOLVE A=1/2H(b1+b2) for b2 2. write 3-square root-36 in standard form Linear Functions 3.Find the slope of the line passing through the points (-2, 4) and (-3, 5). a.1 b.-1 c.-9/5 d.-5/9 Zeros of Polynomial Functions 4.Find the zeros of P(x) = (

### Mass and radius of three of the nine solar planets

I need the mass and radius of three of the nine planets in our solar system. Be sure that the masses are expressed in kilograms and the radii are expressed in meters. I chose Pluto, Venus, and Mars. Using your data, calculate the gravitational acceleration on each of the three planets you selected. The masses should be measure

SOLVE FOR 'X' 9X^2 - 12X - 12 > 0 QUESTION :- SOLVE FOR X 1. 9X^2 -12X -12 >0 SOLUTION: The above given inequality is an quadratic which has two factors 9x^2 -12x-12 > 0 = 9x^2 &#8211;18x + 16x &#8211;12 > 0 = 9x(x-2) + 6(x-2) > 0 = (x -2) (9x + 6)>0 which implies the product of (x -2) & (9x + 6

### Polynomial Rational Function Zeros Calculation

1.LIST THE ZERO OF THE CUBIC FUNCTION AND TELL WHICH, IF ANY, ARE DOUBLE OR TRIPLE ZEROS y = x squared (x-1) 2. USE THE RATIONAL ZERO THEOREM TO FIND ALL POSSIBLE RATIONAL ZEROS OF THE POLYNOMIAL: g(x) = -3x cubic -8x squared +x+ 14 3.USE SYNTHETIC DIVISION TO FIND UPPER AND LOWER BOUNDS OF THE REAL ZEROS OF f. f(x) =

### Quadratic Equation, Maximum, Minimum and Types of Lines

1. Which set of ordered pairs(x,y) represents y as a function of x? Answer A. (2,-8),(1,6),(1,2),(6,1) B. 2,-8,1,6 C. (2,-8),(-8,2),(6,6) D.(2,-8),(-8,1),(2,6) 2. Evaluate the function at the specified value of the independent variable and simplify f(x)=3x squared-square root2x Answers a. 22.757 b. 24.551

### Quadratic Functions, Maxima, Minima, Even Function

1. Given f(x)=16-x squared,and g(x)=4-x, find f/g (x). 2. Find the maximum or minimum value of the quadratic function f(x)-x squared+10x-19. State whether this value is a maximum or minimum. 3. Evaluate the function at at specified value of the independent variable and simplify. F(x)=/x/-2; f(4) 4. Given f(x)=2/x-6

### Expression for period of pendulum

In the expression for the period of a simple pendulum, we do not take into account the mass that is hanging from the string. How is it possible that the mass does not affect the period of the pendulum? It was stated that the displacement that started the pendulum was small. What would happen if we started the pendulum with an ex

### Finance : Interest and the Fisher Effect

What is the nominal interest rate (i) in Canada if the real estate of return is 2.5% and the expected rate was 4.5%. (The Fisher Effect formula should be used in this problem).

### Quadratic Equations, Graphs, Rational Inequalities and Word Problems

Please see the attached file for the fully formatted problems. Includes the following Exercises: -Quadratic Functions and Their Graphs -Quadratic and Rational Inequalities; Equations, Functions and Inequalities -Quadratic Equations, Functions, and Inequalities Maximum height. If a baseball is projected upward from groun

### Differential equations - 2 Water tanks

Two identical water tanks labeled A and B are resting at the same elevation and are linked via a pipe with a valve. The cross sectional area of each of the tanks is 1m^2. The valve demonstrates linear behavior (volumetric flow is linear with pressure drop) and will allow a flow of 0.5 m^3/min under a pressure drop equivalent to

### Squaring Products and Factors

1 When we square a product, we square each factor in the product. For example (4b)2= 16b2. Explain why we cannot square a sum by simply squaring each term of the sum. For example, (a + b)2 is not equal to a2 + b2. Provide appropriate examples. 2 Take a number. Add 1. Square the result. Then subtract from that result

### Factor out the GCF in each expression. Factor each polynomial completely. Use grouping to factor each polynomial completely. Find the LCD for the given rational expressions

Factor out the GCF in each expression. 59. 2x^3-6x^2+8x 60. 6x^3+18x^2-24x *61. 12x^4t+30x^3t-24x^2t^2 *62. 15x^2y^2-9xy^2+6x^2y Factor each polynomial completely. 60. 32x^2y-2y^3 61. 3ab^2-18ab+27a Use grouping to factor each polynomial completely. 66. 3x+3z+ax+az 67. x^3+x^2-4x-4

### Exponential and logarithmic functions

A. Convert to logarithmic equations. For example, the logarithmic form of "23 = 8" is "log2 8 = 3". a) 16 3/2 = 64 b) ex = 5 B. Write the logarithmic equation in exponential form. For example, the exponential form of "log5 25 = 2" is "52 = 25". a) log 3 27 = 3 b) log e 1 = 0 c) log 125 25 = 2/3 C. Us

### Graphical representation of functions

1. Give an example of an exponential function. Convert this exponential function to a logarithmic function. Plot the graph of both the functions and post to the discussion forum. Discuss these functions and their graphs with your classmates. 2. Given the values 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, x, and y, form each of the follow

### Solve for the resultant displacement

1) A team of surveyors mark off distances represented by vectors of (85m, 55 degrees), (43m, 0 degrees) and (37m, 345 degrees). Solve for the resultant displacement. 2) Find the resultant force. (463 N, 137 degrees), (258 N, 268 degrees) and (379 N, 128 degrees)

### Important Information about Exponential and Logarithmic Functions

A. Convert to logarithmic equations. For example, the logarithmic form of "23 = 8" is "log2 8 = 3". a) 16 3/2 = 64 b) ex = 5 B. Write the logarithmic equation in exponential form. For example, the exponential form of "log5 25 = 2" is "52 = 25". a) log 3 27 = 3 b) log e 1 = 0 c) log 125 25 = 2/3 C. Use the

### Factor Group and Torsion Group

Heres my problem. Consider the group <R,+> (reals under addition) and its normal subgroups Z (integers) and Q (rationals0. (These are normal because R is abelian, of course.) (i) Find an element of Q/Z of order 350. (ii) Show that Q/Z is the torsion subgroup of R/Z. This problem is quite straightforward if you use the defini

### Finding slope and intercept of a line, and solving equations

1. Find the slope and intercept for the line 2y-x-4=0 2. Find the slope and intercept for the line 6/9y+2/3x-5=0 3. For the line y= 3x-3 find a line parallel to it that passes through the point (-1,0) 4. For the line y= 2x+2 find a line parallel to it that passes through the points (2,0) (4,4) 5. For the set of p

### Heat Equation : Non-Homogeneous PDE

Please see the attached file for the fully formatted problem. 2. (30 points) A thin, one-dimensional rod of heat-conducting material with length L = pi is internally and uniformly heated at a rate of alpha degrees per unit time. This means that the temperature of the rod, u(x, t), satisfies the inhomogeneous heat equation ..

### Investment allocation

Matrix Algebra Investment Allocation Problem Donald Trump has some pocket change he wants to invest to make \$3380. His stock broker suggested four (4) investment possibilities to accomplish this goal. The investments and their expected yields are listed in the table below. Investment Rate of Return Risk Level Magellan

### 5 Algebra Problems : Inequalities and Systems of Equations Word Problems

1. Solve the following equation for the variable y. 5x - 3y + 9 = 0 2.Solve the following problem by identifying a variable, writing an equation that describes the situation, and then solving the equation. Find two consecutive even integers that have a sum of 450. 3.Solve the following problem by identifying a variable,

### Stokes's Problem : Calculating drag coefficients around a falling sphere.

Please see the attached problem statement.

### 5 Algebra Problems : Solving Equations

1.Solve the following equation 19 - 3n = - 2n 2.Solve the following equation 2(a - 4) + 4 = 5(9 - a) 3.Solve the following equation and check your answer. (1/2b)- (1/2)= 1/4b 4.Solve the following equation 0.6(x - 50) = 18 - 0.3(40 - 10x) 5.Solve the following equation for the variable x. t - 5x = 4x

### Graph

Refer to the graph given below and identify the graph that represents the corresponding function. Justify your answer. y = 3x y = log3x Plot the graphs of the following functions. 1. f(x)=7 2. f(x)=4 x - 3 3. f(x)=(1/5x 4. f(x)= 3 log x 5. f(x) = log x +2 See Attachment for Graph

### Plotting Graphs of Given Functions

Refer to the graph given below and identify the graph that represents the corresponding function. Justify your answer. y = 3x y = log3x See attachment for Graph Plot the graphs of the following functions. Scan the graphs and plot them. 1. f(x)=7 2. f(x)=4 x - 3 3. f(x)=(1/5x 4. f(x)= 3 log x 5. f(x) = log x

### Exponential and Logarithmic Functions: Real-Life Applications

1. Explain the relevance and application of exponential functions in real-life situations. 2. Explain the relevance and application of logarithmic functions in real-life situations. 3. Think of a real-life situation that can be represented by a logarithmic function, translate the situation to the function, and solve the

### 20 Algebra Problems : Sequences, Series, Combinations and Permutations

Please see the attached file for the fully formatted problems. 1. Write the first four terms of the sequence an = 64(1/4)n , for n=0, 1, 2, 3,... a) 16, 4, 1, ¼ b) 60, 56, 52, 48 c) 64, 16, 4, 1 d) 256, 1024, 16384, 262144 2. Write the given series in expanded form without summation notation. a) -x2-x3

### Algebra : Four Word Problems

1. A rectangular garden has dimensions of 18 feet by 13 feet. A gravel path of equal width is to be built around the garden. How wide can the path be if there is enough gravel for 516 square feet. 2. A business invests \$10,000 in a saving account for two years. At the beginning of the second year, and additional \$3500 is inve

### Quadratic Equations: Formulation of Real-Life Problems and Graph

Please see the attached file for the fully formatted problems. 1. Can a graph be used to solve any quadratic equation? Why or why not? 2. Look at the graph below and comment on the sign of D or the discriminant. From the quadratic equation based on the information provided and find its solution. 3. Formulate two word