# Math

• Math
Lets assume that you have a graph with a shaded region bounded by the line segments with endpoints (0,3),(0,9),(15/2,9/2),(10,0) and (3,0) (forming a pentagonal shaded region.)(See attachment.))...

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Hello! To prove this trigonometric identity, we need to know the formulas for sine of a sum and sine of a difference. They are as follows: sin ( x + y ) = sin ( x ) cos ( y ) + cos ( x ) sin ( y...

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We are asked to graph the solution set for the following system of linear inequalities: {([2x+4y>16],[-x+3y>=7]) Each linear inequality in two variables divides the plane into half-planes....

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Hello! We need to prove this trigonometric identity. It is not hard, but we have to know some formulas. The first is the formula of cosine of the sum of two angles, which expresses cos ( x + y )...

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We are given that identically sized bags of fertilizers contain ingredients as follows: formulation A has 18 parts nitrogen, 4 parts phosphorous, and 5 parts potassium, while formulation B has 20...

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We are asked to find the amount of three different foodstuffs to prepare in order to meet the requirements of particular vitamins/minerals. The amount of each for each foodstuff is given below:...

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We are asked to solve the following system using the Gauss-Jordan elimination method: 2x+3y-2z=122x-3y+2z=-44x-y+3z=-4 We put the coefficients into an augmented matrix:...

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In simpler terms, this question is asking, "arrange this group in order of increasing age, then identify the top 25% of eldest members of the group". The ages need to be tallied, with each instance...

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We are asked to verify the trigonometric identity 2csc(2x)=sec(x)csc(x). To verify an identity we start on one side of the equation and through logical steps transform the expressions to the...

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We are given the following information about chicken sandwiches. Let x represent the grams of fat. Then the mean of 11 sandwiches is bar(x)=20.6 with a standard deviation of s_x=9.8 Let y (the...

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If we are given a system of linear equations, there are a few different situations that can arise. A system can be consistent (there exists some solution) or inconsistent (there are no solutions.)...

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We are given a matrix which has the prices of models of buildings in three different areas. The prices of all houses will be increased by 3%; we are asked to write a matrix with the new prices. The...

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To determine the bounded region, graph the given equations.(See Figure 1). Then, shade the bounded region. Since the axis of rotation is horizontal, in cylindrical method, the rectangular strip to...

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Hello! Essentially, there are two unknowns: for the price at Marys, denote it as x (dollars), and the price at Cal's as y (dollars). We are given two statements about these prices. The first...

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Let us assign variables: let m be the price of the system at Mary's and let c be the price of the system at Cal's. We are told that the price at Mary's, m, is $220 less than twice the price at... 1 Educator Answer • Math Use the information given to set up equations as follows: Assign variables: Let x be the amount invested in stocks, y the amount invested in bonds, and z the amount invested in money markets. (1)... 1 Educator Answer • Math We are asked to approximate the definite integral int_(0)^(3) e^(-x^2)dx One method is to use upper and lower sums. We divide the region into n rectangles bounded by the x-axis and the curve such... 1 Educator Answer • Math I'm not able to solve this exact problem for you per the eNotes terms of use, but let me talk through a similar problem for you. Afterward, you should be able to use the steps shown here to solve... 1 Educator Answer • Math We are asked to find the midpoint of the segment joining the intersection points of the curve y=x^2-4x+4 and the line y=x+c (we are told that m is a constant and m=1—we let c vary.) **If you... 1 Educator Answer • Math In order to subtract one fraction from another fraction, you will need to find the lowest common denominator. The lowest common denominator is the smallest number that can be exactly divided... 1 Educator Answer • Math We are asked to find the equation of the line with slope m=3/4 and containing the point (-8,4). Recognize that a line is determined by two points (through two points there is exactly one line.)... 1 Educator Answer • Math This problem is solved by looking at the definitions of certain terms. APR (annual percentage return) is the percent that you would pay on the balance if you left it in the bank for a year with no... 1 Educator Answer • Math We are given that int_(0)^(1)(15xsqrt(x^2+9))dx=50sqrt(10)-135 and we are asked to evaluate int_(1)^(0)(15usqrt(u^2+9))du . These are definite integrals. If we restrict the variables to the... 1 Educator Answer • Math We are asked to create the 95% confidence interval for the mean number of nights that people stayed for vacation. We are told that the sample size was 1500, and the sample mean is 7.5. We are also... 1 Educator Answer • Math Hello! Although$10000 is a number, it does not influence the answer. Let's select 4 students one by one. The first student may be any of those 8 possible. After this choice, one less student...

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We are asked to find the confidence level of the mean of the population that a sample was drawn from. The data from the sample is bar(x)=21, n=32, sigma=3 with a 95% confidence (alpha=.05 )...

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We are given that there are a maximum of 19.15 hours of sunlight on June 21 (day 172) and a minimum of 5.62 hours on December 21 (day 355.) We are told that the underlying function is periodic, and...

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We are asked to show that the system of equations 2x-y=-4 and 8x-4y=8 has no solutions. A system of linear equations is said to be consistent if it has solutions. If there are two linear equation...

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We are asked to solve the system of equations using Gaussian elimination (or Gauss-Jordan elimination.) The system: 3x-2y+z=3x+3y-4z=-72x-3y+5z=8x-8y+9z=17 The idea is to place the coefficients...

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A manager gives gift cards to every 80th customer. On Saturday, 1210 customers entered, while on Sunday, 1814 customers entered. We are asked to find the number of people who received gift cards....

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We are given that Jenny finished 12 of 20 piano lessons from her book and that Liam finished the same percentage from his book of 30 lessons. We are asked to find the number of lessons Liam...

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I assume you are asked to show that the finite sum (this is a series; the sum of the elements of some sequence): 3+6+9+...+3n=(3n(n+1))/2 We can rewrite the equation as :...

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The equations indeed represent two straight lines, because they are both linear (have the form A x + B y = C ). To find the point of intersection is the same as to solve the system of these...

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(1) We are asked to find the point of intersection of the lines y=3x+4 and y=-2x+9. There are several methods to find this point, assuming it exists. Given the equations of two lines, the graphs of...

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In this question, x represents the quantity demanded in units of 1000, and p represents unit price in dollars. The equation of the demand curve is 3x + 4p - 48 = 0. We rewrite this equation in the...

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Let's start by looking at the component parts of the number sentence. Five is being multiplied by zero. The product of that answer then has one fifth added to it. Everything in the parentheses is...

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1) For f(x) = 3x + 9, we can rewrite as y = 3x + 9 and the reverse the x and y, which yields x = 3y + 9. If we solve for y, we'll have the inverse function. x = 3y + 9x - 9 = 3yy = 1/3x - 3 2)...

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We are asked to graph the functions C(x)=12x+17000 and C(x)=20x+16000. See the attachment for the graphs. C(x)=12x+17000 is in green while C(x)=20x+16000 is in blue. C(x)=12x+17000 is a linear...

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There are 4 answers for each multiple choice question and each of them has only one correct answer. If any answer is chosen at random the probability of it being correct is 1/4. The probability...

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The boat moves up and down with the passing waves. I take the height of the boat to be a sinusoidal function. And the height of the boat is zero at the start of the cycle. The distance between the...

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f(x) = 2x g(x) = x + 3 First let us find (fog)(x) (fog)(x) = f(g(x) = f(x+3) = 2(x+3) = 2x + 6 ==> (fog)(x) = 2x + 6 Now let us find (gof)(x): (gof)(x)...

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You need to evaluate the definite integral of the given funtion to find the area under its graph such that: int_1^n (x^2+ sqrt(1+2x)) dx  You need to use the property of linearity of integrals...

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The given relation  tan lambda = (cos phi_n*tan lambda- mu)/(cos phi_n + mu*tan lambda)  cannot be proved. As seen from the link provided in the question the back drive efficiency is given by...

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You need to find the limit of the function tan 2x , x-gtpi/2 , hence you need to substitute pi/2 for x in the equation of the function such that: lim_(x-gtpi/2) tan 2x = tan 2(pi/2)...

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In the problem we are given the length of two of the sides of the triangle and we have two of the angles. The sum of the three angles of a triangle is equal to 180 degrees. Using this, the third...

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First, it depends on how you interpret the dv term. The most obvious way is to interpret it as (dv)/dx which is how I'll treat it. There are two things to remember with regard to differential...

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Hello! Because the task contains expressions dx / dt and dy / dt, we know that x and y are functions of t : x = x ( t ), y = y ( t ) . Here t is an independent variable....

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We are asked to evaluate int_(-oo)^(oo)e^(-x^2)xdx I. The easy way is to recognize xe^(-x^2)` as an odd function. ( f(-x)=-f(x) ). Since the limits of integration are symmetric about the origin,...