Free Essay

w2 - 2w -15 = 15-15

w2- 2w -15 = 0

(w – 5) (w+3) = 0

w-5 = 0 w +3 = 0 w-5 + 5 = 5+ 0 w +3-3 = 0 - 3 w = 5 w = -3

w = 5, -3

(5)2 – 2(5) = 15

25 – 10 = 15

15 = 15 True

(-3)2 – 2 (-3) = 15

9 + 6 = 15

15 =15

This is the original quadratic equation. In order to solve it, we will set it equal to zero.

Subtract 15 from both sides of the equal sign

Now that our trinomial is equal to zero we can start factoring the equation. In order to do that we have to factor the trinomial into two binomials because we cannot use the completing the square method.

The reason why I picked -5 and 3 is because when we multiply both numbers we get -15 and when we add them they equal -2.

Now we will find the value of the variables by isolating them. Solution

Let’s check our first solution (5) by plugging it in to our original quadratic equation.

Our second solution also equals to 15.

Problem #82

3v2 + 4v -1 = 0

x= -b±b2-4ac2a

a = 3 b =4 c =-1

v = -4±42-4(3)(-1)2(3)

The second quadratic equation will be solved using the quadratic formula.

Quadratic Formula

These three variables will be plugged into our formula.

Now we will multiply the given values

v = -4±286

v = -4±(4)(7)6 27

v = -4±276 Divide by 2 (numerator and denominator)

v = --2±73

v = {.215 , -1.549}

After simplifying the equation we can see that our discriminant b2 – 4ac is equal to 16 + 12 or 28. This means that our quadratic equation will have two solutions.

Our next step will be simplify our radical.

Our next step will be to simplify our equation and divide the rest of the quadratic formula by 2 in order to simplify it one more time.

Approximately

Free Essay

...Sailboat Stability MAT222 Ms. Scarf July 29, 2014 Sailboat Stability This weeks assignment is found on page 605 of our math book, question number 103. Focus is solving formulas and using a vocabulary that describes the steps in the equations in mathmatical terms. This weeks focus is radical equations/formulas. The specific problem assigned gives real world value in understanding sailboats and the mathematical understanding of when the stability could be compromised or ideal. The problem is as follows: Sailboat stability. To be considered safe for ocean sailing, the capsize screening value C should be less than 2. For a boat with a beam (or width) b in feet and displacement d in pounds, C is determined by the function. C=4d-1/3 b (Dugopolski,2012) There are three parts to this problem a, b, and c. Each one will be worked out. a)Find the capsize screening value for the Tartan 4100, which has a displacement of 23,245 pounds and a beam 13.5ft. Using the formula and substituting the values given for the variables of d and b: C=4(23245)-1/3(13.5) First work the exponent by using the reciprocal due to the negative value C=4(.035)(13.5) Multiply all C=1.89 This is the capsize screening value(notice it is below 2 as needed) b) Solve for d of the formula C=4d-1/3b Start isolating d by dividing both sides by 4b C/4b=d-1/3 Now resolve...

Words: 514 - Pages: 3

Free Essay

...Solving Proportions MAT222 Week 1 Assignment September 22, 2014 Solving Proportions Solving for a proportion can be used within numerous real-world problems, such as finding the population of an area. Conservationists are able to predict the population of bear’s in their area by comparing information collected from two experiments. In this problem, 50 bears in Keweenaw Peninsula were tagged and released so conservationists could estimate the bear population. One year later, the conservationist took random samples of 100 bears from the same area, proportions are able to be used in order to determine Keweenaw Peninsula’s bear population. “To estimate the size of the bear population on the Keweenaw Peninsula, conservationists captured, tagged, and released 50 bears. One year later, a random sample of 100 bears included only 2 tagged bears. What is the conservationist’s estimate of the size of the bear population (Dugolpolski, 2012)?” In order to figure the estimated population, some variables need to first be defined and explain the rules for solving proportions. The ratio of originally tagged bears to the entire population is (50/x). The ratio of recaptured tagged bears to the sample size is (2/100). 50x=2100 is how the proportion is set up and is now ready to be solved. Cross multiplication is necessary for this problem. The extremes are (100) and (50). The means are (x) and (2). 100(50)=2x New equation, and now solve for (x). 50002=2x2 Divide both...

Words: 608 - Pages: 3

Premium Essay

...Composition and Inverse MAT222: Week 5 Assignment April 6, 2014 Composition and Inverse For this week’s assignment we are given the task of learning how to solve Composition and Inverse math problems. This week’s assignment focuses on the following problem: f(x)=2x+5 g(x)=x2-3 h(x)= 7-x / 3 The first thing I will do is compute (f – h)(4). (f – h)(4)=f(4) – h(4). Each function may be calculated separately and will be subtracted due to the rules of composition. f(4)=2(4)+5 We will then substitute the 4 from the problem and plug it into the x. f(4)=8 +5 We will be using order of operations in order to evaluate the function. f(4)=13 h(4)=(7-4) / 3 The same process will be used in this function where we will plug in f(4) and h(4) then the problem will look like: h(4)=3/3 h(4) = 1 (f – h)(4)=13-1 (f – h)(4)=12 This is the solution after substituting the values into the problem. The next step will consist of the two pairs of functions will composed into each other. In order to do this I will first have to find the solution for the function g(x). In order to do this I will be calculating it and then substituting for the x value in the f(x). This rule will function because the g function will be replacing the f function. Therefore this rule will help us (f▫g)(x)= f(g(x)). (f▫g)(x)=f(g(x)) (f▫g)(x)=f(x2-3) f will work on the rule of g and g will be replacing x. (f▫g)(x)=2(x2 - 3)-5 we will be using the rule of f and it will be applied...

Words: 692 - Pages: 3