How do you make a T chart for the problem y=2x^2+4x-5

Solution:

First, you have to have a clear idea what y = 2x^2+4x-5 means. This is an equation that tells you that, for any value of x, you can find y by dividing by multiplying x by x, and then multiplying that by two, adding 2 times x and finally subtracting 5. Does that sound familiar?

Now, what is the table you have to make? You will list several values of x (which you will be using as x-coordinates in your graph), and for each one use the equation to find what y is. We’ll show the work:

For x = 1, y = 2*1*1    +    4*1   –   5    =    1

For x = 2, y = 2*2*2    +    4*2   –   5    =  11

For x = 3, y = 2*3*3    +    4*3   –   5    =  25

For x = 4, y = 2*4*4    +    4*4   –   5    =  43

For x = 5, y = 2*5*5    +    4*5   –   5    =  65

Do you see what we did there? We just replaced x in the equation by each value of x, and did the multiplication and addition.

Now your table will look like this:

x |  y

–+—–

1 | 1

2 | 11

3 | 25

4 | 43

5 | 65

We’ve only shown the x,y values for 1 through 5, out there are an infinite number of x values that you could plug in, including negative numbers and fractions. You can use the resulting T chart to help you create a graph, which will look like this:

A 925 N crate is being pushed across a level floor by a force of 325 N at an angle of 25 degrees above the horizontal. The coefficient of kinetic friction is 0.25. Find the magnitude of the acceleration of the crate.

Solution:

First, let’s define what a Newton (N) is: “The Newton (N) is defined as the amount of force that, when acting on a 1 kg mass, produces an acceleration of 1 m/s/s (one meter per second per second). Therefore, 1 N = 1 kg =D7 1 m/s/s.”

The force of friction opposing the 325 N force is .25 * 925 N (which is equal to 231.25 N). The force pulling the crate is 325 N * cos(25), i.e. 294.55 N. (This is the component of force acting parallel to the floor.)

Take the difference between these two and you will have the net force pulling the crate (which is 63.3 N). Using Newton’s equation F = ma, you will find the acceleration by dividing the net force by the mass of the crate (the mass is 925 =/(one standard gravity [9.80665 m/s/s], or 94.32 kg). The acceleration is therefore 63.3 N / 94.32 kg, which equals 0.671 m/s/s.

The total area of a cylinder is 40. If height = 8, find the radius. (The formula for total area used in class is: Total area = 2πrh + 2πr²)

Solution:

The total area is  40π=2πrh+2πr^2
=2πr*8 + 2πr²
=16πr + 2πr²
=16r + 2r²

If we rearrange the terms and divide the terms by 2 (in order to simplify the equation), we get:

r² + 8r – 20 = 0

(r+10)  (r-2) = 0

r = 2  or  -10

Therefore, r = 2 (assuming that -10 is not an option!).

I need to know how to do problems like this, I want to know how to solve, and simplify them, and also finding slopes. Like these kinds of problems(Write the equation, 3x + 5y = 15, in the slope intercept form (y = mx + b))

Solution:

1. Start with an equation like 3x + 5y = 15
2. Move 3x to the other side, so 5y = 15 – 3x
3. Divide both sides by 5, so y = 3 – x
4. Another way of writing this is y = -.6x + 3, or y=mx = b, where m=-0.6 and b = 3
5. If m = -0.6, that means that the slope = -0.6

Find the descriminant of x^2-7x+2=0 and describe the natural roots

Solution:

1. When you have an equation in the form of ax² + =x + c = 0, the solution is x = where  D = b² – 4ac
2. D stands for discriminant, and values of x are the natural roots

• If D > 0, then the values of x are real and distinct.

• If D = 0, then the values of x are real and equal

• If D < 0, then the values of x are unreal

1. In your question, x² – 7x + 2 = 0, so the values of a, b and c are as follows:

• a = 1

• b = -7

• c = 2

1. D = b² – 4ac = 49 – 8 = 41 (this is the value of the discriminant)
2. Since D > 0, then the values of x (the natural roots) are real and distinct

The Trail of Tears in 1838-1839 & the Battle of Wounded Knee in 1890 were significant because they A. demonstrate the technological superiority of the US troops over the indigenous peoples of North America B. typify the harsh treatment of Native peoples at the hands of the US government C. exemplify the determination of the American government to bring unity to North America & undermine any attempts at recession D. clarify the US government’s position on slavery & free soil” E. added large portions of land to the US which had been controlled by foreign powers

Solution:

We feel that the best answer is “B”, as both events involved the deaths of large number of native Americans, including non-combatants:

1. The Trail of Tears: “The Trail of Tears was the relocation and movement of Native Americans, including many members of the Cherokee, Creek, Seminole, and Choctaw nations among others in the United States, from their homelands to Indian territory (present day Oklahoma) in the Western United States. The phrase originated from a description of the removal of the Choctaw Nation in 1831. Many Native Americans suffered from exposure, disease, and starvation while en route to their destinations, and many died, including 4,000 of the 15,000 relocated Cherokee.” (Wikipedia)
2. Battle of Wounded knee: “On December 29, 1890, 365 troops of the U.S. 7th Cavalry regiment, supported by four Hotchkiss guns, surrounded an encampment of Miniconjou (Lakota) and Hunkpapa Sioux (Lakota) near Wounded Knee Creek, South Dakota. The Sioux had been cornered and agreed to turn themselves in at the Pine  ridge Agency in South Dakota. They were the very last of the Sioux to do so. They were met by the 7th Cavalry, who intended to disarm them and ensure their compliance. During the process of disarming the Sioux, a deaf tribesman named Black Coyote could not hear the order to give up his rifle and was reluctant to do so. A scuffle over Black Coyote’s rifle escalated into an all-out battle, with those few Sioux warriors who still had weapons shooting at the 7th Cavalry, and the 7th Cavalry opening fire indiscriminately from all sides, killing men, women, and children, as well as some of their own fellow troopers. The 7th Cavalry quickly suppressed the Sioux fire, and the surviving  Sioux fled, but U.S. cavalrymen pursued and killed many who were unarmed. By the time it was over, about 146 men, women, and children of the Lakota Sioux had been killed. Twenty-five troopers also died, some believed to have been the victims of friendly fire as the shooting took place at point blank range in chaotic conditions. Around 150 Lakota are believed to have fled the chaos.” (Wikipedia)

In trapezoid ABCD the median MN cuts diagonals AC =D at p and q repectively, BC=12, and AD=20 Determine PQ please explain your steps. i know the median is 16 and I know the correct answer is 4, I know there is a formula but we have not proved it.

Solution:

First, let’s draw the trapezoid so that we can visualize the problem. We have not drawn the trapezoid exactly to scale, but this should be accurate enough for our purposes:

Now, we know that MN = 16 because the median equals the average of the top and bottom of the trapezoid

We also know that the distance of Mp = 6, because it just be half the length of BC (the sides of triangle AMp are half the size of the sides of triangle ABC because the triangles are similar and we know that AM is half the length of AB since MN is the median).Similarly,the length of qN = 6.

Now it’s easy to solve for pq:

1. Mp + pq + qN = MN = 16
2. 6 + pq + 6 = 16
3. pq = 4

If i was just given the container specification which is the shape of base is triangle, the height of box 40 in and the volume 720 cu in. the question is what dimensions were necessary for you to deteremine before you could build your box. How did you find the missing dimensions?

Solution:

Let’s assume that the sides of the box are vertical. In that case, the volume of the container would be the area of the base times the height. Since we know the volume is 720 cu. in., and the height is 40 =n, then we know that the area of the base is 18 sq. in. = 18*40=720).

We don’t have enough information to find the lengths of the sides of the container’s triangular base. There are many shapes of triangles whose area is equal to 18 sq. inches. We would need to know the lengths of at least two sides of the base of the container, plus the angle formed by these two sides. We can then use the cosine rule (see below) to figure out the required length of the third side.

The “cosine rule”

In the triangle below, the three sides have lengths a, b and c. Angle A is opposite side a; similarly for B and C.

The cosine rule is as follows:  a²=b²+c²– 2bc (cos(A))

This allows us to work out the required length of the third side of the triangle if we know the length of two sides and the angle between them.

How do you find the area of a base on a 3-D rectangle?

Solution:

1. The base of the 3D rectangle is in the shape of a 2D rectangle.
2. Multiply the length of this 2D rectangle by its width to let the area

What is the cardinality of the following set. P(S) stands for power set. Find p (p ((S) for S = {a, b}

Solution:

1.    The cardinality of a set is a measure of the “number of elements of the set”. For example, the set A = {2, 4, 6} contains = elements, and therefore A has a cardinality of 3.
2.    Given a set S, the power set of S, written , P(S), is the set of all subsets of S, including the empty set and S itself.
3.    If S={a, b}, then P(S) ={{},{a},{b},{a,b}} and the Cardinality of P(S) is 4.