Question

What are some things you will be learning in 11th grade math?

Answer 1

math.....

Answer 2

problems

Answer 3

An airplane flies against the wind from A to B in 8 hours. The same airplane returns from B to A, in the same direction as the wind, in 7 hours. Find the ratio of the speed of the airplane (in still air) to the speed of the wind.
Find the area between two concentric circles defined by

x2 + y2 -2x + 4y + 1 = 0

x2 + y2 -2x + 4y - 11 = 0
Find all values of parameter m (a real number) so that the equation 2x2 - mx + m = 0 has no real solutions.
The sum an integer N and its reciprocal is equal to 78/15. What is the value of N?
m and n are integers so that 4m / 125 = 5n / 64. Find values for m and n.
Simplify: 3n + 4001 + 3n + 4001 + 3n + 4001
P is a polynomial such that P(x2 + 1) = - 2 x4 + 5 x2 + 6. Find P(- x2 + 3)
For what values of r would the line x + y = r be tangent to the circle x2 + y2 = 4?
Solutions to the Above Problems

Let x = speed of airplane in still air, y = speed of wind and D the distance between A and B. Find the ratio x / y

Against the wind: D = 8(x - y), with the wind: D = 7(x + y)

8x - 8y = 7x + 7y, hence x / y = 15
Rewrite equations of circles in standard form. Hence equation x2 + y2 -2x + 4y + 1 = 0 may be written as

(x - 1)2 + (y + 2) 2 = 4 = 22
and equation x2 + y2 -2x + 4y - 11 = 0 as
(x - 1)2 + (y + 2) 2 = 16 = 42

Knowing the radii, the area of the ring is Pi (4)2 - Pi (2)2 = 12 Pi
The given equation is a quadratic equation and has no solutions if it discriminant D is less than zero.

D = (-m)2 - 4(2)(m) = m2 - 8m

We nos solve the inequality m2 - 8m < 0

The solution set of the above inequality is: (0 , 8)

Any value of m in the interval (0 , 8) makes the discriminant D negative and therefore the equation has no real solutions.
Write equation in N as follows

N + 1/N = 78/15

Multiply all terms by N, obtain a quadratic equation and solve to obtain N = 5.
4m / 125 = 5n / 64


Cross multiply: 64 4m = 125 5n

Note that 64 = 43 and 125 = 53

The above equation may be written as: 4m + 3 = 5n + 3

The only values of the exponents that make the two exponential expressions equal are: m + 3 = 0 and n + 3 = 0, which gives m = - 3 and n = - 3.
3n + 4001 + 3n + 4001 + 3n + 4001 = 3(3n + 4001) = 3n + 4002
P(x2 + 1) = - 2 x4 + 5 x2 + 6

Let t = x2 + 1 which also gives x2 = t - 1

Substitute x2 by t - 1 in P to obtain: P(t) = - 2 (t - 1)2 + 5 (t - 1) + 6 = -2 t 2 + 9t - 1

Now let t = - x2 + 3 and substitute in P(t) above to obtain

P(- x2 + 3) = -2 (- x2 + 3) 2 + 9 (- x2 + 3) - 1 = -2 x 4 + 3 x 2 + 8
Solve x + y = r for y: y = r - x

Substitute in the equation of the circle:

x2 + (r - x)2 = 4

Expand: 2 x2 -2 r x + r 2 - 4 = 0

If we solve the above quadratic equation (in x) we will obtain the x coordinates of the points of intersection of the line and the circle. The 2 points of intersection "become one" and therefore the line and the circle become tangent if the discriminant D of the quadratic equation is zero. Hence

D = (-2r)2 - 4(2)(r2 - 4) = 4(8 - r2) = 0

Solve for r to obtain: r = 2sqrt(2) and r = - 2sqrt(2)

Answer 4

HOLY pellet!!!!!!!!!!!!1

Answer 5

this is what you will learn

Answer 6

thats llong

Answer 7

that is just math

Answer 8

Understand and practice writing as a recursive process.
1.2 Use writing, speaking, and visual expression for personal
understanding and growth.
1.3 Communicate in speech, writing, and multimedia using content,
form, voice, and style appropriate to the audience and purpose.
1.4 Develop and use the tools and practices of inquiry and research —
generating, exploring, and refining important questions; creating
a hypothesis or thesis; gathering and studying evidence; drawing
conclusions; and composing a report.
1.5 Produce a variety of written, spoken, multigenre, and multimedia
works, making conscious choices about language, form, style,
and/or visual representation for each work.
2.1 Develop critical reading, listening, and viewing strategies.
2.2 Use a variety of reading, listening, and viewing strategies to
construct meaning beyond the literal level.
2.3 Develop as a reader, listener, and viewer for personal, social,
and political purposes, through independent and collaborative
reading.
3.1 Develop the skills of close and contextual literary reading.
3.2 Read and respond to classic and contemporary fiction, literary
nonfiction, and expository text, from a variety of literary genre
representing many time periods and authors.
3.3 Use knowledge of literary history, traditions, and theory to
respond to and analyze the meaning of texts.
3.4 Examine mass media, film, series fiction, and other texts from
popular culture.
4.1 Understand and use the English language effectively in a variety
of contexts and settings.
4.2 Understand how language variety reflects and shapes
experience.

Answer 9

that is English