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# Mathematics

## Discover

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### Help with this math question?

Determine which of the following matrix equations represents the solution to the system:

2x + y = 2

5x + 3y = 13.

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### How do you solve this math word problem? PLEASE HELP ME AND EXPLAIN STEP BY STEP!!!?

A lumberyard charges \$ 1 per cut to trim boards. Bob buys a 12-ft board and wants it out into twelve 1-ft pieces. How much will he be charged for the cutting? The correct answer is \$11.

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### Am I right?

Hello, I'm 14 years old, I'm currently in 8th grade and I'm practicing math so answer here if I'm right.

X + X = 2X

X × X = X²

X + Y = XY

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### which set of values for x should be tested to determine the possible zeros of y = x^3 + 6x^2 - 10x + 35? (multiple choice)?

It's a cubic equation...

so possible zeros are when

0 = (x-a)(x-b)(x-c)

==> 0 =x^3 -(a+b+c)x^2 + (ab + ac+bc)x -abc

so

-a*b*c = 35

factoring 35... one of the factors must be negative

So, looking at absolute values

|1| * |1| * |35|

|1| * |5| * |7|

so c) is not right -- 12 is not among the factors above

d) is not right -- one of the factors must be possibly negative

a) is out, since one of the factors must be 1 or -1

which leaves b) as the answer

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### Can someone help me with this equation? Reducing to linear form using logs?

If you've worked it out, I think you should have posted your work and then asked for someone to review it. Otherwise it looks like you just want someone else to do the work.

In any case, I'll do my best to help.

Original equation:

T = 2π√(l/g)

Take the log of both sides:

log(T) = log[2π√(l/g)]

Use the product rule to turn the log of a product in a sum of logs:

log(T) = log(2) + log(π) + log[√(l/g)]

Looking at the third log, we know that a square root can be rewritten as raising something to the ½ power:

log(T) = log(2) + log(π) + log[(l/g)^½]

Using the power rule, we can bring ½ to the front:

log(T) = log(2) + log(π) + ½ log(l/g)

Finally, use the quotient rule to split the last log into a subtraction of logs.

log(T) = log(2) + log(π) + ½[log(l) - log(g)]

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### The solution an algebraic equation.?

It would be useful to memorize the following:

lim (1 + 1/x)^x = e

x→∞

let x = n/r

(1+r/n)^(nt) = (1 + 1/x)^(xrt)

= ((1 + 1/x)^(x))^(rt)

lim ((1 + 1/x)^(x))^(rt) = e^(rt)

x→∞

Thus

2P = Pe^(rt)

t = ln(2)/r

Because ln(2) is approximately 70% (and less-frequent compounding increases t),  this leads to the "Rule of 72": for a given rate of return r%, your investment will double in approximately 70/r or 72/r years.

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### The rectangle is 84m long and 57m wide what is the length use the value 3.14 and do not round. ?

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given

t = 1 min x 1hour/60min = 0.0166 hours

d = 50 m  x 31 = 1550 m x km/1000m = 1.55km

solving the trains speed

s = d/t

s = 1.55 km/ 0.0166 hours

s = 93.37 km/h or 93 km/h    Answer//

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### Math questions ?

Are all the question weighted equally? Are all the questions equally difficult?

75 minutes * 60 seconds = 4500 seconds

If you divide that total time by 128 questions, you get the average per question.

4500 / 128 ≈ 35 seconds / question

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### Finding Derivative of a Point?

g(x) = 4x² - 2x + 15 ← this is a function

g(5) = 100 - 10 + 15 = 105 → the representative curve of the function passes through (5 ; 105)

g'(x) = 8x - 2 ← this is its derivative

g'(5) = 40 - 2 = 38 ← this is in fact the slope of the tangent line to the curve at point (5 ; 105)

g(x) = 4x² - 2x + 15 ← this is the function → to calculate the derivative:

Lim [g(x₀ + h) - g(x₀)] / h

h → 0

Lim [ { 4.(x₀ + h)² - 2.(x₀ + h) + 15 } - { 4x₀² - 2x₀ + 15 } ] / h

h → 0

Lim [ { 4.(x₀² + 2x₀.h + h²) - 2x₀ - 2h + 15 } - 4x₀² + 2x₀ - 15 ] / h

h → 0

Lim [4x₀² + 8x₀.h + 4h² - 2x₀ - 2h + 15 - 4x₀² + 2x₀ - 15] / h

h → 0

Lim [8x₀.h + 4h² - 2h] / h

h → 0

Lim h.[8x₀ + 4h - 2] / h

h → 0

Lim (8x₀ + 4h - 2) = 8x₀ - 2

h → 0

g'(x₀) = 8x - 2

g'(5) = 40 - 2 = 38 ← this is the same result (above)

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### Solve the system: y=14x2+2x−6 y=−14x2−3x+6?

The parabolas above intersect in two places, at (a , b) and (c , d), where a, b, c, and d are all integers. a + b + c + d =

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### How far is a 5k?

3 ounces short of 1 cup.

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### find the sum of (7t + 6 ) + (-4t -2)?

Remove the brackets

Hence

7t + 6 +-4t +-2

Remember +/- becomes minus (-)

7t + 6 - 4t - 2

3t + 4

Done!!!!

Remember for +/-  double signs .

+ + = +

+ - = -

- + = -

- - = +

If no sign is given read it as plus(+).

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