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3 years ago

What is the slope of the line that passes through the points (26, 7) and (-39, 12)?

Mathematics

1 answer:

Digiron [165]3 years ago

8 0

Answer:

$m=-\frac{1}{13}$

Step-by-step explanation:

we know that

The formula to calculate the slope between two points is equal to

$m=\frac{y2-y1}{x2-x1}$

we have the points

(26, 7) and (-39, 12)

substitute the values in the formula

$m=\frac{12-7}{-39-26}$

$m=\frac{5}{-65}$

simplify

$m=-\frac{1}{13}$

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Step-by-step explanation:

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Class 11

>>Maths

>>Trigonometric Functions

>>Trigonometric Equations

>>Solve for x: sin x + sin 2x...

Question

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Solve for x:sinx+sin2x+sin3x=cosx+cos2x+cos3x in the interval 0≤x≤2π.

Medium

Solution

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We write the given equation as

(sinx+sin3x)+sin2x=(cosx+cos3x)+cos2x

or 2sin2xcosx+sin2x=2cos2xcosx+cos2x

or sin2x(2cosx+1)=cos2x(2cosx+1)

or (sin2x−cos2x)(2cosx+1)=0

∴sin2x−cos2x=0 or 2cosx+1=0

If sin2x−cos2x=0, then tan2x=1,

Hence 2x=nπ+π/4

or x=(4n+1)

.(1)

If 2cosx+1=0, then cosx=−1/2 (2)

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2π

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6n±2

We seek values of x in the interval 0≤x≤2π

In this interval (1) gives

x=π/8,5π/8,9π/8,13π/8. (n=0,1,2,3)

and (2) gives x=2π/3,4π/3. (for n=0,1)

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x=π/8,5π/8,2π/3,9π/8,4π/3,13π/8.

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2 years ago

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3 years ago

A simple random sample of n measurements from a population is a subset of the population selected in a manner such that which of

Ierofanga [76]

Answer:

a) sample of size n from the population has an equal chance of being selected.

b) Every member of the population has an equal chance of being included in the sample.

Step-by-step explanation:

Simple random sampling:

It is a type of probabilistic sampling.
It is an unbiased representation of population.
The probability of selection is equal for every observation.
A sample is taken in such a way that each member has an equal probability of being selected.
A simple random sample is a subset of a statistical population in which each member of the subset has an equal probability of being chosen.
Thus,the correct interpretation is given by,

a) sample of size n from the population has an equal chance of being selected.

b) Every member of the population has an equal chance of being included in the sample.

c) The simplest method of selection is used to create a representative sample.

The statement is false.

There is no pattern or technique used for selection. The selection is purely random.

d) Each subset of the population has an equal chance of being included in the sample.

The statement is false.

Each object of the population has an equal chance of being included in the sample. and not each subset.

e) Every sample of size n from the population has a proportionally weighted chance of being selected.

The given statement is false.

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