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3 years ago

Here are the first five terms of an arithmetic sequence.

Mathematics

1 answer:

qaws [65]3 years ago

6 0

9514 1404 393

Answer:

the difference of squares is 24(3n+2), so a multiple of 24

Step-by-step explanation:

The sequence has a first term of 7 and a common difference of 6, so the n-th term is ...

a[n] = a1 +d(n -1)

a[n] = 7 + 6(n -1)

a[n] = 6n +1

Then the (n+1)-th term is ...

a[n+1] = 6(n+1) +1 = 6n +7

The difference of the squares of these terms is ...

a[n+1]^2 -a[n]^2 = (6n+7)^2 -(6n+1)^2

= (36n^2 +84n +49) -(36n^2 +12n +1)

= 72n +48

= 24(3n +2) . . . . . always a multiple of 24

The difference of squares of terms n and n+1 is 24(3n+2), a multiple of 24.

_____

<em>Check</em>

The difference between squares for n=1 and n=2 is 13^2 -7^2 = 169 -49 = 120. The formula tells us the difference is 24(3·1 +2) = 24·5 = 120, in agreement.

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If sin x = 12÷13 where 0° <x<90°<br>find the value of 1-cos ×cos( x)

s2008m [1.1K]

Answer:

This is how tackle this type of problem:

Draw a right triangle with the indicated sides: side opposite the angle = 12 and hypotenuse = 13

Then, calculate the 3rd side by Pythagoras: x2 + 122 = 132

x2 = 169 - 144

x2 = 25

x = 5

Now, we have all 3 sides of our diagram triangle, so we can find all the trig ratios for the angle.

Next, we use the double angle formula to simplify cos(x + 30) = cos x cos 30 - sin x sin 30

= 5/13 . √3/2 - 12/13 . 1/2

= 5√3 /26 - 6/13

= (5√3 - 12) / 26

Step-by-step explanation:

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3 years ago

Why is the rise the value for the numerator and the run the value for the denominator?

julsineya [31]

Because change in y for the rise is if it goes up or down and change in x for the run to see if it goes left or right

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3 years ago

rationalize root six divided by root three minus root two. <img src="https://tex.z-dn.net/?f=%5Cfrac%7B%5Csqrt%7B6%7D%20%7D%7B%5

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Answer:

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Step-by-step explanation:

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Step-by-step explanation:

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4 years ago

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The points (2, 5) and (6,-3) fall on a particular line. What is its equation in slope-intercept form?

Pachacha [2.7K]

Answer:

y = -2x + 9

Step-by-step explanation:

slope intercept form : y = mx + b

where m = slope and b = y intercept

first let's find the slope

slope formula :

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

where the x and y values are derived from the given points

here we are given (2,5) and (6,-3)

(x1,y1) = (2,5) so x1 = 2 and y1 = 5

(x2,y2) = (6,-3) so x2 = 6 and y2 = -3

we now plug these values into the formula

recall formula

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

plug in x1 = 2, y1 = 5, x2 = 6 and y2 = -3

m = (-3 - 5) / ( 6 - 2 )

m = (-8)/(4)

m = -2

the slope is -2

now to find the y intercept we plug in the slope and the x and y value of a given point into slope intercept form and solve for b

y = mx + b

given point : (2,5) x = 2 , y = 5, m = -2

5 = -2(2) + b

5 = -4 + b

9 = b

so the equation would be y = -2x + 9

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3 years ago