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3 years ago

What is the equation that matches the graph?

Mathematics

1 answer:

Korolek [52]3 years ago

3 0

The answer is C. 1/3 represents the slope and -3 represents the y intercept.

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Use induction to show that 12 + 22 + 32 + ... + n2 = n(n+1)(2n+1)/6, for all n > 1.

dlinn [17]

Answer with Step-by-step explanation:

Let $P(n)=1^2+2^2+3^2+.....+n^2=\frac{n(n+1)(2n+1)}{6}$

Substitute n=2

Then $P(2)=1+2^2=5$

$P(2)=\frac{2(2+1)(4+1)}{6}=5$

Hence, P(n) is true for n=2

Suppose that P(n) is true for n=k >1

$P(k)=1^2+2^2+3^2+...+k^2=\frac{k(k+1)(2k+1)}{6}$

Now, we shall prove that p(n) is true for n=k+1

$P(k+1)=1^2+2^2+3^2+...+k^2+(k+1)^2=\frac{(k+1)(k+2)(2k+3)}{6}$

LHS

$P(k+1)=1^2+2^2+3^2+.....+k^2+(k+1)^2$

Substitute the value of P(k)

$P(k+)=\frac{k(k+1)(2k+1)}{6}+(k+1)^2$

$P(k+1)=(k+1)(\frac{k(2k+1}{6})+k+1)$

$P(k+1)=(k+1)(\frac{2k^2+k+6k+6}{6})$

$P(k+1)=(k+1)(\frac{2k^2+7k+6}{6})$

$P(k+1)=(k+1)(\frac{2k^2+4k+3k+6}{6})$

$P(k+1)=\frac{(k+1)(k+2)(2k+3)}{6}$

LHS=RHS

Hence, P(n) is true for all n >1.

Hence, proved

4 0

3 years ago

I need help :) please and thank u if u get it right i will give u brainlist :))))):)))))

Kobotan [32]

The slope is -2. The y-intercept is (0,1).

6 0

3 years ago

How many months are equal to 45 days

Pie

Answer:

1.47945 months

Step-by-step explanation:

5 0

3 years ago

Which equation shows the point-slope form of the line that passes through (3, 2) and has a slope of 1/3?

Vilka [71]

Answer:

Option 2: $y - 2 = \frac{1}{3}(x-3)$ is the correct answer.

Step-by-step explanation:

The equation of a line with given point(x1,y1) and slope m is given by:

$y-y_1 = m(x-x_1)$

The line passes through (x1,y1)

Given

$(x_1,y_1) = (3,2)\\m = \frac{1}{3}$

=> x1 = 3

=> y1 = 2

Putting the values of x1, y1 and slope(m) in the point-slope form, the equation of line is:

$y - 2 = \frac{1}{3}(x-3)$

Hence,

Option 2: $y - 2 = \frac{1}{3}(x-3)$ is the correct answer.

3 0

3 years ago

Using the information in the diagram, what is the height of the tree to the nearest foot?

Ray Of Light [21]

The answer is 80 ft.

Based on the diagram we know that the tree triangle and the building triangle are similar triangles where the lengths of each are proportional to the other.

The lengths of the triangle the tree makes are half of the lengths of the building triangle. So this problem can be solved using ratio and proportion:

to solve for x, all you need to do is cross multiply then divide.

The answer is then 80ft.

Another way to solve this is just by using logic. If the lengths of the tree triangle is half of the building, simply divide the lengths of the building triangle by two.

160ft/2 = 80ft.

5 0

2 years ago