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PSYCHO15rus [73]
3 years ago
7

As the earth rotates, it travels a distance of 80 miles in 5 minutes. At this constant rate, which equation best represents y, t

he total distance the earth travels in x minutes?

Mathematics
1 answer:
solniwko [45]3 years ago
6 0

Answer:

y=16x

Step-by-step explanation:

So, you are given the equation as if y=total distance the earth travels in x minutes. If you are given that you travel 80 miles in 5 minutes, you can plug  these value into the variables they are representing and solve for the constant.

Visual:

y=xk          y=miles        x=minutes         k=constant

Plug in your values and you get:

80=5k

Now, you solve for k by diving 5 on both sides, which leaves you with k=16.

Now you plug your value for k into the original equation, leaving you with y=16x

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Use sigma notation to represent the sum of the first seven terms of the following sequence -4,-6,-8.....
lina2011 [118]

Answer:Answer:

\sum\left {{7} \atop {1}} \right -n(3+n)

Step-by-step explanation:

Given the sequence -4,-6,-8..., in order to get sigma notation to represent the sum of the first seven terms of the sequence, we need to first calculate the sum of the first seven terms of the sequence as shown;

The sum of an arithmetic series is expressed as S_n = \frac{n}{2}[2a+(n-1)d]

n is the number of terms

a is the first term of the sequence

d is the common difference

Given parameters

n = 7, a = -4 and d = -6-(-4) = -8-(-6) = -2

Required

Sum of the first seven terms of the sequence

S_7 = \frac{7}{2}[2(-4)+(7-1)(-2)]\\\\S_7 =  \frac{7}{2}[-8+(6)(-2)]\\\\S_7 =  \frac{7}{2}[-8-12]\\\\\\S_7 = \frac{7}{2} * -20\\\\S_7 = -70

The sum of the nth term of the sequence will be;

S_n = \frac{n}{2}[2(-4)+(n-1)(-2)]\\\\S_n = \frac{n}{2}[-8+(-2n+2)]\\\\S_n = \frac{n}{2}[-6-2n]\\\\S_n =  \frac{-6n}{2} -  \frac{2n^2}{2}\\S_n = -3n-n^2\\\\S_n = -n(3+n)

The sigma notation will be expressed as \sum\left {{7} \atop {1}} \right -n(3+n). <em>The limit ranges from 1 to 7 since we are to  find  the sum of the first seven terms of the series.</em>

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