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Goshia [24]
3 years ago
13

While training for a marathon, Jeff wants to increase the number of miles he runs each day. On the first day of training, Jeff r

uns 5 miles. He plans on increasing the number of miles he runs a day by 1 for the remainder of the week. Write a series to model the situation.
Also the series doesn't have to be more than seven numbers*****
Mathematics
1 answer:
user100 [1]3 years ago
6 0

Answer:

The series is 5 , 6 , 7 , 8 , 9 , 10 , 11

Step-by-step explanation:

* Lets revise the arithmetic series

- In the arithmetic series there is a constant difference between

 each two consecutive numbers

- Ex:

# 2  ,  5  ,  8  ,  11  ,  ……………………….  (constant difference is 3)

# 5  ,  10  ,  15  ,  20  ,  …………………………  (constant difference is 5)

# 12  ,  10  ,  8  ,  6  ,  ……………………………  (constant difference is -2)

* General term (nth term) of an Arithmetic series:

- If the first term is a and the common diffidence is d, then

 U1 = a  ,  U2  = a + d  ,  U3  = a + 2d  ,  U4 = a + 3d  ,  U5 = a + 4d

- So the nth term is Un = a + (n – 1)d, where n is the position of the

 number in the series

* Lets solve the problem

- Jeff wants to increase the number of miles he runs each day

∴ He will add the initial value by constant number each day

- He plans on increasing the number of miles he runs a day by 1

∴ The constant value is 1 mile

-  On the first day of training, Jeff runs 5 miles

∴ The first value is 5 miles

∴ The series is arithmetic

∵ a = 5 , d = 1

- He do that for the remainder of the week

∵ The week has 7 days

∴ The series has 7 terms

∵ The rule of the series is Un = a + (n - 1)d

∵ a = 5 and d = 1

∴ Un = 5 + (n - 1)(1)

∴ Un = 5 + n - 1

∴ Un = 4 + n ⇒ n is the position of the number

- Substitute n from 1 to 7 to find the series

∴ The series is 5 , 6 , 7 , 8 , 9 , 10 , 11

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jeka57 [31]

<u>Answer</u>

C. 39.71


<u>Explanation</u>

33 = p - 6.71

The first step is to make the like terms to be on the same side.

Add 6.71 on both sides of the eqution

33 +  6.71 = p - 6.71 + 6.71

39.71 = p


∴ p = 39.71

4 0
2 years ago
-2/7 - (-4/3) -1/3 what is the answer
seraphim [82]
You have to first make like terms 

-\frac{2}{7} -(-  \frac{4}{3})-  \frac{1}{3} &#10;
**you want the denominator to be 21 

\frac{-6+28-7}{21} =  \frac{15}{21}= \frac{5}{7}
3 0
3 years ago
Step by step<br> Please urgent
kotegsom [21]

Answer:

Below in bold.

Step-by-step explanation:

1) ( a^2 + b^2 = (a + b)^2 - 2ab

= 29 - 2(6)

= 29-12

= 17.

2).  (x - y)^2 = x^2 + y^2 - 2xy

so 20 = 18 - 2xy

2xy = 18-20 = -2

xy = -1.

3). 1/x + x = 7

(1/ x + x)^2 = 1/x^2  + x^2 +x/x + x/x

= 1/x^2 + x^2 + 2

But(1/x + x)^2 = 7^2 = 49

so 1/x^2 + x^2 + 2 = 49

so 1/x^2 + x^2 = 49 - 2 = 47.

6 0
3 years ago
Emily has x amounts of apples, Peter has 4 apples less than Emily and Joshua has 2 times the number of apples of Peter. The tota
VladimirAG [237]

Answer:

Emily: 13, Peter: 9, Joshua: 18

Step-by-step explanation:

Emily = x

Peter = Emily - 4 = x - 4

Joshua = 2(Peter) = 2(x - 4)

Total = 40 = Emily + Peter + Joshua = (x) + (x - 4) + 2(x - 4)

40 = 2x - 4 + 2x -8

40 = 4x - 4 - 8

40 = 4x - 12

52 = 4x

x = 13

Emily = 13

Peter = 13 - 4 = 9

Joshua = 2(13 - 4) = 2(9) = 18

13 + 9 +18 = 40

5 0
2 years ago
If somone can help. ​
dexar [7]

Answer:

c cause it says length = 5x

4 0
3 years ago
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