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2 years ago

Two cyclists start from 98 miles apart and begin racing toward each

Mathematics

2 answers:

crimeas [40]2 years ago

6 0

Answer:

um 18 and 21

Step-by-step explanation:

kati45 [8]2 years ago

3 0

The speed of one bicyclist was 14.5mph, speed of the other bicyclist was 17.5mph.

Let the speed of one bicyclist=x mph

Let the speed of the other bicyclist=(x+3) mph

Hence:

Speed of one bicyclist:

3x+3(x+3)+2=98

3x+3x+9+2=98

6x=87

Divide both side by 6x

x=87/6

x=14.5 mph

Speed of the other bicyclist:

x+3 mph

14.5 mph+3 mph

=17.5 mph

Inconclusion the speed of one bicyclist was 14.5mph, speed of the other bicyclist was 17.5mph.

Learn more here:

brainly.com/question/18839894

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The sequence$$1,2,1,2,2,1,2,2,2,1,2,2,2,2,1,2,2,2,2,2,1,2,\dots$$consists of $1$'s separated by blocks of $2$'s with $n$ $2$'s i

kicyunya [14]

Consider the lengths of consecutive 1-2 blocks.

block 1 - 1, 2 - length 2

block 2 - 1, 2, 2 - length 3

block 3 - 1, 2, 2, 2 - length 4

block 4 - 1, 2, 2, 2, 2 - length 5

and so on.

Recall the formula for the sum of consecutive positive integers,

$\displaystyle \sum_{i=1}^j i = 1 + 2 + 3 + \cdots + j = \frac{j(j+1)}2 \implies \sum_{i=2}^j = \frac{j(j+1) - 2}2$

Now,

$1234 = \dfrac{j(j+1)-2}2 \implies 2470 = j(j+1) \implies j\approx49.2016$

which means that the 1234th term in the sequence occurs somewhere about 1/5 of the way through the 49th 1-2 block.

In the first 48 blocks, the sequence contains 48 copies of 1 and 1 + 2 + 3 + ... + 47 copies of 2, hence they make up a total of

$\displaystyle \sum_{i=1}^48 1 + \sum_{i=1}^{48} i = 48+\frac{48(48+1)}2 = 1224$

numbers, and their sum is

$\displaystyle \sum_{i=1}^{48} 1 + \sum_{i=1}^{48} 2i = 48 + 48(48+1) = 48\times50 = 2400$

This leaves us with the contribution of the first 10 terms in the 49th block, which consist of one 1 and nine 2s with a sum of $1+9\times2=19$ .

So, the sum of the first 1234 terms in the sequence is 2419.

8 0

2 years ago

Cuál es la operación de 2/3mas6/9

adoni [48]

Answer:

Draw a 3-D of a terrain indicating different fault behaviors. Use the terrain below. Be sure that the entire terrain should cover at least three type of fault. Labcl the fault arcas and its part

8 0

3 years ago

Help me please!!!!!!!!!!

77julia77 [94]

Answer:

Step-by-step explanation:

I am not sure though. Sorry if it is wrong :(

8 0

3 years ago

A rectangular photograph has an area of 65 square inches. If the length of the photo is 3 inches less than twice it's height, fi

tankabanditka [31]

A = L * H
A = 65
L = 2H - 3

65 = H(2H - 3)
65 = 2H^2 - 3H
-2H^2 + 3H + 65 = 0
(-Hh + 13)(H + 5) = 0

-2H + 13 = 0
-2H = -13
H = -13/-2
H = 6.5 <== height is 6.5 inches

H + 5 = 0
H = -5....this wont work because it is negative

L = 2H - 3
L = 2(6.5) - 3
L = 13 - 3
L = 10 <== length is 10 inches

4 0

3 years ago

List the steps that should be used to solve the equation f(x) = g(x) by graphing when f(x) = (1/2)² - 3 and g(x) = 3x + 5?

jolli1 [7]

value of x is: $x=\frac{-31}{12}$

Step-by-step explanation:

We need to solve the equation f(x)=g(x)

where $f(x)=(\frac{1}{2})^2-3$

and $g(x) = 3x + 5$

Solving to find f(x)=g(x)

Putting values of f(x) and g(x)

$f(x)=g(x)\\(\frac{1}{2})^2-3=3x + 5\\\frac{1}{4}-3=3x + 5\\Subtarct\,\,5\,\,on\,\,both\,\,sides:\\\frac{1}{4}-3-5=3x + 5-5\\\frac{1}{4}-8=3x\\Taking\,\,LCm\,\,on\,\,left\,\,side\\\frac{1-8*4}{4}=3x\\\frac{-31}{4}=3x\\Divide\,\,both\,\,sides\,\,by\,\,3\\x=\frac{-31}{4*3}\\x=\frac{-31}{12}$

So, value of x is: $x=\frac{-31}{12}$

The graph will be a straight line x= -2.58 or x = -31/12

Keywords: Composition of Functions

Learn more about Composition of Functions at:

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7 0

3 years ago