An athlete us jumping. However, everytime she jumps she gets a bit more tired, and every jump goes 1/2 as far as her prior jump. Now, for her very first jump, she goes 1/2 of a foot. On her second jump, she goes 1/4 of a foot, and so on and so forth. How many jumps does it take to get to travel 1 foot

Answers

Answer 1

Answer:

She can never travel a distance of 1 foot for the given condition.

Step-by-step explanation:

In every jump, she goes 1/2 as far as her prior jump.

In the 1st jump, she covered a distance, d_1= \frac 1 2 foot.

The distance covered in the 2nd jump

[tex]d_2= \frac 12 \times d_1 = = \frac 12 \times \frac 12= \frac 1 4[/tex] (given)

So, the distanve covered in the 3rd jump

[tex]=\frac 12 \times d_2= \left(\frac 1 2\right )^2\times \frac 1 2= \left(\frac 1 2\right)^{3-1}\times \frac 1 2.[/tex]

Similarly, the distance covered in the [tex]r^{th}[/tex] jump

[tex]=\left(\frac 12 \right)^{r-1}\times \frac 1 2.[/tex]

Assuming she requires [tex]n[/tex] jumps to travel 1 foot of distance.

So, the sum of all the distances covered in n jumps = 1 foot

[tex]\Rightarrow \frac 1 2 + \frac 1 4 + \cdots + \left(\frac 12 \right)^{r-1}\times \frac 1 2+\cdots+ \left(\frac 12 \right)^{n-1}\times \frac 1 2=1[/tex]

[tex]\Rightarrow \frac 1 2 + \left(\frac 12 \right)^2 + \cdots + \left(\frac 12 \right)^{r}+\cdots+ \left(\frac 12 \right)^{n}=1[/tex]

This a geometric progression, G.P., of [tex]n[/tex] terms having common ration, r= 1/2 and the first term [tex]a_1= 1/2[/tex].

As sum of all the n terms of  G.P [tex]=\frac {a_1(r^n-1)}{r-1}[/tex],

[tex]\Rightarrow \frac {1/2((1/2)^n-1)}{1/2-1}=1[/tex]

[tex]\Rightarrow - \left(\left(\frac 1 2\right)^n-1\right)=1[/tex]

[tex]\Rightarrow \left(\frac 1 2\right)^n-1=-1[/tex]

[tex]\Rightarrow \left(\frac 1 2\right)^n=-1+1=0[/tex]

[tex]\Rightarrow \frac {1}{2^n}=0[/tex]

This is only possible, mathematically, when [tex]n\rightarrow \infty[/tex], But in real life situation reaching infinity is not possible.

Hence, she can never travel a distance of 1 foot for the given condition.


Related Questions

What are benefits of good study habits? Check all that apply.
improved academic performance
reduced stress
better performance in extra-curricular activities
remembering information
O an effective use of time



Electives class

Answers

Answer:

1, 3, 4 i hope this helps ;)

Step-by-step explanation:

Answer: a c d

Step-by-step explanation:

Guys pls answer this for me in a minute it is really hard

Answers

The answer to the question is B
The answer is B... hope it helps

Plz help with this problem

Answers

Answer:

A)2x+7

Step-by-step explanation:

-x+5+3x+2

2x+7

Simplify 3over-9/3over-12

Answers

Answer:

i got

[tex] \frac{4}{3} [/tex]

I may be wrong but if not mark brainliest


Ms. Darden is selling handmade gloves at the school flea market. It costs her $9 to make one pair of gloves. At the fair she sells the pairs of gloves for $15 each. If she sold 45 pairs of gloves, what was her
total profit?
S: TPIAMTF

Answers

Answer:

270$

Step-by-step explanation:

Simplify the expression
16+(-3)-3/7j-5/7j+4​

Answers

the simplified version is
119j-8/7j

Estimate: 1/4 x 21 ≈

Answers

Answer:

5

Step-by-step explanation:

Check all fractions equivalent to 2⁄8.
Check all that are true.

1⁄2

1⁄6

4⁄16

1⁄4

4⁄12

Answers

1/4 and 4/16 are equivalent to 2/8

10 x = − 19 Give your answer as an improper fraction in its simplest form.

Answers

Answer:

10/19

Step-by-step explanation:

Answer:

-19/10

Step-by-step explanation:

10x= - 19

divide 10 by each side to get -1.9

convert -1.9 to a fraction -1u9/10

then convert it to an improper fraction -19/10

hope this helps;)

help!!!! due now ( right answer's only)

Answers

Answer:

Minimum, Vertex(1,-7) and sorry what do you mean by aos? i dont get that please type in the comments I'll answer that too. Hope you understand the rest

Step-by-step explanation:

The vertex of a parabola means the stationary point/turning point which is denoted by the following:

[tex]x=\frac{-b}{2a} \\[/tex]

and for y we just simply put the value of x that we get into the equation so lets get started

The equation [tex]y=x^2-2x-6[/tex] is a quadratic equation

and if we compare it by the standard form [tex]y=ax^2+bx+c[/tex] we get the following values

a=1 , b=-2 , c=-6

and now for the vertex

[tex]x=\frac{-b}{2a}[/tex]

[tex]x=\frac{-(-2)}{2(1)} \\x=\frac{2}{2} \\x=1[/tex]

and now for y

[tex]y=x^2-2x-6\\y=(1)^2-2(1)-6\\y=1-2-6\\y=-7[/tex]

so the vertex is (1,-7)

and the graph is minimum not maximum because the value of a is greater than 0 if the value of a>0 then the graph is minimum and if the value of a<0 meaning a is negative the graph is maximum and here in the equation a=1 which means a>0 then our graph is minimum.

Answer:

hey we were talking in the comment section with someone else 16 min ago and that chat maxed out so he made another one and wants you to come back. Just letting you know.

Step-by-step explanation:

is this a function? im lost and don't understand math

Answers

Answer:

No

Step-by-step explanation:

To be a function, there can only be 1 output for each input.

3/4 has two outputs (3 and 5), so this is not a function.

Factor complete x^2 +2x-15

Answers

Answer:

( x - 3 ) ( x + 15 )

Step-by-step explanation:

Answer:

3  and  5 , as  − 3 + 5 = 2  

∴ ( x − 3 ) ( x + 5 )

U2 L5 Modeling Equations With Variables On Both Sides 1) Solve 5x−4 = 3x +8. a. Model. b. Perform the step to have variables (circles) on only one side. c. Write the resulting step. d. Perform the step to have the variables (circles) alone on one side. e. Write the resulting step. f. Divide the variables (circles) and numbers (squares) into equal groups. g. Show the value of one group. 2) Solve −4x +7 = −7x−8. a. Model. b. Perform the step to have variables (circles) on only one side. c. Write the resulting step. d. Perform the step to have the variables (circles) alone on one side. e. Write the resulting step. f. Divide the variables (circles) and numbers (squares) into equal groups. g. Show the value of one group.

Answers

Answer:

x = 6

x = -5

Step-by-step explanation:

Solving (1)

5x - 4 = 3x + 8

Bring variables to one side

5x - 3x = 8 + 4

The result is

2x = 12

Solve for x

½ * 2x = ½ * 12

x = 6

Solving (2)

-4x + 7 = -7x - 8

Bring variables to one side

7x - 4x = -7 - 8

The result is

3x = -15

Solve for x

⅓ * 3x = -15 * ⅓

x = -5

mr george has a bank balance of 42 dollar at the start of the mouth.after he depostite 6 dollar the new balance is

Answers

Answer:

48 dollars.

Step-by-step explanation:

If Mr. George starts with 42, and adds 6, his new balance should equal 48 because you add the two numbers.

$42-$6=$36 i believe

A school district needs to arrange transportation for at least 360 students for a field trip. The district can use large buses or small buses. The large buses hold 60 students each and have an operating expense of $300 for the day. The small buses hold 45 students each and have an operating expense of $200 for the day. The district only has chaperones for, at most, seven buses. What is the minimum cost for the transportation for the field trip if each bus has chaperones? $1,400 $1,600 $1,700 $1,800

Answers

Answer:

The minimum cost for the transportation for the field trip is $1700

Step-by-step explanation:

Let x be the no. of large buses and y be the no. of small buses

Number of students in large bus = 60

Number of students in x large buses = 60x

Cost of 1 large bus =$300

Cost of x large buses = 300x

Number of students in small bus = 45

Number of students in y small buses = 45y

Cost of 1 small bus =$200

Cost of y small buses = 200y

Cost = 300x+200y

We are given that A school district needs to arrange transportation for at least 360 students

[tex]60x+45y \geq 360[/tex]

The district only has chaperones for, at most, seven buses.

[tex]x+y \leq 7[/tex]

Plot the lines on graph

[tex]60x+45y \geq 360[/tex] --- Black region

[tex]x+y \leq 7[/tex] --- Red region

Feasible points :

At(3,4)

Cost  = 300x+200y=300(3)+200(4)=1700

At(7,0)

Cost  = 300x+200y=300(7)+200(0)=2100

At(6,0)

Cost  = 300x+200y=300(6)+200(0)=1800

So, The minimum cost for the transportation for the field trip is $1700

Answer:

1700

Step-by-step explanation:

2020 edge


Jon is stuck on the side of a cliff. Jon is at the midpoint from the ground to the top of the
cliff. Jon is 40 + 2 feet away from the bottom of the cliff. The cliff is 200 feet tall.
Solve for x.
How far is Jon from the top of the cliff

Answers

Complete question is;

Jon is stuck on the side of a cliff. Jon is at the midpoint from the ground to the top of the cliff. Jon is 40 + 2x feet away from the bottom of the cliff. The cliff is 200 feet tall.

Solve for x.

How far is Jon from the top of the cliff

Answer:

x = 30 ft

Jon is 100 ft from the top of the cliff

Step-by-step explanation:

We are told that Jon is at the mid point of the Cliff.

Since The cliff is 200 feet tall, the Jon is; 200/2 ft = 100 ft from either the top or bottom.

Now, we are told that Jon is 40 + 2x from the bottom of the cliff.

Thus;

40 + 2x = 100

Subtract 40 from both sides;

40 - 40 + 2x = 100 - 40

2x = 60

x = 60/2

x = 30 ft

And Jon is 100 ft from the top of the cliff as earlier seen

Help, please. I will give brainliest to anyone that answers first. ​

Answers

Answer:

5000 I think bc 5 times 1000 is 500

Answer:

Step-by-step explanation:

1000 meter = 1 kilometer

1 km= 1000 meter

constant proportionality

y/x=k

y is km , x is meter

1/1000=k

y=1/1000 x (x is the number of meters)

meter                              Km

250                                0.25

12                                   12/1000=0.012

1                                      1/1000

kilometer                      meter

5                                   5000

20                                20000

0.3                               300

How many terms are in the expression 76-3a + 4b + 5a?

Answers

Answer:

4

Step-by-step explanation:

In Algebra a term is either a single number or variable, or numbers and variables multiplied together. Terms are separated by + or − signs

A man starts out on a trip driving his car at a constant rate of 48 mph. A man riding a motorcycle starts out on the same route 1.5 hours later, traveling at a constant rate of 64 mph. How long will the car have been traveling when the motorcycle catches up?

Answers

Answer:

6 hours

Step-by-step explanation:

.To find a shoe size, the manufacturer uses the equation S = 3f - 22, where S
represents the shoe size and f represents the heel-to-toe length of the foot, in
inches. Which of the following is the same equation solved for fin terms of
S?

Answers

See attachment for math work and answer.

Answer:

Adelaide has a credit card with a company that charges $3.00 for every day a payment is late. If she paid $492.93 for a bill that is 3 days late, how much was the bill without the late fee?

A. $486.93

B. $483.93

C. $489.93

D. $480.93

Step-by-step explanation:

help me with this question

Dolly earns $6.40 per hour. She worked 28.25 hours last week. How much did Dolly earn last week?

Answers

Answer:

180.8

Step-by-step explanation:

multiply 6.40 with the hour 28.25

Hope this helps!

Multiply $6.40 by the number of hours and you will get $180.80

NEED HELP FAST

the submarine is at a depth of -166 2/7 feet when the scientists detect a signal frequency from the ocean floor. they dive farther down to a depth of -180 4/7 feet to check the signal. the net change in their depth is [] feet​

Answers

Answer:

-24 2/7

Step-by-step explanation:

-180 4/7 -166 2/7

-180 -166 = -24

4/7-2/7 = 2/7

-24 2/7

Answer:

I hope this helps

Step-by-step explanation:

Triangle ABC is translated 4 units down and 6 units right, resulting in triangle A'B'C'.
What are the coordinates of the point B'?
A. (-6,7)
B. (-1,6)
C. (4, -3)
D. (6,-1)

Answers

Answer:

The new coordinate of B' will be ( -1, 6)

The translated coordinate of the point B' will be (-1,6).

What is translation?

The process of changing the location of the image on the coordinate system will be known as the translation.

A coordinate plane is a 2D plane that is formed by the intersection of two perpendicular lines known as the x-axis and y-axis. A coordinate system in geometry is a method for determining the positions of the points by using one or more numbers or coordinates.

Given that the coordinates of point B of the triangle are (1,6). The translated coordinates will be,

B = ( 3, 0 )

Translated 4 units down and 6 units right,

B' = ( 3 - 4 , 0 + 6 )

B' = ( -1, 6 )

To know more about translation follow

https://brainly.com/question/12861087

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HELP!!
Write a story problem in which you would have to multiply 5 × -1/3 to find the answer.

Answers

Zack has a Fahrenheit thermometer which shows a temperature of 29ºF. He says his temperature is above freezing. Jack has a Celsius thermometer. He disagrees and says that the temperature is below zero on his thermometer. Who is right and what is the temperature in degrees Celsius? SOLUTION

To convert Fahrenheit to Celsius, we first subtract 32. That gives us -3.

Then we multiply by 5/9 to convert to Celsius. When we do this, 3 goes into the denominator and we get -3/9 which is -1/3. Finally we multiply this fraction by 5: 5×-1/3=-5/3=-1.67°C or -1⅔°C.

So Jack was right. The negative value means the temperature is below zero, that is, below freezing. The temperature is 1⅔°C below zero.

I need help in this before 11:59 please

Answers

Step-by-step explanation:

√7 * √7 = 7 , which is not a irrational number

Hi if you can answer this i'll mark u brainllest
Im really bad at mathhh :(

Answers

Answer:

1.yes

2. yes, and yes [tex]\frac{4}{1}[/tex]

3. yes, its a whole number.

4.yes

5. whole, intenger, rational, real

Step-by-step explanation:

√600 and ∛56 and show work

Answers

Answer:

√600 is around 24.5 while ∛56 is around 3.83

Step-by-step explanation:

Method: TRIAL AND ERROR

For √600, we can follow trial and error method:

30^2 is 900, so too big

20^2 is 400, so too small

25^2 is 625, too big

24^2 is 576, too small

Considering that 600 is between 24^2 and 25^2, we can try in between:

24.5^2 is 600.25, which is very close, therefore 24.5 is the answer

For ∛56, we can also follow trial and error method:

5^3 is 125

4^3 is 64

3^3 is 27

Considering that 56 is somewhere between 3^3 and 4^3, and that it's much more closer to 4^3, we can try 3.6^3, which is: 46.656;

3.7^3 is 50.6

3.8^3 is 54.8

3.9^3 is 59

3.85^3 is 57

3.84^3 is 56.6 (still larger)

3.83^3 is 56.1

So the answer is 3.83

But the method above works when using calculator, best for a calculator exam. If calculator is not allowed, you can find the difference between the two possible answers (e.g: 27 and 64 (3^3 and 4^3) following the above, to find out ∛56.) Of course, 56 is much nearer to 4^3, so we can assume that the answer is around 3.8.

Hope this helped. :)

~ Janice, year 10

4x - 8 = 12
4x - 8 + 8 = 12 + 8
4x = 20
4/4x = 20/20
x=

Answers

Answer:

x=5

Step-by-step explanation:

If 4x=20 then all we need to do is to divide both sides by 4 and we get x=5. Also, if replace x with 5 within any of the equations it works.

Hope this helps!

The solution is: The value of x is: x=5

Here, we have,

given that,

the expression is: 4x - 8 = 12

we get,

4x - 8 = 12

or, 4x - 8 + 8 = 12 + 8

or, 4x = 20

now, we have,

If 4x=20 then all we need to do is to divide both sides by 4 and we get x=5.

i.e. 4x/4  = 20/4

or, x = 5

Also, if replace x with 5 within any of the equations it works.

Hence, The solution is: The value of x is: x=5

To learn more on Expression click:

brainly.com/question/14083225

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Which graph shows four points that represent equivalent ratios?

Answers

Answer:

b

Step-by-step explanation:

Only option b from the available options represents equivalent ratios.

What is ratio?

The ratio can be defined as the number that can be used to represent one quantity as a percentage of another. Only when the two numbers in a ratio have the same unit can they be compared. Ratios are used to compare two objects.

Equivalent ratios are the ratios that are the same when we compare them. Two or more ratios can be compared with each other to check whether they are equivalent or not.

The function of a line that shows the equivalent ratio always goes through the origin point of a cartesian plane.

The general form of the equation that shows the equivalent ratio:

Y = MX

Where M is Slope

therefore, From the given Options only option b is representing equivalent ratios.

Learn more about ratios here:

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Complete Question:

3-4 what is the answer I am dumb plz helq

Answers

Answer:

Its -1. Do not call yourself dumb, though, negatives are the easiest subject

Step-by-step explanation:

loll it’s -1 ! don’t worry you’re not stupid
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