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Komok [63]
3 years ago
10

Done-fourth of a race is one-eighth of a mile long. How long is the entire race?

Mathematics
1 answer:
Veseljchak [2.6K]3 years ago
8 0

Answer:

I believe the answer would be '1/2 a mile long'.

Step-by-step explanation:

Apologies if it's wrong that's just the answer i got when i did it in my head.

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Drag the choices into the boxes to explain how all real numbers have a decimal expansion.
KATRIN_1 [288]

The decimal forms of some real numbers, like( 3/16), terminate, while the decimal forms of other real numbers, like(4 2/11 ), do not terminate, but have a repeating pattern. Still, other real numbers, like(5 squared ), have decimal forms that neither terminate nor repeat.

Step-by-step explanation:

1. The decimal forms of some real numbers, like( ), terminate

A number is terminating if it has decimal with finite number

So, \frac{3}{16}= 0.1875 as decimal stops after 4 digits so it is terminating.

2.  the decimal forms of other real numbers, like( ), do not terminate, but have a repeating pattern.

A number that do not terminate, but have a repeating pattern.

So, 4 \frac{2}{11} =\frac{44}{11}=4.1818181

3. have decimal forms that neither terminate nor repeat

5^2 = 25 it neither terminates nor repeat

So, answers will be:

The decimal forms of some real numbers, like( 3/16), terminate, while the decimal forms of other real numbers, like(4 2/11 ), do not terminate, but have a repeating pattern. Still, other real numbers, like(5 squared ), have decimal forms that neither terminate nor repeat.

Keywords: Decimals

Learn more about decimals at:

  • brainly.com/question/10941043
  • brainly.com/question/4390083

#learnwithBrainly

6 0
3 years ago
F(x)= 2x^3- x^2 +x+ 1 is divided by 2x +1.
ololo11 [35]

Answer:

Step-by-step explanation:

               x^2

           --------------------------------------------------

2x + 1  /  2x^3     -     x^2    +      x      +    1

               2x^3    +    x^2

              -----------------------

                                    0 + x + 1

                                        x + 1

The quotient is  x^2 + ------------

                                       2x + 1

8 0
3 years ago
The circumference of a circle is 15π units. How many units long is its diameter? (Use only the digits 0 - 9 and the decimal poin
Lyrx [107]

Answer:

c

Step-by-step explanation:

4 0
2 years ago
What is the equation of the circle with center (0, 0) that passes through the point (-8, 3)?
77julia77 [94]

 

hello :<span>
<span>an equation of the circle Center at the A(a,b) and ridus : r is :
(x-a)² +(y-b)² = r²
in this exercice : a =0 and b = 0 (Center at the origin)
r = OP....p(-8,3)
r² = (OP)²
r² = (-8-0)² +(3-0)² = 64+9=73
an equation of the circle that satisfies the stated conditions.
Center at the origin, passing through P(-8, 3) is :  x² +y² = 73</span></span>

7 0
3 years ago
4. a) A ping pong ball has a 75% rebound ratio. When you drop it from a height of k feet, it bounces and bounces endlessly. If t
Klio2033 [76]

First part of question:

Find the general term that represents the situation in terms of k.

The general term for geometric series is:

a_{n}=a_{1}r^{n-1}

a_{1} = the first term of the series

r = the geometric ratio

a_{1} would represent the height at which the ball is first dropped. Therefore:

a_{1} = k

We also know that the ball has a rebound ratio of 75%, meaning that the ball only bounces 75% of its original height every time it bounces. This appears to be our geometric ratio. Therefore:

r=\frac{3}{4}

Our general term would be:

a_{n}=a_{1}r^{n-1}

a_{n}=k(\frac{3}{4}) ^{n-1}

Second part of question:

If the ball dropped from a height of 235ft, determine the highest height achieved by the ball after six bounces.

k represents the initial height:

k = 235\ ft

n represents the number of times the ball bounces:

n = 6

Plugging this back into our general term of the geometric series:

a_{n}=k(\frac{3}{4}) ^{n-1}

a_{n}=235(\frac{3}{4}) ^{6-1}

a_{n}=235(\frac{3}{4}) ^{5}

a_{n}=55.8\ ft

a_{n} represents the highest height of the ball after 6 bounces.

Third part of question:

If the ball dropped from a height of 235ft, find the total distance traveled by the ball when it strikes the ground for the 12th time. ​

This would be easier to solve if we have a general term for the <em>sum </em>of a geometric series, which is:

S_{n}=\frac{a_{1}(1-r^{n})}{1-r}

We already know these variables:

a_{1}= k = 235\ ft

r=\frac{3}{4}

n = 12

Therefore:

S_{n}=\frac{(235)(1-\frac{3}{4} ^{12})}{1-\frac{3}{4} }

S_{n}=\frac{(235)(1-\frac{3}{4} ^{12})}{\frac{1}{4} }

S_{n}=(4)(235)(1-\frac{3}{4} ^{12})

S_{n}=910.22\ ft

8 0
3 years ago
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