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OlgaM077 [116]
3 years ago
12

John is walking around a circular track with a radius of 50 ft. If he walks the equivalent of 140 degrees, find the total distan

ce he has walked around the track to the nearest Foot.​
Mathematics
1 answer:
Vera_Pavlovna [14]3 years ago
8 0

Answer: 122 ft

<u>Step-by-step explanation:</u>

s = r Ф   (Ф must be in radians)

Given: r = 50

          Ф = 140°

                 \dfrac{\pi}{180^o}=\dfrac{x}{140^o}  

                 \dfrac{140^o\pi}{180^o}=x

                     \dfrac{7\pi}{9}=x

s=50\bigg(\dfrac{7\pi}{9}\bigg)\\\\\\.\quad =\dfrac{350\pi}{9}\\\\\\.\quad =122\ ft

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A student gets 68 marks n therefore gets 85 percent total marks are?
mihalych1998 [28]

Answer:

There are 80 marks in total.

Step-by-step explanation:

Let the number of total marks be x.

The percentage score of the student can be written as the ratio

\displaystyle \frac{68}{x} = 85\%.

However,

\displaystyle 85\% = \frac{85}{100}.

Equating the two:

\displaystyle \frac{68}{x} = \frac{85}{100}.

Cross-multiply (that is: multiple both sides by 100x, the product of the two denominators) to get

85x = 68\times 100.

\displaystyle x = \frac{68\times 100}{85} = 80.

In other words, there are 80 marks in total.

4 0
4 years ago
Line j passes through points 1,6 and 7,1 line k is parallel to line j. What is the slope of line k?
Mashutka [201]
Slope formula m = (y2-y1) / (x2 - x1)
m = (1 - 6) / 7 - 1)
m = -5 / 6

Slope or parallel lines are the same
Slope = -5/6
6 0
3 years ago
The driver of the bus filled the gas tank with gas by putting in 21 gallon. If the gas gauge was at five-eighths before she fill
vazorg [7]

Answer:

56 gallons

Step-by-step explanation:

When her gas tank is full, she has x gallons in the tank.

when she went to the gas station, she had (5/8) of x gallons of gas in her tank. she added 21 gallons into her tank, then she had x gallons in her tank.

(5/8)x + 21 = x

subtract x and 21 from both sides

(5/8)x - x = -21

factor out an x from the left side

x(5/8 - 1) = -21

simplify the parenthesis

x(-3/8) = -21

multiply both sides by -8/3

x= 56 gallons

8 0
4 years ago
1) Suppose f(x) = x2 and g(x) = |x|. Then the composites (fog)(x) = |x|2 = x2 and (gof)(x) = |x2| = x2 are both differentiable a
Rufina [12.5K]

Answer:

This contradict of the chain rule.

Step-by-step explanation:

The given functions are

f(x)=x^2

g(x)=|x|

It is given that,

(f\circ g)(x)=|x|^2=x^2

(g\circ f)(x)=|x^2|=x^2

According to chin rule,

(f\circ g)(c)=f(g(c))=f'(g(c)g'(c)

It means, (f\circ g)(c) is differentiable if f(g(c)) and g(c) is differentiable at x=c.

Here g(x) is not differentiable at x=0 but both compositions are differentiable, which is a contradiction of the chain rule

3 0
3 years ago
Hallie bikes 1 5/8 km before lunch and 6 1/4 km after lunch. How much farther does Hallie bike after lunch than before lunch? Ex
EleoNora [17]

Answer:

4 \frac{5}{8} km

Step-by-step explanation:

To find how much farther Hallie biked after lunch compared to the amount she biked before lunch, we can subtract the amounts:

6 \frac{1}{4}-1\frac{5}{8}

However, we can only subtract fractions that have the same denominator, so we need to convert \frac{1}{4} to a fraction with a denominator of 8:

\frac{1}{4}=\frac{2}{8}

Now, we can't subtract 2 from 8, so we need to 'borrow' from the 6 to make the fraction larger:

6\frac{2}{8}=5\frac{10}{8}

Now subtract: 5\frac{10}{8}-1\frac{5}{8}=4\frac{5}{8}

4 0
3 years ago
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