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frez [133]
1 year ago
10

Nina can ride her bike 63,360 feet in 3,400 seconds, and sophia can ride her bike 10 miles in 1 hour. What is nina’s rate in mil

es per hour if there are 5,280 feet in a mile? Which girl bikes faster?
Mathematics
1 answer:
stira [4]1 year ago
4 0

Answer:

Nina's rate in MPH:  12.706 miles per hour

Nina is faster than Sophia.

Step-by-step explanation:

For this problem, we will convert feet per second into miles per hour, and then compare Nina's rate to Sophia's rate.

We are given Nina rides at 63360 feet in 3400 seconds.  To convert this to miles per hour, we need to know that there are 5280 feet in 1 mile, and 3600 seconds in 1 hour.  Now that we now these conversions, let's find the rate in miles per hour.

(63360 feet / 3400 seconds) * (1 mile / 5280 feet) * (3600 seconds / 1 hour) = 12.706 miles per hour.

So we know that Nina rides her bike at 12.706 miles per hour and are given that Sophia rides her bike in 10 miles in 1 hour.

With this, we can say Nina rides faster than Sophia by 2.706 miles per hour (12.706 - 10).

Cheers.

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Answer:

1.692 m/min

Step-by-step explanation:

Let \theta be the angle between the two sides and x be the length of the third side. By cosine rule,

x^2 = 12^2+14^2-2\times12\times14\cos\theta = 340 - 336\cos\theta

x= \sqrt{340 - 336\cos\theta}

We differentiate x with respect to \theta by applying chain rule.

\dfrac{dx}{d\theta} = \dfrac{336\sin\theta}{2\sqrt{340 - 336\cos\theta}} = \dfrac{168\sin\theta}{\sqrt{340 - 336\cos\theta}}

Rate of change of \theta is 2

\dfrac{\theta}{dt} = 2

Rate of change of x is

\dfrac{dx}{dt} = \dfrac{dx}{d\theta}\times\dfrac{d\theta}{dt}

\dfrac{dx}{dt} = \dfrac{168\sin\theta}{\sqrt{340 - 336\cos\theta}} \times2=\dfrac{336\sin\theta}{\sqrt{340 - 336\cos\theta}}

At 60°,

\dfrac{dx}{dt} = \dfrac{336\sin60}{\sqrt{340 - 336\cos60}} = 1.692 \text{ m/min}

4 0
1 year ago
There are some nickels dimes and quarters in a large piggy bank for every two nickels there are 3 dimes for every two dimes that
creativ13 [48]

We are given

piggy bank has nickels , dimes and quarters

Let's assume

number of nickels =n

every two nickels there are 3 dimes

so, number of dimes are

=\frac{3}{2}n

=1.5n

every two dimes that are 5 quarters there

so, number of quarters are

=\frac{5}{2}\times 1.5n

=3.75n

so, total number of coins = number of nickels + number of dimes +number of quarters

total number of coins =n+1.5n+3.75

there are 500 coins

so, we get

n+1.5n+3.75n=500

now, we can solve for n

6.25n=500

divide both sides by 6.25

so, we get

n=80

number of dimes is 1.5n

=1.5\times 80

=120

number of quarters  is 3.75n

=3.75\times 80

=300

so,

Number of nickels =80

Number of dimes =120

Number of quarters =300............Answer

6 0
2 years ago
Two containers are mathematically similar.Their volumes are 54cm³ and 128cm³.The height of the smaller container is 4.5cm.Calcul
alexira [117]

Answer:

6 cm

Step-by-step explanation:

If the linear scale factor of two solids is k, then the volume scale factor is k^3.

The volume scale factor is 128/54 = 64/27 = (4/3)^3.

The linear scale factor is 4/3.

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Answer: The height of the larger container is 6 cm.

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I ask you to say it’s wrong and why for the other people that have this question and use this.

Thank you,
Have a nice day.
Hope this helps you in some way.
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Answer:

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