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Alik [6]
3 years ago
12

Mr. Howard and Ms. Egan enjoy running on the weekends. They both usually run at a steady pace and try to meet in the middle. The

y are 14 miles apart. Mr. Howard can run 3 miles in 30 minutes. Ms. Egan can run 4 miles in 30 minutes.
Mathematics
1 answer:
antoniya [11.8K]3 years ago
3 0

Given :

Distance between them, D = 14 miles .

Mr. Howard can run 3 miles in 30 minutes.

Ms. Egan can run 4 miles in 30 minutes.

To Find :

Time taken by them to meet.

Solution :

Mr Howard speed, v_H=\dfrac{3}{0.5}=6\ mph .

Mr Egan speed, v_e=\dfrac{4}{0.5}=- 8\ mph . [ Since they run in opposite direction ]

Their relative speed :

v=v_E-v_H\\\\v = 8-(-6) \ mph \\\\v = 14 \ mph

Time taken by them to meet :

T = \dfrac{14}{14}\ hours\\\\T = 1 \ hours

Hence, this is the required solution.

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A rectangular school banner has a length of 36 inches and a width of 52 inches. A sign is made that is similar to the school ban
zalisa [80]

Answer:

<u>4212 : 1573</u> is the ratio.

Step-by-step explanation:

Given:

Length of rectangular school banner is 36 inches and width is 52 inches.

And, the sign made is similar to banner.

The sign's length is 22 inches.

Now, we have to find the ratio of the area of the banner to the area of the sign.

So, we have dimensions of rectangular school banner:

Length = 36 inches.

Width = 52 inches.

But, we have only length of sign:

Length = 22 inches.

Now, we have to find the width of sign by using cross multiplication method:

Let the width of sign be x.

<em>As, sign is similar to banner.</em>

So, if 36 inches is equivalent to 52 inches.

Then, 22 inches is equivalent to x.

\frac{36}{52} =\frac{22}{x}

<em>By cross multiplying we get:</em>

<em />36x=1144<em />

<em>Dividing both sides by 36 we get:</em>

x=31\frac{7}{9} .

<em>Hence, the width of sign is </em>31\frac{7}{9}<em> inches.</em>

Now, we find the area of banner and the area of sign by putting formula:

Area of banner = length × width.

Area\ of\ banner=36\times 52

Area\ of\ banner=1872\ square\ inches.

Now, area of sign:

Area\ of\ sign=length\times width\\\\Area\ of\ sign=22\times 31\frac{7}{9} \\\\Area\ of\ sign=22\times \frac{286}{9} \\\\Area\ of\ sign=\frac{6292}{9} \ square\ inches.

Now, to get the ratio of the area of the school banner to the area of the sign:

1872:\frac{6292}{9}

=\frac{1872}{\frac{6292}{9} } \\\\=\frac{16848}{6292}

<em>On simplifying we get:</em>

=\frac{4212}{1573}

=4212:1573.

Therefore, the ratio of the area of the school banner to the area of the sign is 4212:1573.

8 0
3 years ago
Help me pls!! Only if you know it 30 points
noname [10]

Answer:

true

Step-by-step explanation:

Because as it go's down the other go's up

6 0
3 years ago
3 regions are defined in the figure find the volume generated by rotating the given region about the specific line
anastassius [24]

The volume generated by rotating the given region R_{3} about OC is \frac{4}{g}  \pi

<h3>Washer method</h3>

Because the given region (R_{3}) has a look like a washer, we will apply the washer method to find the volume generated by rotating the given region about the specific line.

solution

We first find the value of x and y

y=2(x)^{\frac{1}{4} }

x=(\frac{y}{2} )^{4}

y=2x

x=\frac{y}{2}

\int\limits^a_b {\pi } \, (R_{o^{2} }  - R_{i^{2} } )       dy

R_{o} = x = \frac{y}{2}

R_{i} = x= (\frac{y}{2}) ^{4}

a=0, b=2

v= \int\limits^2_o {\pi } \, [(\frac{y}{2})^{2} - ((\frac{y}{2}) ^{4} )^{2} )  dy

v= \pi \int\limits^2_o= [\frac{y^{2} }{4} - \frac{y^{8} }{2^{8} }}  ] dy

v= \pi [\int\limits^2_o {\frac{y^{2} }{4} } \, dy - \int\limits^2_o {\frac{y}{2^{8} } ^{8} } \, dy ]

v=\pi [\frac{1}{4} \frac{y^{3} }{3}  \int\limits^2_0 - \frac{1}{2^{8} }  \frac{y^{g} }{g} \int\limits^2_o\\v= \pi [\frac{1}{12} (2^{3} -0)-\frac{1}{2^{8}*9 } (2^{g} -0)]\\v= \pi [\frac{2}{3} -\frac{2}{g} ]\\v= \frac{4}{g} \pi

A similar question about finding the volume generated by a given region is answered here: brainly.com/question/3455095

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A scientist counts 25 bacteria present in a culture and finds that the number of bacteria triples each hour. The function y = 25
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6 0
3 years ago
Read 2 more answers
Please help i dont understand
Elena L [17]

Answer:

I think number one is 19

Step-by-step explanation:

8 0
3 years ago
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