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3 years ago

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Emily and Holly took a road trip together. Emily drove at an average of 45 miles per hour for the first 3/7 of the total distanc

e, and Holly drove the last 24 miles at an average rate of 54 miles per hour. How long did the trip take the two of them? Give your answer in terms of hours.

1 answer:

Elan Coil [88]3 years ago

3 0

Emily drove 3/7 of the total distance and holly drove the rest which explains that holly drove 4/7 of the whole distance.

if 4 parts of the distance equals 24 miles, then 1 part would be 24/4 is 6.
since emily drove 3 parts of the whole distance, it is 6 × 3 = 18 miles.

travelling time of emily = 18/45 = 0.4 hr
travelling time of holly = 24/54 = 0.4 hr
--> total traveling time = 0.8 hr

i hope it is right

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If the area of the region bounded by the curve $y^2 =4ax$ and the line $x= 4a$ is $\frac{256}{3}$ Sq units, then the value of $a$ will be $2$ .

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An area bounded by two curves is the area under the smaller curve subtracted from the area under the larger curve. This will get you the difference, or the area between the two curves.

Area bounded by the curve $=\int\limits^a_b {x} \, dx$

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$y^2 =4ax$

⇒ $y=\sqrt{4ax}$

$x= 4a$ ,

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Now comparing both given equation to get the intersection between points;

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Area bounded by the curve $= \[ \int_{0}^{4a} y \,dx \]$

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$\frac{256}{3}= \[\sqrt{4a} \int_{0}^{4a} \sqrt{x} \,dx \]$

$\frac{256}{3}= \[2\sqrt{a} \int_{0}^{4a} x^{\frac{1}{2} } \,dx \]$

$\frac{256}{3}= 2\sqrt{a} \left[\begin{array}{ccc}\frac{(x)^{\frac{1}{2}+1 } }{\frac{1}{2}+1 }\end{array}\right] _{0}^{4a}$

$\frac{256}{3}= 2\sqrt{a} \left[\begin{array}{ccc}\frac{(x)^{\frac{3}{2} } }{\frac{3}{2} }\end{array}\right] _{0}^{4a}$

$\frac{256}{3}= 2\sqrt{a} *\frac{2}{3} \left[\begin{array}{ccc}(x)^{\frac{3}{2}\end{array}\right] _{0}^{4a}$

On applying the limits we get;

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Hence, we can say that if the area of the region bounded by the curve $y^2 =4ax$ and the line $x= 4a$ is $\frac{256}{3}$ Sq units, then the value of $a$ will be $2$ .

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