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insens350 [35]
2 years ago
9

2) A rectangle's length is 6 less than twice it's width. If the perimeter of the rectangle is 66 feet, what

Mathematics
1 answer:
Fudgin [204]2 years ago
3 0

Answer:

13 and 20! Hope this helps!

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If the area of the region bounded by the curve y^2 =4ax and the line x= 4a is 256/3 Sq units, using integration find the value o
almond37 [142]

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 .

<h3>What is area of the region bounded by the curve ?</h3>

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

We have,

y^2 =4ax  

⇒ y=\sqrt{4ax}

x= 4a,

Area of the region  =\frac{256}{3}  Sq units

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

y^2=16a^2

y=4a

So,

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

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

\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;

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

\frac{256}{3}= \frac{4}{3} \sqrt{a} *\sqrt{(4a)^{3} }

\frac{256}{3}= \frac{4}{3} \sqrt{a} *  8 *a^{2}   \sqrt{a}

\frac{256}{3}= \frac{4}{3} *  8 *a^{3}

⇒ a^{3} =8

a=2

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 .

To know more about Area bounded by the curve click here

brainly.com/question/13252576

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1 year ago
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What's 12748 rounded to the nearest thousand
FinnZ [79.3K]
12748 rounded to the nearest thousand is 13000
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2 years ago
To find 40% of 75 and calculate 2 of 5 . 75 . Does her calculation Correct value for 40% of 75
pickupchik [31]

Answer:

Yes, her calculation is correct. The value of 40% of 75 is 30.

Step-by-step explanation:

The value of 40% of 75 is

\frac{40}{100}\times 75=\frac{3000}{100}=30

The value of \frac{2}{5} of 75 is

\frac{2}{5}\times 75=2\times 15=30

From the above calculation it is noticed that the value of 40% of 75 and \frac{2}{5} of 75 are same, therefore the calculation is correct and the  value of 40% of 75 is 30.

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Joe is training for a race in 30 days he needs to run a total of 135 Miles how many miles will Joe need to run each day to be re
labwork [276]

Answer:

4.5 miles

Step-by-step explanation:

Joe wants to divide his 135-mile goal into 30 equal pieces. Each (daily) piece will be ...

... (135 mi)/(30 da) = 4.5 mi/da

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3 years ago
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What is the area of a rectangles with the side lengths 5 inches and 1/3 inches? ​
sveticcg [70]

Answer:

area of a rectangle is length multiplied by breath, which is the multiplication of 5 an 1/3

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