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Grace [21]
3 years ago
5

jenny wrapped 30 gifts,jenny wrapped 5 times as many gifts as hong let n be the number of gifts that hong wrapped

Mathematics
2 answers:
Whitepunk [10]3 years ago
7 0

n = 6

6 x 5 = 30

hope this helped, please mark brainliest. :)

Anvisha [2.4K]3 years ago
3 0

If you write it in equation form it would be: 5n = 30

To simplify, use the division property of equality to make it 5n ÷ 5 = 30 ÷ 5

This gets you n = 6. So, Hong wrapped 6 gifts.

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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

#SPJ2

                                         

                                       

                                           

8 0
2 years ago
Read 2 more answers
The perimeter of this figure is 42.5 cm. Find the area of this figure.
11111nata11111 [884]
The picture in the attached figure

let
AB=x

we know that
perimeter of the figure=10*x
perimeter=42.5 cm
so
42.5=10*x
x=42.5/10
x=4.25 cm

area of the figure=area of rectangle +area of square
area of rectangle=4.25*(4.25*3)----> 54.1875 cm²
area of square=4.25²----> 18.0625 cm²

area of the figure=54.1875+18.0625-----> 72.25 cm²

the answer is
72.25 cm²

3 0
3 years ago
Please help it would be greatly appreciated:)
mixer [17]

Answer:

I really don't know but can u help with mine-_-

6 0
3 years ago
Read 2 more answers
What is the solution of the following system of linear equations?<br> y = x - 7<br> 2y + x=1
andrew-mc [135]

Answer:

x=5

y=-2

Step-by-step explanation:

I just took this!

Hope I helped

5 0
3 years ago
Create an example of a irrational value between 2 and 3
jonny [76]

Answer:

the number of irrational numbers between 2 and 3 are √5, √6, √7, and √8,

Step-by-step explanation:

these are not perfect squares and cannot be simplified further.

#HopeIthelps

5 0
3 years ago
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