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Aleks [24]
2 years ago
13

There are 120 people in a sport centre.

Mathematics
1 answer:
otez555 [7]2 years ago
6 0

Answer:

71/120

Step-by-step explanation:

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Using differential calculus, maximize the volume of a box made of cardboard (top is open) as shown in Figure A. 15, subject to t
lana [24]

The maximum volume of the box is 40√(10/27) cu in.

Here we see that volume is to be maximized

The surface area of the box is 40 sq in

Since the top lid is open, the surface area will be

lb + 2lh + 2bh = 40

Now, the length is equal to the breadth.

Let them be x in

Hence,

x² + 2xh + 2xh = 40

or, 4xh = 40 - x²

or, h = 10/x - x/4

Let f(x) = volume of the box

= lbh

Hence,

f(x) = x²(10/x - x/4)

= 10x - x³/4

differentiating with respect to x and equating it to 0 gives us

f'(x) = 10 - 3x²/4 = 0

or, 3x²/4 = 10

or, x² = 40/3

Hence x will be equal to 2√(10/3)

Now to check whether this value of x will give us the max volume, we will find

f"(2√(10/3))

f"(x) = -3x/2

hence,

f"(2√(10/3)) = -3√(10/3)

Since the above value is negative, volume is maximum for x = 2√(10/3)

Hence volume

= 10 X 2√(10/3)  -  [2√(10/3)]³/4

= 2√(10/3) [10 - 10/3]

= 2√(10/3) X 20/3

= 40√(10/27) cu in

To learn more about Maximization visit

brainly.com/question/14682292

#SPJ4

Complete Question

(Image Attached)

3 0
1 year ago
Find the linear approximation of f(x)=lnx at x=1 and use it to estimate ln(1.38).
RideAnS [48]
\bf f(x)=y=ln(x)\qquad 
\begin{cases}
x=1\\
y=ln(1)\to y=0
\end{cases}\\\\
-----------------------------\\\\
\left. \cfrac{dy}{dx}=\cfrac{1}{x} \right|_{x=1}\implies 1\impliedby m
\\\\\\
\textit{now, we know that }
\begin{cases}
x=1\\
y=0\\
m=1
\end{cases}\implies y-0=1(x-1)\implies y=x-1

now, you're asked to use it when ln(1.38), which is just another way of saying x = 1.38

so set x = 1.38 and see what "y" is
5 0
3 years ago
Diego has purchased a $159,000 home with a 30-year mortgage at 5.05%. He can make a monthly payment of $1,300. If he were to mak
Gemiola [76]

Answer: 173 months MY GUY!

Step-by-step explanation:

3 0
3 years ago
1) What radius of a circle is required to inscribe an equilateral triangle with an area of 15.588 in2 and an altitude of 5.196 i
Andrej [43]
We know that
 the distance from the centroid of the triangle to one of the vertices is the radius of the circle <span>required to inscribe an equilateral triangle.

[distance </span>centroid of the triangle to one of the vertices]=(2/3)*h
h=the <span>altitude  of the equilateral triangle-----> 5.196 in
so
</span>[distance centroid of the triangle to one of the vertices]=(2/3)*5.196
[distance centroid of the triangle to one of the vertices]=3.464 in----> 3.5 in

the radius is equal to the distance of the centroid of the triangle to one of the vertices
hence
the radius is 3.5 in

the answer is
the radius is 3.5 in

8 0
3 years ago
Read 2 more answers
Simplify: 5 -3 • 5 5<br><br> 25 8<br> 25 -15<br> 5 -3<br> 5 2
Lostsunrise [7]
5 -3 * 5 5 simplified = 160!!!
7 0
2 years ago
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