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tia_tia [17]
3 years ago
8

If 1200 cm2 of material is available to make a box with a square base and an open top, find the largest possible volume of the b

ox
Mathematics
1 answer:
Colt1911 [192]3 years ago
4 0

Answer:

The largest possible volume V is ;

V = l^2 × h

V = 20^2 × 10 = 4000cm^3

Step-by-step explanation:

Given

Volume of a box = length × breadth × height= l×b×h

In this case the box have a square base. i.e l=b

Volume V = l^2 × h

The surface area of a square box

S = 2(lb+lh+bh)

S = 2(l^2 + lh + lh) since l=b

S = 2(l^2 + 2lh)

Given that the box is open top.

S = l^2 + 4lh

And Surface Area of the box is 1200cm^2

1200 = l^2 + 4lh ....1

Making h the subject of formula

h = (1200 - l^2)/4l .....2

Volume is given as

V = l^2 × h

V = l^2 ×(1200 - l^2)/4l

V = (1200l - l^3)/4

the maximum point is at dV/dl = 0

dV/dl = (1200 - 3l^2)/4

dV/dl = (1200 - 3l^2)/4 = 0

3l^2= 1200

l^2 = 1200/3 = 400

l = √400

I = 20cm

Since,

h = (1200 - l^2)/4l

h = (1200 - 20^2)/4×20

h = (800)/80

h = 10cm

The largest possible volume V is ;

V = l^2 × h

V = 20^2 × 10 = 4000cm^3

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If the ratio of the sides of two squares is 3:1, what is the ratio of their perimeters?
Anvisha [2.4K]

Answer:

Ratio of the perimeters =3:1

Step-by-step explanation:

We have given that : Ratio of the sides of two squares is 3:1

To find : Ratio of their perimeters

Solution : Let the length of the sides are 3:1 = 3x : x

                  Formula of perimeter of square = 4(side)

Using the formula ,

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Perimeter of 2 square = 4×x= 4x

Ratio of the perimeter of 1 square and 2 square = 12x : 4x

                                                                                 = 3 : 1


8 0
3 years ago
If x+a is a factor of 2x²+2ax+5x+10,find a.
vazorg [7]

If x+a is a factor of the polynomial, it means that -a is a root of the polynomial.

In fact, if a polynomial p(x) has a root x_0 (i.e. p(x_0)=0), then the polynomial is divisible by (x-x_0)

In your case, you know that the polynomial is divisible by (x+a)=(x-(-a)), so -a is a solution.

Let's evaluate p(-a) and set it to zero:

2(-a)^2+2a(-a)+5(-a)+10 = 0 \iff 2a^2-2a^2-5a+10=0 \iff -5a+10 = 0 \iff a = 2

We can check the answer: if a=2 the polynomial becomes

2x^2+2(2)x+5x+10 = 2x^2+9x+10

And we're claiming that -a=-2 is a root of this polynomial:

2(-2)^2+9(-2)+10 = 2\cdot 4 - 18 + 10 = 0

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