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aleksklad [387]
3 years ago
15

Please and thank you , 10 points​

Mathematics
1 answer:
Sonbull [250]3 years ago
3 0
I don’t know the answer but pls do not click the link the other person sent!! it is a scam
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A piece of cardboard is 15 inches by 30 inches. A square is to be cut from each corner and the sides folded up to make an open-t
solmaris [256]

Answer:

Maximum volume = 649.519 cubic inches

Step-by-step explanation:

A rectangular piece of cardboard of side 15 inches by 30 inches is cut in such that a square is cut from each corner. Let x be the side of this square cut. When it was folded to make the box the height of box becomes x, length becomes (30-2x) and the width becomes (15-2x).

Volume is given by  

V = V = Length\times Width\times Height\\V = (30 - 2x)(15-2x)x= 4x^3-90x^2+450x\\So,\\V(x) = 4x^3-90x^2+450x

First, we differentiate V(x) with respect to x, to get,

\frac{d(V(x))}{dx} = \frac{d(4x^3-12x^2+9x)}{dx} = 12x^2 - 180x +450

Equating the first derivative to zero, we get,

\frac{d(V(x))}{dx} = 0\\\\12x^2 - 180x +450 = 0

Solving, with the help of quadratic formula, we get,

x = \displaystyle\frac{5(3+\sqrt{3})}{2}, \frac{5(3-\sqrt{3})}{2},

Again differentiation V(x), with respect to x, we get,

\frac{d^2(V(x))}{dx^2} = 24x - 180

At x =

\displaystyle\frac{5(3-\sqrt{3})}{2},

\frac{d^2(V(x))}{dx^2} < 0

Thus, by double derivative test, the maxima occurs at

x = \displaystyle\frac{5(3-\sqrt{3})}{2} for V(x).

Thus, largest volume the box can have occurs when x = \displaystyle\frac{5(3-\sqrt{3})}{2}}.

Maximum volume =

V(\displaystyle\frac{5(3-\sqrt{3})}{2}) = (30 - 2x)(15-2x)x = 649.5191\text{ cubic inches}

8 0
3 years ago
Which expression matches the verbal description below?
Ronch [10]

Answer:

Quotient = division of one number by another

\implies \textsf{quotient of 30 and 6} = \sf \dfrac{30}{6}

\implies \textsf{3 subtracted from } \sf \dfrac{30}{6}=\dfrac{30}{6}-3

The quotient of 30 and 6 can also be written as the ratio 30 : 6

Therefore, the solution is (30:6) - 3

8 0
2 years ago
Read 2 more answers
Solve 10(y+7)=12y for y
12345 [234]

Answer:

y=35

Step-by-step explanation:

10(y+7)=12y

10y+70=12y

70=12y-10y

70=2y

70/2=y

35=y

therefore, y=35

7 0
3 years ago
Read 2 more answers
A total of 396 tickets were sold for the school play. They wee either adult tickets or student tickets. The number of student ti
Flura [38]

We know that this problem is in the ratio of 1:3 1 being adult tickets and 3 being student tickets. If we divide 396 by 4 to get 1 part, then we have the answer.

396/4=99

Answer: 99 adult tickets

7 0
3 years ago
You need to purchase supplies for an employee appreciation picnic. Your boss gives you the shopping list below and asks that you
Natalka [10]

To get the units needed, divide the given number of items needed shown in the above portion of table, with the package size given in the below portion. Then multiply with given prices. Round off the numbers to whole numbers.

Now, money needs to be spent in Quality Groceries-

(5*15.5)+(2*6.23)+(7*3.79)+(2*2.75)+(2*4.33)+(5*7.55)

=$ 168.40

Now, money needs to be spent in Fresh Market-

(7*12.4)+(3*4.99)+(7*3.55)+(3*2.55)+(2*5.55)+(5*6.99)

=$ 180.32

So, the answer is option B.


3 0
3 years ago
Read 2 more answers
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