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3 years ago

What are the prime numbers between 50 and 60

Mathematics

2 answers:

jonny [76]3 years ago

7 0

They are 53 and 59 ok :)

FinnZ [79.3K]3 years ago

4 0

53 and 59 are the primes between 50 and 60

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Find the dimensions of the open rectangular box of maximum volume that can be made from a sheet of cardboard 11 in. by 7 in. by

11111nata11111 [884]

Answer:

The dimension of the open rectangular box is $8.216\times 4.216\times 1.392$ .

The volume of the box is 8.217 cubic inches.

Step-by-step explanation:

Given : The open rectangular box of maximum volume that can be made from a sheet of cardboard 11 in. by 7 in. by cutting congruent squares from the corners and folding up the sides.

To find : The dimensions and the volume of the open rectangular box ?

Solution :

Let the height be 'x'.

The length of the box is '11-2x'.

The breadth of the box is '7-2x'.

The volume of the box is $V=l\times b\times h$

$V=(11-2x)\times (7-2x)\times x$

$V=4x^3-36x^2+77x$

Derivate w.r.t x,

$V'(x)=4(3x^2)-2(36x)+77$

$V'(x)=12x^2-72x+77$

The critical point when V'(x)=0

$12x^2-72x+77=0$

Solve by quadratic formula,

$x=\frac{18+\sqrt{93}}{6},\frac{18-\sqrt{93}}{6}$

$x=4.607,1.392$

Derivate again w.r.t x,

$V''(x)=24x-72$

Now, $V''(4.607)=24(4.607)-72=38.568>0$ (+ve)

$V''(1.392)=24(1.392)-72=-38.592$ (-ve)

So, there is maximum at x=1.392.

The length of the box is $l=11-2x$

$l=11-2(1.392)=8.216$

The breadth of the box is $b=7-2x$

$b=7-2(1.392)=4.216$

The height of the box is h=1.392.

The dimension of the open rectangular box is $8.216\times 4.216\times 1.392$ .

The volume of the box is $V=l\times b\times h$

$V=8.216\times 4.216\times 1.392$

$V=48.217\ in.^3$

The volume of the box is 8.217 cubic inches.

5 0

3 years ago

HELP!! <br> Determine the length of side CB.

bazaltina [42]

Answer:

3√2 is the answer as:

sin45°=p/b

1/√2= AC/CB

1/√2= 3/CB

cross multiplication

CB = 3√2

4 0

3 years ago

Question 1 (1 point)

KatRina [158]

Answer:

97.2

Step-by-step explanation:

5 0

3 years ago

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What is the area of this parallelogram?

Hunter-Best [27]

Answer:

28 in²

Step-by-step explanation:

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2 years ago

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If the limit of f(x) as x approaches 8 is 3, can you conclude anything about f(8)?

natali 33 [55]

If the limit of f(x) as x approaches 8 is 3, can you conclude anything about f(8)? The answer is No. We cannot. See the explanation below.

<h3>What is the justification for the above position?</h3>

Again, 'No,' is the response to this question. The justification for this is that the value of a function does not depend on the function's limit at a given moment.

This is particularly clear when we consider a question with a gap. A rational function with a hole is an excellent example that will help you answer this question.

The limit of a function at a position where there is a hole in the function will exist, but the value of the function will not.

<h3>What is limit in Math?</h3>

A limit is the result that a function (or sequence) approaches when the input (or index) near some value in mathematics.

Limits are used to set continuity, derivatives, and integrals in calculus and mathematical analysis.

Learn more about limits:
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6 0

1 year ago