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3 years ago

Someone please answer this corectly!!

Mathematics

1 answer:

Alex_Xolod [135]3 years ago

6 0

Answer:

I think the answer would be

8 < Rad 70 < 9

Step-by-step explanation:

Hope it was correct & helpful ^__^ .

You might be interested in

1. Let U the set of students of the university of Cambridge. Let the subsets of U:

Marysya12 [62]

Answer:

A) A ∩ C means in both sets, in this case A and C, and in this question all students both over 20 years and with social stratum of 1, 2 and 3.

B) A ∪ B means in either set or both, both will do, in this case meaning all students in A or B or any in between, and in this question all students over 20 years and/or are women.

C) As is already explained above, B ∪ C means in this question all students that are women and/or have social stratum of 1, 2, and 3.

D) This is the same as A). Refer to A).

E) A ∪ C is already explained above, and in this question means all students over 20 years and/or have social stratum of 1, 2, and 3.

F) Same as E). Refer to E).

G) Same as A). Refer to A).

H) A ∩ B ∩ C means in students in all three sets simultaneously, and in this question all students that are over 20 years, women, and with social stratum of 1, 2 and 3.

I) A - B, in set theory would mean all students in A but not in B, in other words the difference. In this question, it would mean all students over 20 years that are not women.

J) (A - B) ∩ C would mean, as already explained above, all students over 20 years that are not women and with social stratum of 1, 2 and 3. Usually, it's easier to treat all unions or intersections or whatnot inside brackets as one whole thing, kind of like how you do algebra.

K) B 4 C is nonsensical, there is nothing in set theory like this.

L) Same as K).

The given description between C) and D) would be that they are the same, and comparing F) and G), it seems that the question is trying to make the point that they are almost the same but defined differently.

Step-by-step explanation:

Hope this helped!

6 0

2 years ago

A box with a hinged lid is to be made out of a rectangular piece of cardboard that measures 3 centimeters by 5 centimeters. Six

kherson [118]

Answer:

x = 0.53 cm

Maximum volume = 1.75 cm³

Step-by-step explanation:

Refer to the attached diagram:

The volume of the box is given by

$V = Length \times Width \times Height \\\\$

Let x denote the length of the sides of the square as shown in the diagram.

The width of the shaded region is given by

$Width = 3 - 2x \\\\$

The length of the shaded region is given by

$Length = \frac{1}{2} (5 - 3x) \\\\$

So, the volume of the box becomes,

$V = \frac{1}{2} (5 - 3x) \times (3 - 2x) \times x \\\\V = \frac{1}{2} (5 - 3x) \times (3x - 2x^2) \\\\V = \frac{1}{2} (15x -10x^2 -9 x^2 + 6 x^3) \\\\V = \frac{1}{2} (6x^3 -19x^2 + 15x) \\\\$

In order to maximize the volume enclosed by the box, take the derivative of volume and set it to zero.

$\frac{dV}{dx} = 0 \\\\\frac{dV}{dx} = \frac{d}{dx} ( \frac{1}{2} (6x^3 -19x^2 + 15x)) \\\\\frac{dV}{dx} = \frac{1}{2} (18x^2 -38x + 15) \\\\\frac{dV}{dx} = \frac{1}{2} (18x^2 -38x + 15) \\\\0 = \frac{1}{2} (18x^2 -38x + 15) \\\\18x^2 -38x + 15 = 0 \\\\$

We are left with a quadratic equation.

We may solve the quadratic equation using quadratic formula.

The quadratic formula is given by

$x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}$

Where

$a = 18 \\\\b = -38 \\\\c = 15 \\\\$

$x=\frac{-(-38)\pm\sqrt{(-38)^2-4(18)(15)}}{2(18)} \\\\x=\frac{38\pm\sqrt{(1444- 1080}}{36} \\\\x=\frac{38\pm\sqrt{(364}}{36} \\\\x=\frac{38\pm 19.078}{36} \\\\x=\frac{38 + 19.078}{36} \: or \: x=\frac{38 - 19.078}{36}\\\\x= 1.59 \: or \: x = 0.53 \\\\$