Which one of the following is not closed under the operation being performed

Mathematics

1 answer:

Sergeu [11.5K]3 years ago

4 0

Remember that polynomials are closed under addition, subtraction, and multiplication, but they are not closed under division. The only division you have there is B; therefore the correct answer is B.

A. $(14x-2)3(x-2)=14 x^{2} -90x+10$ . The result is still a polynomial; therefore, answer A is incorrect.

B. $\frac{(14x-2)}{3(x-2)} = \frac{14}{3}$ with a remainder of 26. The result is not a polynomial anymore; therefore, B is the correct answer.

C. $(14x-2)+3(x+2)=17x+4$ . The result is still a polynomial; therefore, answer C is incorrect.

D. $(14x-2)+3(x+2)=17x+4$ . The result is still a polynomial; therefore, answer D is incorrect.

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A rectangular solid with a square base has a volume of 2,744 cubic inches. (Let w represent the length of the sides of the squar

vaieri [72.5K]

Answer:

For minimum surface area, the base length and height are equal in length and <u>equal to 14 inches.</u>

Step-by-step explanation:

Given:

Volume of rectangular solid (V) = 2744 cubic inches

Length of base side = 'w'

Height of solid = 'h'

We know that,

Volume = Area of base × Height

$2744=(w\times w)\times h\\\\2744=w^2h\\\\h=\frac{2744}{w^2}-----(1)$

Now, surface area of the solid is given as:

$Surface\ area=2\times (base\ area)+4(hw)\\\\Surface\ area=2w^2+4hw$

Plug in 'h' value from equation (1). This gives,

$Surface\ area=2w^2+4\times\frac{2744w}{w^2}\\\\Surface\ area=2(w^2+\frac{5488}{w})$

Now, for minimum surface area, the derivative of surface area with respect to length 'w' must be 0.

Differentiating both sides with respect to 'w' and equating it to 0, we get:

$\frac{dS}{dw}=0\\\\\frac{d}{dw}[2(w^2+\frac{5488}{w})]=0\\\\2w-\frac{5488}{w^2}=0\\\\2w=\frac{5488}{w^2}\\\\w^3=\frac{5488}{2}\\\\w=\sqrt[3]{2744}= 14\ in$