Question and Answers Forum

AllQuestion and Answers: Page 349

Question Number 186481 Answers: 0 Comments: 0

Question Number 186476 Answers: 0 Comments: 0

Question Number 186473 Answers: 0 Comments: 0

A metallic cube is subjected to heating such that as the metal expands, the total surface area increases at rate of 6.25 cm^2 s^(−1) . Calculate the rate at which each side of the cube is increasing when the volume is 51.2 cm^3 .

$$\mathrm{A}\:\mathrm{metallic}\:\mathrm{cube}\:\mathrm{is}\:\mathrm{subjected}\:\mathrm{to} \\ $$$$\mathrm{heating}\:\mathrm{such}\:\mathrm{that}\:\mathrm{as}\:\mathrm{the}\:\mathrm{metal} \\ $$$$\mathrm{expands},\:\mathrm{the}\:\mathrm{total}\:\mathrm{surface}\:\mathrm{area} \\ $$$$\mathrm{increases}\:\mathrm{at}\:\mathrm{rate}\:\mathrm{of}\:\mathrm{6}.\mathrm{25}\:\mathrm{cm}^{\mathrm{2}} \mathrm{s}^{−\mathrm{1}} . \\ $$$$\mathrm{Calculate}\:\mathrm{the}\:\mathrm{rate}\:\mathrm{at}\:\mathrm{which}\:\mathrm{each} \\ $$$$\mathrm{side}\:\mathrm{of}\:\mathrm{the}\:\mathrm{cube}\:\mathrm{is}\:\mathrm{increasing}\:\mathrm{when} \\ $$$$\mathrm{the}\:\mathrm{volume}\:\mathrm{is}\:\mathrm{51}.\mathrm{2}\:\mathrm{cm}^{\mathrm{3}} . \\ $$

Question Number 186468 Answers: 1 Comments: 0

Simplify ((1^2 ∙2!+2^2 ∙3!+3^2 ∙4!+∙∙∙+n^2 (n+1)!−2)/((n+1)!)) to n^2 +n−2

$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{Simplify} \\ $$$$\frac{\mathrm{1}^{\mathrm{2}} \centerdot\mathrm{2}!+\mathrm{2}^{\mathrm{2}} \centerdot\mathrm{3}!+\mathrm{3}^{\mathrm{2}} \centerdot\mathrm{4}!+\centerdot\centerdot\centerdot+{n}^{\mathrm{2}} \left({n}+\mathrm{1}\right)!−\mathrm{2}}{\left({n}+\mathrm{1}\right)!} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{to} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{n}^{\mathrm{2}} +\mathrm{n}−\mathrm{2} \\ $$

Question Number 186464 Answers: 1 Comments: 15

Question Number 186453 Answers: 1 Comments: 0

(1/(1+2))+(1/(1+2+3))+(1/(1+2+3+4))+...+(1/(1+2+3+...+10))=?

$$\frac{\mathrm{1}}{\mathrm{1}+\mathrm{2}}+\frac{\mathrm{1}}{\mathrm{1}+\mathrm{2}+\mathrm{3}}+\frac{\mathrm{1}}{\mathrm{1}+\mathrm{2}+\mathrm{3}+\mathrm{4}}+...+\frac{\mathrm{1}}{\mathrm{1}+\mathrm{2}+\mathrm{3}+...+\mathrm{10}}=? \\ $$

Question Number 186447 Answers: 0 Comments: 1

Question Number 186446 Answers: 0 Comments: 0

Question Number 186445 Answers: 1 Comments: 0

Show that the function y = ∣ x −5 ∣ has no derivative at x = 5.

$$\mathrm{Show}\:\:\mathrm{that}\:\:\mathrm{the}\:\:\mathrm{function}\:\:\mathrm{y}\:=\:\:\mid\:\mathrm{x}\:−\mathrm{5}\:\mid\:\:\mathrm{has}\:\:\mathrm{no}\:\:\mathrm{derivative}\:\:\mathrm{at}\:\:\mathrm{x}\:\:=\:\mathrm{5}. \\ $$

Question Number 186442 Answers: 2 Comments: 0

Question Number 186441 Answers: 1 Comments: 1

Question Number 186439 Answers: 1 Comments: 1

Question Number 186437 Answers: 1 Comments: 2

∫_0 ^( 1) (1/( (√(x(√(x^2 (√(x^3 (√(x^4 +1)))))))) )) dx

$$ \\ $$$$\: \\ $$$$\:\:\:\:\:\:\:\:\:\int_{\mathrm{0}} ^{\:\mathrm{1}} \:\frac{\mathrm{1}}{\:\sqrt{{x}\sqrt{{x}^{\mathrm{2}} \sqrt{{x}^{\mathrm{3}} \sqrt{{x}^{\mathrm{4}} +\mathrm{1}}}}}\:}\:{dx} \\ $$$$\: \\ $$

Question Number 186419 Answers: 3 Comments: 0

If , (( 1 − lo^ g_( 2) (x)))^(1/3) + ((1+^ log_( 2) (x)))^(1/3) −1=0 ⇒ x = ?

$$ \\ $$$$\:\:\mathrm{I}{f}\:,\:\sqrt[{\mathrm{3}}]{\:\mathrm{1}\:−\:{l}\overset{} {{o}g}_{\:\mathrm{2}} \left({x}\right)}\:\:+\:\sqrt[{\mathrm{3}}]{\mathrm{1}\overset{} {+}{log}_{\:\mathrm{2}} \left({x}\right)}\:−\mathrm{1}=\mathrm{0}\:\:\:\:\:\:\:\: \\ $$$$ \\ $$$$\:\:\:\:\:\:\Rightarrow\:\:\:{x}\:=\:?\:\:\:\: \\ $$

Question Number 186416 Answers: 1 Comments: 1

Question Number 186410 Answers: 1 Comments: 1

Question Number 186403 Answers: 0 Comments: 0

Question Number 186402 Answers: 1 Comments: 0

Question Number 186401 Answers: 1 Comments: 0

Question Number 186399 Answers: 1 Comments: 0

Question Number 186376 Answers: 1 Comments: 0

Question Number 186370 Answers: 1 Comments: 0

A gear with outer radius of r'=5cm move in a clockwise direction causing an interlocking gear with an outer radius of r"=4cm to move in a counter-clockwise direction at an angular speed of w"=25rev/min. What is the angular speed (w') in the outer gear.

$$ \\ $$A gear with outer radius of r'=5cm move in a clockwise direction causing an interlocking gear with an outer radius of r"=4cm to move in a counter-clockwise direction at an angular speed of w"=25rev/min. What is the angular speed (w') in the outer gear.

Question Number 186361 Answers: 1 Comments: 1

Question Number 186359 Answers: 2 Comments: 0

Question Number 186348 Answers: 0 Comments: 2

QUIZ: If the sum of the numbers 1 to 100 can be calculated with Carl Gauss′s method, then How do we calculate the sum of the numbers starting from 2 and going up to 100 by twos in an easy way with the same method? Or 2+4+6+8+10+...+100=?

$$\mathrm{Q}{UIZ}: \\ $$$${If}\:{the}\:{sum}\:{of}\:{the}\:{numbers}\:\mathrm{1}\:{to}\:\mathrm{100}\:{can} \\ $$$${be}\:{calculated}\:{with}\:{Carl}\:{Gauss}'{s}\:{method}, \\ $$$${then}\:{How}\:{do}\:{we}\:{calculate}\:{the}\:{sum}\:{of}\:{the} \\ $$$${numbers}\:{starting}\:{from}\:\mathrm{2}\:{and}\:{going}\:{up}\:{to} \\ $$$$\mathrm{100}\:{by}\:{twos}\:{in}\:{an}\:{easy}\:{way}\:{with}\:{the}\:{same} \\ $$$${method}? \\ $$$${Or}\:\mathrm{2}+\mathrm{4}+\mathrm{6}+\mathrm{8}+\mathrm{10}+...+\mathrm{100}=? \\ $$

Question Number 186347 Answers: 1 Comments: 1

∫_(−2) ^2 ((x^5 − 1 + 2)/(x^4 + x −2)) dx

$$ \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\underset{−\mathrm{2}} {\overset{\mathrm{2}} {\int}}\:\:\:\:\frac{\boldsymbol{{x}}^{\mathrm{5}} \:−\:\:\mathrm{1}\:\:+\:\:\mathrm{2}}{\boldsymbol{{x}}^{\mathrm{4}} \:\:+\:\:\boldsymbol{{x}}\:\:−\mathrm{2}}\:\:\:\:\boldsymbol{{dx}}\:\:\:\:\:\:\: \\ $$$$ \\ $$

Pg 344 Pg 345 Pg 346 Pg 347 Pg 348 Pg 349 Pg 350 Pg 351 Pg 352 Pg 353

Contact: info@tinkutara.com