1.Calculate the amount of heat produced in an electric heater of resistance 1000 ohms if 6A of current is passed through it for 10 minutes.. 2.400J of heat is produced in 4s in a 4 ohm resistor.Find potential difference across the resistor.. 3. Calculate the power of a source if it produces an energy of 750J in 30s.. 4. Which uses more energy , a 500W TV set in 1 hour or a 1200W toaster in 10 minutes.. 5. Calculate the electrical energy consumed by a 1200W toaster in 10 minutes..

Answers

Answer 1

Answer: Power is determined through multiplying the square of the current, resistance and time. it is also determined by dividing energy by time

1. P = I^2 Rt = 6^2*1000*10*60 = 21. 6 MW
2. P = 4000 J/4s = 1000 W
3. P = 750 J/ 30 s = 25 W
4. P = 500 J/3600s = 0.139 W ; P = 1200J/10/60s = 2 W ; toaster needs more power
5. P = 1200 J/ 600s= 2 W

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Prove that: (a2 - b2)3 + (b2-c2)3+ (c2-a2)3 = 3 (a+b) (b+c) (c+a) (a-b) (b-c) (c-a).

Answers

$L=(a^2-b^2)^3+(b^2-c^2)^3+(c^2-a^2)^3=(*)\n\n(a^2-b^2)^3=a^6-3a^4b^2+3a^2b^4-b^6\n\n(b^2-c^2)^3=b^6-3b^4c^2+3b^3c^4-c^6\n\n(c^2-a^2)^3=c^6-3c^4a^2+3c^2a^4-a^6\n\n(*)=a^6-3a^4b^2+3a^2b^4-b^6+b^6-3b^4c^2+3b^2c^4-c^6+c^6-\dots\n\dots-3c^4a^2+3c^2a^4-a^6\n\n=-3a^4b^2+3a^2b^4-3b^4c^2+3b^2c^4-3c^4a^2+3c^2a^4\n\n=3(-a^4b^2+a^2b^4-b^4c^2+b^2c^4-a^2c^4+a^4c^2)$

$R=3(a+b)(a-b)(b+c)(b-c)(c+a)(c-a)\n\n=3(a^2-b^2)(b^2-c^2)(c^2-a^2)\n\n=3(a^2b^2-a^2c^2-b^4+b^2c^2)(c^2-a^2)\n\n=3(a^2b^2c^2-a^4b^2-a^2c^4+a^4c^2-b^4c^2+a^2b^4+b^2c^4-a^2b^2c^2)\n\n=3(-a^4b^2+a^2b^4-b^4c^2+b^2c^4-a^2c^4+a^4c^2)\n\nL=R$

$(a^2 - b^2)^3 + (b^2 - c^2)3 + (c^2 - a^2)^3 = 3(a + b)(b +c)(c + a)(a - b)(b - c)(c - a)$
$(a^2 - b^2)^3 + (b^2 - c^2)3 + (c^2 - a^2)^3 = 3(a + b)(a - b)(b + c)(b - c)(c + a)(c - a)$
$(a^2 - b^2)^3 + (b^2 - c^2)3 + (c^2 - a^2)^3 = 3(a^2 - b^2)(b^2 - c^2)(c^2 - a^2)$

$(a^2 - b^2)^3 = (a^2 - b2)(a^2 - b^2)(a^2-b^2) = a^6 - 3a^4b^2 + 3a^2b^4 - b^6$
$(b^2 - c^2)^3 = (b^2 - c^2)(b^2 - c^2)(b^2 - c^2) = b^6 - 3^4c^2 + 3b^2c^4 - c^6)$
$(c^2 - a^2)^3 = (c^2 - a^2)(c^2 - a^2)(c^2 - a^2) = c^6 - 3a^2c^4 + 3a^4c^2 - a^6$

$a^6 - 3a^4b^2 + 3a^2b^4 - b^6 + b^6 - 3b^4c^2 + 3b^2c^4 - c^6 + c^6 - 3a^2c^4 + 3a^4c^2 - a^6$
$-3a^4b^2 + 3a^2b^4 - 3b^4c^2 + 3b^2c^4 - 3a^2c^4 + 3a^4c^2$
$3(-a^4b^2 + a^2b^4 - b^4c^2 + b2^c^4 - a^2c^4 + a^4c^2)$

$3(a^2 - b^2)(b^2 - c^2)(c^2 - a^2) = 3(-a^4b^2 + a^2b^4 - b^4c^2 + b^2c^4 - a^2c^4 + a^4c^2)$

$3(-a^4b^2 + a^2b^4 - b^4c^2 + b^2c^4 - a^2c^4 + a^4c^2) = 3(-a^4b^2 + a^2b^4 - b^4c^2 + b^2c^4 - a^2c^4 + a^4c^2$

find the volume of a can of chicken broth that had a diameter of 7.5cm and a height of 11cm. round 5o the neatest tenth

Answers

cans are normally cylinders
Vcylinder=hpir^2

h=11

d/2=r
7.5/2=3.75=r

V=11pi3.75^2
V=11pi14.0625
V=154.6875pi
aprox pi=3.141592 and multiply
V=485.96
round tenth
486.0 cm^3

Chester dives from a board 15 feet above the water he goes 7 feet below the surface of the water What is the total length of Chester’s dive