Answer:
4 ohms
Step-by-step explanation:
The question is "In two minutes a current of 5 amps develops 1,200 heat units in a wire of 8 ohms resistance. What resistance does a similar wire have, which develops 6,000 heat units with a current of 10 amps in 5 minutes?"
Current, I₁ = 5 A
Heat, Q₁ = 1200 units
Resistance, R₁ = 8 ohms
Time, t₁ = 2 min = 120 s
New heat, Q₂ = 6000 units
Current, I₂ = 10 A
New time, t₂ = 5 min = 300 s
We need to find the new resistance.
Heat developed is given by :
![Q=I^2Rt](https://tex.z-dn.net/?f=Q%3DI%5E2Rt)
![\dfrac{Q_1}{I_1^2R_1t_1}=\dfrac{Q_2}{I_2^2R_2t_2}\\\\R_2=\dfrac{Q_2\times I_1^2R_1t_1}{Q_1I_2^2t_2}\\\\R_2=\dfrac{6000\times 5^2\times 8\times 120}{1200\times 10^2\times 300}\\\\=4\ \Omega](https://tex.z-dn.net/?f=%5Cdfrac%7BQ_1%7D%7BI_1%5E2R_1t_1%7D%3D%5Cdfrac%7BQ_2%7D%7BI_2%5E2R_2t_2%7D%5C%5C%5C%5CR_2%3D%5Cdfrac%7BQ_2%5Ctimes%20I_1%5E2R_1t_1%7D%7BQ_1I_2%5E2t_2%7D%5C%5C%5C%5CR_2%3D%5Cdfrac%7B6000%5Ctimes%205%5E2%5Ctimes%208%5Ctimes%20120%7D%7B1200%5Ctimes%2010%5E2%5Ctimes%20300%7D%5C%5C%5C%5C%3D4%5C%20%5COmega)
So, the new resistance is 4 ohms.
Answer:
m∠x = 10°
Step-by-step explanation:
Since we are dealing with a <u>right triangle</u> and its two sides and one angle, we can use <u>trigonometry ratios</u>. Remember them all with the acronym SohCahToa.
"o" is for opposite side, "a" is for adjacent side, "h" is for hypotenuse side.
The ratios are:
sinθ = opposite/hypotenuse
cosθ = adjacent/hypotenuse
tanθ = opposite/adjacent
θ means the "angle of reference", or the angle you know or want to find. This determines which side is adjacent (touching) or opposite (not touching). The hypotenuse (longest side) does not change.
In this triangle, θ = x. The sides we know are hypotenuse and opposite. Therefore, we will use the sinθ ratio.
sinθ = opposite/hypotenuse
sinx = CB/AB Substitute the labels in the diagram
sinx = 4/23 Substitute known values (side lengths)
x = sin⁻¹(4/23) Isolate 'x'. Use calculator to solve.
x = 10.015....° Exact answer
x ≈ 10° Round to the nearest degree
Therefore the measure of angle x (m∠x) is 10°.
Step-by-step explanation:
![\frac{x}{10} = 7](https://tex.z-dn.net/?f=%20%5Cfrac%7Bx%7D%7B10%7D%20%20%3D%207)
x = 7 ×10
x = 70