Calculate the measure of an interior angle of a regular decagon.
Step 1. The sum of all interior angles in a regular n-gon is 180(n-2) where n is the number of sides in the polygon. Use [180(n-2)]/n to calculate the measure of one interior angle where n = 10. [180(10-2)]/10 [180(8)]/10 1440/10 144 Therefore, the measure of an interior angle of a regular decagon is 144°.
A 250-g sample of water is heated from 6.20°C to 85.30°C. Calculate the amount of heat absorbed (in joules) by the water. The specific heat capacity of water is 4.184 J/g°C.
Step 1. Use q = mcΔT where q is the amount of heat absorbed, m is the mass of the water sample, c is the specific heat capacity of water, and ΔT is the change in temperature (final temperature minus initial temperature). The specific heat capacity of water is 4.184 J/g°C. Step 2. Plug in m = 250 g, c = 4.184 J/g°C, and ΔT = 85.30°C - 6.20°C into q = mcΔT, and solve for q. q = (250)(4.184)(85.30-6.20) q = (250)(4.184)(79.10) q = 8.3 x 10^4 Therefore, the amount of heat absorbed by the water is 8.3 x 10^4 J.
Write the equation of the line that passes through P(-6, 11) and is perpendicular to y = 3x + 5.
Step 1. Using the slope-intercept equation y = mx + b where m is the slope and b is the y-intercept, m = 3 in y = 3x + 5. Step 2. The slope of the line that is perpendicular to y = 3x + 5 must be the negative reciprocal of 3. Therefore, m = -1/3 in the equation we are trying to find. Step 3. Plug m = -1/3 and P(-6, 11) into y = mx + b, and solve for b: 11 = -1/3(-6) + b 11 = 2 + b 9 = b Step 4. Using m = -1/3 and b = 9, the equation we are trying to find is: y = (-1/3)x + 9