Area = pi * r^2 Circumference = 2pi *r In both cases, we need a measurement for the radius. We can find that by using the distance formula. radius = [(x2 - x1)^2 + (y2 - y1)^2]^.5 = [(-5 - 1)^2 + (2 - -3)^2]^.5 = [(-6)^2 + 5^2]^.5 = (36 + 25)^...
Area = pi * r^2 Circumference = 2pi *r In both cases, we need a measurement for the radius. We can find that by using the distance formula. radius = [(x2 - x1)^2 + (y2 - y1)^2]^.5 = [(-5 - 1)^2 + (2 - -3)^2]^.5 = [(-6)^2 + 5^2]^.5 = (36 + 25)^...
Let x = original side measure of square lot Let a = original area x^2 = a (x - 3)(x - 5) = a - 185 a = x^2 - 8x +15 + 185 = x^2 - 8x + 200 x^2 = x^2 - 8x + 200 0 = -8x + 200 8x = 200 x = 25 The original square corner...
Average Value = [f(b) - f(a)]/(b - a) = [f(5) - f(0)]/(5 - 0) = [-25e^(-5/2)]/5 = -5e^(-5/2)
Let p = principal Let I = total income r = We would use this equation: I = p(1 + r)^t r = .04 t = 15 I = $35000 * 15 = $525000 p = I/(1 + r)^t = (525000)/(1.04)^15 = $525000/1...
Let c = CD Let m = money market account c + m = 20,000 .06c + .045m = 1120 Multiply first equation by .06. You get: .06c + .06m = 1200 .06c + .045m = 1120 Subtract these two equations. You get: ...
When you put the value of 0 into the function, you come up with a value of 1/0 - 2*Infinity. When you get a value like this, then you must find the limit of this function from the left and the right. However, since there is no value for a logarithmic function raised to any power that will render...
P(1 + r)^t = new balance P(1.08)^17 = $40,000 3.7P = $40,000 P = $10, 810
Let d = daytime rate Let n = nighttime rate Compose the system of equations 20d + 20n = 380 30d + 12n = 276 Multiply the first equation by 3 and the second equation by 2. You get: 60d + 60n = 1140 60d +...
Let x = pure silk thread Let y = mixed thread with silk The total amount of thread to be woven together must add up to 75 kg in mass according to the problem. The newly woven cloth should be made up of 88% silk. If the newly woven cloth is 75 kg in mass, then 88% of this would...
Vertical asymptotes 1. x = -1, x = 3 2. x = -2, x = 0, x = 2 3. x = -1, x = 1 4. x = -1, x = -3 5. x = -2, x = 4 6. x = 3
Let width = x Let length = 3x+2 Area = length * width = 16 x(3x + 2) = 16 3x^2 + 2x = 16 3x^2 + 2x - 16 = 0 (3x + 8)(x - 2) = 0 For distance, we don't use negative answers. So...
a = part of Melissa's earnings b = other part of Melissa's earnings a+b = 12000 .03a + .04b = 440 Multiply the second equation by 25. You get a+b = 12000 .75a + b = 11000 Subtract the second equation from the...
The second freight train traveled for 6 hours at 70 miles per hour. This means that the freight train traveled 420 miles. Since it caught up with the first freight train, then that first train had to have also traveled 420 miles. However, the first freight train had traveled 420 miles over a...
Let's say you own a silk screening business in which you print t-shirts. The cost of printing the t-shirts would be $2 per t-shirt in this particular year plus the cost of ink for the year which is a flat rate of $500. The cost equation for this business would be: C = 500 +...
Car travel = (20 km/hour)(1 hour) + (65 km/hour)(2 hour) + (85 km/hour)(1 hour) = 20 km + 130 km + 85 km = 235 km Average speed = distance/time = (235 km)(4 hours) = 58.75 km/hr
You need to turn both equations into matrices. I can't do that from this tablet though.
h = pounds of high quality coffee l = pounds of low quality coffee h + l = 170 In order for Sarah to make this blended coffee, she needs to make sure that the cost of the input equals the cost of the output. 5.25h + 2.50l = 4.12...
Rewrite the problem as two linear equations r = price of 1 lb. of rice p = price of 1 lb. of potatoes 20r + 30p = 29.80 30r + 12p = 29.52 Multiply first equation by 1.5. You get: 30r + 45p = 44.70 30r...
There are a couple of ways to attack this, but I will choose my way. Let's rewrite the expression as: (x^3 - 8)/(x - 2) + 1/(x - 2) This is equal to our original expression. When factoring a difference of two cubes you get this: a^3...
Since these trigonometric functions are reciprocals of each other, when one is zero the other is at infinity. Therefore the lowest value for the sum of the squares of each the tangent and cotangent function would be where the value of each is 1 or -1 (at pi/4, 3pi/4, 5pi/4, 7pi/4). Therefore,...