Tutor profile: Ruth R.
Juan is building a ramp for loading motorcycles onto a trailer. The trailer is 3.2 feet off of the ground. To avoid making it too difficult to push a motorcycle up the ramp, Juan decides to make the angle between the ramp and the ground 25 degrees. To the nearest hundredth of a foot, find the length of the ramp.
Draw a picture of the ramp to make a triangle. From the 25 degree angle you realize you are given the “Opposite” side which is the 3.2ft. You want the “hypotenuse” of the triangle which would be the actual ramp. So since you are working with the “Opposite” and “Hypotenuse” of the ramp, you will be using the SIN trigonometric function. sin(θ)=opposite/hypotenuse sin(25) = 3.2ft/hypotenuse Now solve for h (the hypotenuse). *Make sure your calculator is in degrees mode, not radians!* sin(25) = 3.2ft/h 0.4226 = 3.2/h 0.4226h = 3.2 h = 7.57217 Length of the ramp will be 7.57 feet long.
What is the slope of the line that is made from the equation 2x – 6y = -16?
The linear equation is currently in standard form but needs to be converted into slope- intercept form in order to find out the slope. Standard Form of a line: Ax + By = C Slope-Intercept Form of a line: y = mx + b Take the equation and solve for x. 2x – 6y = -16 Subtract 2x from both sides of the equation -6y = -2x – 16 Divide both sides by -6 -6y/-6 = -2x/-6 – 16/-6 Simplify all fractions y = 1/3x + 8/3 Since the equation is now in slope-intercept form, it is clear that the slope (m) is 1/3 and the y-intercept (b) is 8/3. The answer is 1/3.
A group of teenagers want to buy tickets to the rodeo. The ticket website uses the equation below to determine the cost of the tickets, y, and the number of tickets, x. 12(2.75x + 1.50) = y The group has pooled their money together and can spend no more than $800 for tickets for the entire group. What is the maximum number of tickets they can purchase?
We know that the group can spend no more than $800, which turns this question into an inequality (<) because $800 is the very most they can spend. We will substitute $800 in for y, the cost of the tickets and solve for x, the number of tickets. 12(2.75x + 1.50) < 800 Now we are going to solve this inequality for x. 12(2.75x + 1.50) < 800 1. Divide each side of the equation by 12. Since (800/12) does not come out to a whole number, we will go ahead and leave it as a decimal and round to the nearest hundredth. 2.75x + 1.50 < 66.67 2. Subtract 1.50 from both sides of the equation 2.75x < 65.17 3. Divide both side of the equation by 2.75. Note: We leave the inequality alone. The only time we reverse the inequality when we are solving is when we divide or multiply by a negative number. x < 23.70 So the answer to the inequality is x < 23.70. To put it in the context of the problem, x is the number of tickets so this is saying that the number of tickets that can be purchased has to be less than or equal to 23.70 to stay under the group’s $800. So how what is the maximum number of tickets the group can purchase? 23 tickets
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