First, familiarize yourself with the math formula, use memorization techniques (ex.flashcards), understand the formulas, and get plenty of sleep.
Answer: b 96 plus 160 cm
Step-by-step explanation:
Step-by-step explanation:
4(3m+4n+4)+5p
4{3m+4(n+1)}+5p
Answer:
a) 27 m/s
b) 30 m/s
c) i) 3
ii) Deceleration
Step-by-step explanation:
The question is not complete, the correct question is given as:
The graph shows information about the speed of a vehicle during the final 50 seconds of a journey. At the start of the 50 seconds the speed is k metres per second. The distance travelled during the 50 seconds is 1.35 kilometres.
(a) Work out the average speed of the vehicle during the 50 seconds
(b) Work out the value of k.
(c) (i) Calculate the gradient of the graph in the final 10 seconds of the journey
(ii) Describe what this gradient represents
Answer:
The graph is attached. The total time = 50 seconds, total distance = 1.35 km = 1350 m
a) The average speed is the ratio of the total distance traveled to the total time taken to cover this distance. The average speed is given by the formula:
![Average \ speed=\frac{total\ distance}{total\ time}\\ Substituting: \\ Average \ speed=\frac{1350\ m}{50\ s} = 27\ m/s](https://tex.z-dn.net/?f=Average%20%5C%20speed%3D%5Cfrac%7Btotal%5C%20distance%7D%7Btotal%5C%20time%7D%5C%5C%20Substituting%3A%20%5C%5C%20Average%20%5C%20speed%3D%5Cfrac%7B1350%5C%20m%7D%7B50%5C%20s%7D%20%3D%2027%5C%20m%2Fs)
b) From the graph, the total distance covered is the area of the graph. The graph is made up of a rectangle and triangle, the area of the graph is equal to the sum of area of rectangle and area of triangle.
c) i) The gradient in the last 10 seconds is the ratio of change in speed to change in time
![Gradient=\frac{change\ in\ speed }{change\ in\ time}=\frac{0-k}{50-40} \\ bt \ k=30\\Gradient=\frac{0-30}{50-40}= \frac{-30}{10} =-3](https://tex.z-dn.net/?f=Gradient%3D%5Cfrac%7Bchange%5C%20in%5C%20speed%20%7D%7Bchange%5C%20in%5C%20time%7D%3D%5Cfrac%7B0-k%7D%7B50-40%7D%20%20%5C%5C%20bt%20%5C%20k%3D30%5C%5CGradient%3D%5Cfrac%7B0-30%7D%7B50-40%7D%3D%20%5Cfrac%7B-30%7D%7B10%7D%20%3D-3)
ii) Since the gradient is negative it means it is deceleration. That is in the in the last 10 seconds the vehicle decelerates at a rate of 3 m/s²
Answer:
The equation is y = 3x + 2
Step-by-step explanation:
The form of the linear equation is y = m x + b, where
- m is the slope of the line which represent the equation
- b is the y-intercept which is value y at x = 0
The rule of the slope is m = Δy/Δx, where
- Δx = x2 - x1 and Δy = y2 - y1
- (x1, y1) and (x2, y2) are two points on the line.
∵ x is the input
∵ Input: 0, 1, 2, 3, 4
∵ y is the output
∵ output: 2, 5, 8, 11, 14
∴ The points on the line are (0, 2), (1, 5), (2, 8), (3, 11), and (4, 14)
→ Use any two points to find m
∵ x1 = 0 and y1 = 2
∵ x2 = 1 and y2 = 5
→ Find Δx and Δy
∴ Δx = 1 - 0 = 1
∴ Δy = 5 - 2 = 3
→ Substitute them in the rule of the slope above
∵ m = ![\frac{3}{1}](https://tex.z-dn.net/?f=%5Cfrac%7B3%7D%7B1%7D)
∴ m = 3
∵ b is the value of y at x = 0
∵ At x = 0, y = 2
∴ b = 2
→ Substitute the values of m and b in the form of the equation above
∵ y = 3x + 2
∴ The equation is y = 3x + 2