Q1) Paul brought a car last year.
It has lost 12½% of its value since then.
It is now valued at £10,500
How much did Paul pay for his car?
-[I got £11812.50... Is that right?~xD]
Q2) A newspaper report stated: "Concorde has flown 7.1x10^7 miles.
This is equivalent to 300 journeys from the earth to the moon.
Calculate the distance from the earth to the moon.
Give you answer to 2sig figs~
Q3) Solve algebraically the equation:
Tan40=2Sinx+1
no to #1
let the original cost be x
it lost 12.5% , so 87.5% of its value is left
.875x = 10500
x = 12000
#2
Is the "journey" to the moon and back, or just one way.
I will assume a return flight.
so distance to the moon = 7.1x10^7 / 600
= appr 118333 miles
#3
Somehow I think you meant
tan40° = 2sin(x+1)
sin(x+1) = .41955
x+1 = 24.806 or x+1 = 155.194
x = 23.806° or 154.194°
If tan40 is tan 40 radians, switch your calculator to rad when finding the inverse sine.
Q1) To find out how much Paul paid for his car, we need to calculate the original value of the car. Let's break down the problem step by step.
1. Start by assigning a variable to the original value of the car, let's call it 'x'.
2. We know that the car has lost 12½% of its value. To find out the current value, we need to subtract this percentage from the original value.
- We can convert the percentage to a decimal by dividing it by 100: 12½% = 12.5/100 = 0.125
- The current value of the car can be calculated as: x - (0.125 * x) = x(1 - 0.125).
3. Now, we are given that the current value of the car is £10,500. We can set up an equation based on this information: x(1 - 0.125) = £10,500.
4. Solve the equation for x:
- Divide both sides of the equation by (1 - 0.125): x = £10,500 / (1 - 0.125)
- Calculate the value of x to find out how much Paul paid for his car.
Using this method, we can now solve the equation to find the original cost of the car.
Q2) To calculate the distance from the earth to the moon based on the given information, follow these steps:
1. The problem states that Concorde has flown 7.1x10^7 miles, which is equivalent to 300 journeys from the earth to the moon.
2. Divide the total miles flown by the number of journeys to find the distance for one journey:
- Distance for one journey = (7.1x10^7 miles) / 300
3. Simplify the expression to calculate the distance from the earth to the moon:
- Distance from the earth to the moon = (7.1x10^7 miles) / 300
Calculating the expression using this method will give you the distance from the earth to the moon.
Q3) To solve the equation algebraically, let's break it down step by step:
1. The equation is tan(40°) = 2sin(x) + 1.
2. We want to isolate sin(x) on one side of the equation, so we can solve for x.
3. Start by subtracting 1 from both sides of the equation: tan(40°) - 1 = 2sin(x).
4. Divide both sides of the equation by 2: (tan(40°) - 1) / 2 = sin(x).
5. Now, we need to find the inverse sine (sin^-1) of both sides to solve for x: sin^-1((tan(40°) - 1) / 2) = x.
6. Use a calculator to evaluate the expression: sin^-1((tan(40°) - 1) / 2) ≈ x.
By following these steps, you can solve the equation algebraically and find the value of x.