prove algebraically that the straight line with equation x = 2y + 5 is a tangent to the circle with equation x^2 + y^2 = 5, i ha
ve 3/5 marks and i tried with perpendicular gradient.
2 answers:
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First Question
For a better understanding of the solution provided here please find the first attached file which has the diagram of the the isosceles trapezoid.
We dropped perpendiculars from C and D to intersect AB at Q and P respectively.
As can be seen in , we can easily find the values of CQ and BQ.
Since,
ft
In a similar manner we can find BQ as:
ft
All these values can be found in the diagram attached.
Thus, because of the inherent symmetry of the isosceles trapezoid, PQ can be found as:
Let us now consider
We can apply the Pythagorean Theorem here to find the length of the diagonal AC which is the hypotenuse of .
feet.
Thus, out of the given options, Option B is the closest and hence is the answer.
Second Question
For this question we can directly apply the formula for the area of a triangle using sines which is as:
Area=(First Side)(Second Side)(Sine of the angle between the two sides)
Thus, from the given data,
Area=
Therefore, Option D is the correct option.
Third Question
For this question we will apply the Sine Rule to the given to us.
Thus, from the triangle we will have:
This gives to be:
Which is not close to any of the given options.
Fourth Question
Please find the second attachment for a better understanding of the solution provided her.
As can be clearly seen from the attached diagram, we can apply the Cosine Rule here to find the return distance of the plane which is CA.
miles.
Thus, Option D is the answer.
Answer:
(a) For the stem-and-leaf plot, we need to organise all data in columns, one column is the stem and a second column is the leaf, but in this case, stems are going to be the digits to the left of the decimal point, and leafs are the digits to the right of the decimal point:
<u>Stem</u> <u> Leaf </u>
0 2 2 2 3 3 4 5 7
1 0 2 3 5 5 8
2 0 3 5
3 0 3
4 0 5 7
5 0 5 6 9
6 0 0 0 5
(b) Relative frequency distribution.
Remember that, a relative frequency is calculated dividing the absolute frequency by the total data, in this case, we approximated to the hundredth.
Length of life Absolute Frequency Relative Frequency % Relative Freq.
0.2 3 0.1 10
0.3 2 0.07 7
0.4 1 0.03 3
0.5 1 0.03 3
0.7 1 0.03 3
1.0 1 0.03 3
1.2 1 0.03 3
1.3 1 0.03 3
1.5 2 0.07 7
1.8 1 0.03 3
2.0 1 0.03 3
2.3 1 0.03 3
2.5 1 0.03 3
3.0 1 0.03 3
3.3 1 0.03 3
4.0 1 0.03 3
4.5 1 0.03 3
4.7 1 0.03 3
5.0 1 0.03 3
5.5 1 0.03 3
5.6 1 0.03 3
5.9 1 0.03 3
6.0 3 0.10 10
6.5 1 0.03 3
Total 30
(c)
To calculate the sample mean we need to sum all number, which results: 83.9. Then, we divide this result to the total 30, which result: 2.80.
The sample range is the difference between the highest and the lowest value: 6.5 - 0.2 = 6.3.
The sample standard deviation is calculated trough the following process:
Step 1: Subtract the mean from each number.
Step 2: Square each result.
Step 3: Add the squared deviations.
Step 4: Divide the sum by one less the total.
Step 5: Take the square root, and there you have it.
Doing this steps, the result is 2.22.
This last process is attached:
