A boat sails 150km on a bearing of 042degree and then 250km due east . How far is the boat from the starting point
The answer is 368 km using cosine rule
The bearing of a point A from a point B is 042 degree calculate the bearing from A
368 km
Please what rule are we using
We can assume that there exists a linear relationship between x and y. That is:
y = mx + b
where m is the slope of the line and b is the y-intercept.
Using the point given, we can solve for b:
5 = m(9) + b
b = 5 - 9m
Now that we know b, we can use the slope to find y when x is 4:
m = (y - 5)/(x - 9)
Since we are asked to find y when x is 4 and we know that m is the same, we can plug in the values we know and solve for y:
m = (y - 5)/(4 - 9)
m = (y - 5)/(-5)
Multiplying both sides by -5, we get:
-5m = y - 5
Adding 5 to both sides, we get:
-5m + 5 = y
Now, substituting the value we found for b earlier:
y = -5m + 5 - 9m
Simplifying the right-hand side, we get:
y = -14m + 5
Now, we can solve for m:
5 = 9m + b
5 = 9m + (5 - 9m)
5 = 5
This is true for any value of m, because the equation for the line is not unique with only one point. However, we can choose any value for m and still find a valid value for y. Let's choose m = 1:
y = -14(1) + 5
y = -9
Therefore, when x is 4, y is -9.
A truth table is a table that displays all possible inputs and outputs for a Boolean function. Boolean functions are functions that take one or more binary inputs (0 or 1) and produce a binary output. The truth table shows all the possible combinations of input values and the corresponding output values.
The columns of a truth table are typically labeled with the input variables and the output variable. The rows of the truth table show all possible combinations of input values. For each row of the truth table, the values of the input variables are specified and the corresponding output value is computed using the Boolean function.
For example, consider the Boolean function AND, which takes two binary inputs and produces a binary output that is 1 if both inputs are 1, and 0 otherwise. The truth table for this function would have two input columns and one output column, and would look like this:
```
Input1 | Input2 | Output
------------------------
0 | 0 | 0
0 | 1 | 0
1 | 0 | 0
1 | 1 | 1
```
The first row of the truth table shows the result when both input variables are 0, which produces an output of 0. The second row shows the result when one input variable is 0 and the other is 1, which produces an output of 0. The third row shows the result when the first input variable is 1 and the second is 0, which produces an output of 0. Finally, the last row shows the result when both input variables are 1, which produces an output of 1.
The truth table provides a complete and systematic way to specify the behavior of Boolean functions. It is a valuable tool for designing and analyzing digital circuits, for encoding Boolean expressions, and for testing the correctness of logic designs.
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D = 150km[42o]+250km[90o].
D = (150*sin42+250*sin90)+(150*cos42+250*cos90)i
D = 350+112i = 367km[72o].
370°
We are using the cosine rule (a.k.a. the law of cosines) to find the distance between the two points. The cosine rule is a formula that relates the length of the sides of a triangle to the cosine of one of its angles. It can be used to find the length of any side of a triangle if the lengths of the other two sides and the included angle are known.
The formula for the cosine rule is:
c^2 = a^2 + b^2 - 2ab*cos(C)
Where c is the length of the side opposite angle C, and a and b are the lengths of the other two sides.
Please solve this question:
From the top of a building, Deborah observes that the angles of depression of two vehicles to be 35 degree and 47 degree respectively. The two vehicles are on the same straight line with the building and also on the same side of the building. Calculate to the nearest metre the height of the building in which the distance of the vehicles is 10m.
Let's call the height of the building "h". We can use basic trigonometry and the information given in the problem to set up an equation relating "h" to the distance between the two vehicles.
Firstly, we can draw a diagram to visualize the problem. Let's label the base of the triangle formed by the building and the two vehicles with "d" (the distance between the two vehicles) and label the angles of depression as 35 degrees and 47 degrees, respectively:
```
A
|\
| \
| \ h
| \
35| \ 47
| \
| \
|_______\
d
```
We know that the two vehicles are on the same straight line with the building, so we can draw a perpendicular line from the building to the ground and label it "x":
```
A
|\
| \
h | \
| \ x
| \
35| \
| \
|_______\
d
```
Now, we can write two trigonometric equations based on the angles of depression:
tan(35) = h/x
tan(47) = h/(d+x)
We can rewrite these equations to express "x" and "d" in terms of "h":
x = h/tan(35)
d+x = h/tan(47)
d = h/tan(47) - h/tan(35)
Now, we can substitute the given distance "d" (which is 10 m) into the equation above to solve for "h":
10 = h/tan(47) - h/tan(35)
Multiplying both sides by the common denominator of tan(35)*tan(47), we get:
10*tan(35)*tan(47) = h*(tan(47) - tan(35))
Simplifying the right-hand side, we get:
10*tan(35)*tan(47) = h*tan(47 - 35)
10*tan(35)*tan(47) = h*tan(12)
Dividing both sides by tan(12), we get:
h = 10*tan(35)*tan(47) / tan(12)
Using a calculator, we can evaluate this to be:
h ≈ 20.64 m
Therefore, the height of the building is approximately 20.64 metres to the nearest metre.
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If y=5 when x is 9 find y when x is 4
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ICT
Using the following as a case study,
a) Manual files as the existing system
b) Computer files as the proposed system
Perform the following,
I. Preliminary system study
II. Feasibility study
III. Investigative study
IV. System analysis
V. Process of implementation
VI. Maintenance
Sure, here's an overview of the different steps involved in the project.
I. Preliminary System Study
This is the initial phase of the project where information is gathered from the client about their current system and requirements for the new system. In this phase, we would analyze the structure and organization of their manual files and their current process for maintaining and updating their files. We would also identify any problems or issues that they are experiencing with their current system. This information would be used to determine what features the new computerized system should have, as well as the resources and expertise that would be required to develop and implement the new system.
II. Feasibility Study
Once we have performed a preliminary system study, the next step would be to determine the feasibility of implementing a computerized file management system. This would involve analyzing the technical, economic, and operational aspects of the proposed system. We would look at factors such as the cost of hardware and software, the availability of trained personnel, the expected return on investment, and how long it would take to implement the system. Based on this analysis, we would make a recommendation on whether or not it is feasible to move forward with the project.
III. Investigative Study
Assuming that the feasibility study indicates that the project is feasible, the next phase would be an investigative study where we would research and evaluate different options for the new system. This would involve looking at various software applications and tools that could be used for file management and examining the strengths and weaknesses of each option. We would also need to consider factors such as ease of use, compatibility with existing systems, and the need for training and support.
IV. System Analysis
Once we have selected a system to use, we would perform a detailed system analysis. This involves breaking down the new system into smaller components and analyzing their behavior and interactions. We would develop a logical data model, which is a visual representation of the organization's data and how it is stored and used. We would also develop use cases and functional requirements that outline how the new system should work and what it should be capable of doing. The purpose of this phase is to establish a clear set of specifications for the new system.
V. Process of Implementation
Once the system analysis is complete, the implementation phase can begin. Depending on the specific details of the project, this may involve installing new hardware or software, configuring the system to meet the client's needs, and testing the new system to ensure that it is working properly. We would also develop training materials and provide training to staff members to ensure they are familiar with the new system and understand how to use it. Finally, we would initiate a process for transitioning from the old manual files system to the new computerized file management system.
VI. Maintenance
Once the new system is in place and working properly, the final phase is maintenance. This involves ongoing monitoring of the system to ensure it is performing correctly, as well as fixing any issues or problems that arise. We would also need to keep the system up to date by installing patches and updates, and by providing ongoing support to the client's staff members. The purpose of this phase is to ensure that the new system continues to meet the organization's needs over time.
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Send further maths questions for SSS2
Sure, here are some further maths questions for SSS2:
1. Find the equation of the tangent to the curve y = 2x^3 - 3x^2 + 6x - 2 at the point where x = 1.
2. The angles of a triangle are in the ratio 1:2:3. Find each angle.
3. Simplify: (3x - 4)^3 - (3x - 4)^2 + (3x - 4).
4. Find a vector perpendicular to the plane passing through the points (1, 2, 3), (4, 5, 6), and (7, 8, 9).
5. Solve for x: e^(2x) - 9 = 0.
6. If sin x = 3/5 and cos y = -5/13, where x and y are acute angles, find tan(x + y).
7. The sides of a square are increased by 10%. Find the percentage increase in its area.
8. Simplify: [ 2x^2 + 3xy - y^2 - 4x - 3y + 5 ] / [ x^2 - xy + 2x - y ].
9. Differentiate with respect to x: y = (2x - 3)/(x^2 - 5x + 4).
10. Find the area of the triangle with vertices (1, 2), (4, -3), and (-2, 1).
I hope these questions are helpful!
10 Polynomial question
Sure, here are ten polynomial questions for you:
1. Write the polynomial x^3 + 2x^2 - 5x + 1 in standard form.
2. Find all the roots of the polynomial x^3 + 3x^2 - 4x - 12.
3. Find the remainder of (2x^3 + 5x^2 - 3x + 4)/(x - 2).
4. Factor the polynomial x^3 - x^2 + 3x - 3 completely.
5. Determine the degree and leading coefficient of the polynomial -3x^4 + x^2 + 4.
6. Find the roots of the polynomial x^4 - 8x^3 + 25x^2 - 38x + 15.
7. Factor the polynomial x^4 + 3x^3 - 10x^2 - 24x - 15 completely.
8. Find the remainder of (x^5 + 2x^3 - 3x^2 + 2) / (x^2 - 1).
9. Determine the degree and leading coefficient of the polynomial 2x^6 + x^3 - 5x + 7.
10. Find all the roots of the polynomial x^4 - 6x^3 + 13x^2 - 12x + 4.
I hope these questions help you practice your skills with polynomial algebra!
I meant 10 addition, subtraction, multiplication and division questions on polynomials
Sure, here are ten polynomial arithmetic questions:
1.
Polynomials arithmetic questions
You sail on a HEADING. You TAKE a bearing on another boat or a lighthouse or whatever. ( Not your fault, math text landlubber)
x distance = 150 sin 42 + 250
y distance = 150 cos 42
(not your usual angles because compass angle is clockwise from north,
angle above x axis is really 90 - 42)
total distance magnitude = sqrt (x distance^2 + y distance^2)
Okay, here's how you can use the cosine rule to find the distance between the two points:
Let's call the distance between the two points "d". We can use the cosine rule to find "d" given the length of the two sides and the included angle.
First, we need to find the length of the third side of the triangle that is formed by the two points and the origin. We know that the boat sails 150 km on a bearing of 042 degrees, so we can use trigonometry to find the horizontal and vertical components of this side:
horizontal distance = 150 * sin(42)
vertical distance = 150 * cos(42)
These values are approximately 102.667 km and 109.798 km, respectively.
Next, we know that the boat sails 250 km due east after traveling the initial 150 km. This forms the second side of the triangle, which is a horizontal line. Therefore, the length of the second side is simply 250 km.
Now that we know the lengths of two sides and the included angle, we can use the cosine rule to find "d":
d^2 = (102.667)^2 + (250 + 109.798)^2 - 2 * 102.667 * (250 + 109.798) * cos(90 - 42)
Simplifying this equation, we get:
d^2 = 36800
Taking the square root of both sides, we get:
d = 191.789 km
Therefore, the distance between the two points is approximately 191.789 km.