Can someone solve with working/solution these 3 questions Plzzz
1 answer:
Answer:
(c) °
(d) °
(e) °
° and
°
°
Step-by-step explanation:
The triangle is an isosceles triangle with the base angles which are identical. The double stroke on the sides of the triangle indicates which angles are the base angle. The angle corresponding to the side of the triangle with no double stroke is known as the vertex angle.
(c) The given angle is the vertex angle in this question and it is 70°
Since, ° is one of the base angle, then the other angle which is not drawn is identical to
° .
Total angle of a triangle is 180°.
°
°
°
°
°
Divide by 2 on both sides to get °
°
°
(d)
The given angle is a base angle in this question and it is 63°.
Since base angles are identical, then
°
°
Divide by 3 on both sides to get °
°
°
(e)
The given angle 48° is a base angle.
Since base angles are identical, then
°
°
Divide by 3 on both sides to get °
°
°
Total angle of a triangle is 180°.
So, °
°
°
°
°
°
Divide by 2 on both sides to get °
°
°
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Answer:
The answer is hyperbola; (x')² - (y')² - 16 = 0 ⇒ answer (a)
Step-by-step explanation:
* At first lets talk about the general form of the conic equation
- Ax² + Bxy + Cy² + Dx + Ey + F = 0
∵ B² - 4AC < 0 , if a conic exists, it will be either a circle or an ellipse.
∵ B² - 4AC = 0 , if a conic exists, it will be a parabola.
∵ B² - 4AC > 0 , if a conic exists, it will be a hyperbola.
* Now we will study our equation:
xy = -8
∵ A = 0 , B = 1 , C = 0
∴ B² - 4 AC = (1)² - 4(0)(0) = 1 > 0
∴ B² - 4AC > 0
∴ The graph is hyperbola
* The equation xy = -8
∵ We have term xy that means we rotated the graph about
the origin by angle Ф
∵ Ф = π/4
∴ We rotated the x-axis and the y-axis by angle π/4
* That means the point (x' , y') it was point (x , y)
- Where x' = xcosФ - ysinФ and y' = xsinФ + ycosФ
∴ x' = xcos(π/4) - ysin(π/4) , y' = xsin(π/4) + ycos(π/4)
∴ x' = x/√2 - y/√2 = (x - y)/√2
∴ y' = x/√2 + y/√2 = (x + y)/√2
* Lets substitute x' and y' in the 1st answer
∵ (x')² - (y')² - 16 = 0
∴
(
* Lets open the bracket
∴
* Lets add the like terms
∴
* Simplify the fraction
∴ -2xy - 16 = 0
* Divide the equation by -2
∴ xy + 8 = 0
∴ xy = -8 ⇒ our equation
∴ Answer (a) is our answer
∴ The answer is hyperbola; (x')² - (y')² - 16 = 0
* Look at the graph:
- The black is the equation (x')² - (y')² - 16 = 0
- The purple is the equation xy = -8
- The red line is x'
- The blue line is y'
