Answer:
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1 A notebook costs $4.30 plus sales tax. If Lila paid $4.58 for her new notebook, how much was the sales tax rate? A 5.5% B 6.5%
1 answer:
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Answer:
The answer is parabola; (y')² - 8x' = 0 ⇒ answer (b)
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:
* x² - 8y = 0
∵ A = 1 , B = 0 , C =
∴ B² - 4AC = (0)² - 4(1)(0) = 0
∵ B² - 4AC = 0
∴ it will be a parabola.
∵ Ф = 90°
* The point (x , Y) will be (x' , y')
∵ x = x'cosФ - y'sinФ and y = x'sinФ + y'cosФ
∵ cos(90) = 0 and sin(90) = 1
∴ x = -y' and y = x'
* lets substitute x and y in the first equation
∴ (-y')² - 8(x') = 0
∴ (y')² - 8x' = 0
* We notice that the x' took the place of y and y' took the place of x
∴ The parabola rotated around the origin by 90°
∴ The equation of the parabola is (y')² - 8x' = 0
* The answer is parabola, with angle of rotation 90°
* The equation is (y')² - 8x' = 0
* Look to the graph
- The blue is x² - 8y = 0
- The green is (y')² - 8x' = 0
Answer:
Step-by-step explanation:
Use the form a sin ( bx- c) + d to find the variables used to find the amplitude, period, phase shift, and vertical shift.
a = 3
b = 2
c = 0
d = 0
Find the amplitude | a |
Amplitude: 3
Find the period using the formula 2π ÷ IbI
Period: π
Find the phase shift using the formula
Phase Shift: 0
Find the vertical shift : d
Vertical Shift: 0
List the properties of the trigonometric function.
Amplitude: 3
Period: π
Phase Shift: 0 ( 0 to the right)
Vertical Shift: 0
Select a few points to graph.
x f ( x )
0 0
π ÷ 4 3
π ÷ 2 0
3 π ÷ 4 -3
π 0
The Trignometric function can be graphed using the amplitude, period, phase shift, vertical shift, and the points.
Amplitude: 3
Period: π
Phase Shift: 0 ( 0 to the right)
Vertical Shift: 0
x f ( x )
0 0
π ÷ 4 3
π ÷ 2 0
3 π ÷ 4 -3
π 0