Mrs.Roberts charges 25 for a basic cake that serves 12 people. If you want a large cake, it costs an additional $1.25 per servin
1 answer:
The total cost of a cake that serves 20 people is $35.
<u>Step-by-step explanation</u>:
- Total cost = y
- Number of additional servings = x
- The number of additional servings = 20 - 12 = 8. (x=8)
<u>The equation can be formed as</u>:
- Total cost = basic cost + (No. of additional serving
cost per additional serving)
- y = 25 + x1.25
- Substitute x=8 in the above equation
- y = 25 + 8(1.25)
- y =25+10
- y = 35
Therefore, the total cost of a cake that serves 20 people is $35.
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<h3>Answer:</h3>
Equation of the ellipse = 3x² + 5y² = 32
<h3>Step-by-step explanation:</h3><h2>Given:</h2>- The centre of the ellipse is at the origin and the X axis is the major axis
- It passes through the points (-3, 1) and (2, -2)
- The equation of the ellipse
The equation of an ellipse is given by,
Given that the ellipse passes through the point (-3, 1)
Hence,
Cross multiplying we get,
- 9b² + a² = 1 ²× a²b²
- a²b² = 9b² + a²
Multiply by 4 on both sides,
- 4a²b² = 36b² + 4a²------(1)
Also by given the ellipse passes through the point (2, -2)
Substituting this,
Cross multiply,
- 4b² + 4a² = 1 × a²b²
- a²b² = 4b² + 4a²-------(2)
Subtracting equations 2 and 1,
- 3a²b² = 32b²
- 3a² = 32
- a² = 32/3----(3)
Substituting in 2,
- 32/3 × b² = 4b² + 4 × 32/3
- 32/3 b² = 4b² + 128/3
- 32/3 b² = (12b² + 128)/3
- 32b² = 12b² + 128
- 20b² = 128
- b² = 128/20 = 32/5
Substituting the values in the equation for ellipse,
Multiplying whole equation by 32 we get,
3x² + 5y² = 32
<h3>Hence equation of the ellipse is 3x² + 5y² = 32</h3>Answer:
y = 0
Step-by-step explanation:
The given sinusoidal equation is
The general form of the sin function is presented as follows;
y = A·sin(B·(x - C)) + D
Where;
A = The amplitude
The period, T = 2·π/B
The frequency, f = B/2·π
C = The horizontal shift
D = The vertical shift
By comparison with the given sine function, we have;
The amplitude, A = 2
The frequency, f = B/2·π = π/2/(2·π) = 1/4
The frequency, f = 1/4 Hz
C = The horizontal shift = 3/(π/2) = 6/π
The vertical shift, D = 0
Given that the mid line of the parent function, sin(x), is the line y = 0, and that the vertical shift is 0, the midline of the function, , is therefore, the line;
y = 0.