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OLga [1]
2 years ago
11

The function f(theta) and g(theta) are sine functions where f(0) = g(0) = 0. The amplitude of f(theta) is twice the amplitude of

g(theta). The period of f(theta) is one-half the period of g(theta). If g(theta) has a period of 2x, and f(pi/4) = 4, write the function rule for g(theta). Explain your reasoning.
Mathematics
1 answer:
lana66690 [7]2 years ago
6 0
Because the values of both functions is 0 at ∅ = 0, both have an equilibrium position of 0.
Next, we can use the given value of f(∅) to find the amplitude:
4 = Asin(π/4)
4 = A(√2 / 2)
A = 8 / √2
We halve this amplitude to find the amplitude of g(∅):
A = 4 / √2
The period is 2π/2 = π

g(∅) = 4sin(∅/2) / √2
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A car was purchased for $25,000. Research shows that the car has an average yearly depreciation rate of 18.5%. Create a function
vitfil [10]

Answer:

V(t) = 25000 * (0.815)^t

The depreciation from year 3 to year 4 was $2503.71

Step-by-step explanation:

We can model V(t) as an exponencial function:

V(t) = Vo * (1+r)^t

Where Vo is the inicial value of the car, r is the depreciation rate and t is the amount of years.

We have that Vo = 25000, r = -18.5% = -0.185, so:

V(t) = 25000 * (1-0.185)^t

V(t) = 25000 * (0.815)^t

In year 3, we have:

V(3) = 25000 * (0.815)^3 = 13533.58

In year 4, we have:

V(4) = 25000 * (0.815)^4 = 11029.87

The depreciation from year 3 to year 4 was:

V(3) - V(4) = 13533.58 - 11029.87 = $2503.71

7 0
2 years ago
The measure of the vertex angle in an isosceles triangle is six less than four time the measure of the base angle. find the meas
blagie [28]
An isosceles triangle is a special type of triangle that has two equal sides. Consequently, the two base angles are also equal. Since the interior angles of a triangle should sum up to 180°, the general equation should be

180° = 2*Base angle + Vertex angle

Let the base angle be x. Thus, the vertex angle is equal to
Vertex angle = 4x - 6
Substituting,
180 = 2x + 4x - 6
x = 31°

Vertex angle = 4(31°) - 6 
Vertex angle = 118°
5 0
2 years ago
Write -2x 2(-5x 2 +4x 3) in standard form.
Anvisha [2.4K]
This in standard form is -28x + 10. 
6 0
2 years ago
A sample statistic , such as x bar, that estimates the value of the corresponding population parameter is known as
Orlov [11]
A sample statistic , such as x bar, that estimates the value of the corresponding population parameter is known as a control chart.
6 0
2 years ago
A landscape supply business charges $35 to deliver mulch. The cost of the mulch is $29.
Scorpion4ik [409]

Answer:

$209

Step-by-step explanation:

we know that

The equation of the line in slope intercept form is equal to

y=mx+b

where

m is the slope

b is the y-coordinate of the y-intercept (initial value)

Let

x ----> the volume of mulch in cubic yards

y ----> the total cost in dollars

we have that

The slope of the linear equation is

m=29\ \frac{\$}{yd^3}

b=\$35 ----> flat fee to deliver mulch

The linear equation is

y=29x+35

For x=6 yd^3

substitute in the equation and solve for y

y=29(6)+35

y=\$209

4 0
2 years ago
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