What is the cosine ratio for angle F?

Answer:

Step-by-step explanation:

We will utilize the exponential decay formula described as

A = P(1 - r/n)^(nt)

Where

A symbolizes the value after a time period t.

n refers to the timeframe for value loss calculation

t indicates the number of years.

P stands for the population value.

r indicates the rate of decrease.

Based on the provided data,

P = 23000

r = 8% = 8/100 = 0.08

n = 1

Thus, the exponential decay function fitting this situation is

A = 23000(1 - 0.08/n)^1)^ t

A = 23000(0.92)^t

If A = 15000, it follows that

15000 = 23000(0.92)^t

0.92^t = 15000/23000 = 0.6522

Taking logarithm of both sides to base 10

Log(0.92^t) = log(0.6522)

t log(0.92) = log(0.6522)

- 0.036t = - 0.1856

t = - 0.1856/- 0.036

We find t = 5 years rounded to the nearest year

Starting with the equation Y - 4x = 7, we can express y as y = 4x + 7. Now, substitute this expression into the second equation 2y + 4x = 2: 2(4x + 7) + 4x = 2, which simplifies to 8x + 14 + 4x = 2. After that, we gather like terms: 12x = 2 - 14, yielding 12x = -12, hence x = -1. Plugging x into the equation y - 4(-1) = 7 also reveals: y + 4 = 7, which gives y = 3. Thus, the solution arrives at (-1, 3).

Since the ball achieves a peak height of 18 meters at 1 second, it will begin descending thereafter. Therefore, we anticipate that the height will drop below 18 m after 1.5 sec.

f(x) = –10x2 + 20x + 8
f(x) = –10(1.5^2) + 20(1.5) + 8
f(x) = 15.5 m

<span> </span>

The question clearly seeks the highest values from both functions, meaning the vertices of each.

<span>The graph depicting the path of Ed’s football indicates the vertex's coordinates (the peak of the graph).
</span>
Specifically,

(h,k) = (1.5, 7.5)

Where (h,k) represents the vertex's location.

Conversely,<span>the trajectory of Steve's football is defined by the equation:
y = - 2x
²</span> + 5x + 4<span>To find the axis of symmetry, we use the formula:x = - b
÷ 2a
Where:

a = -2</span>
b = 5

Consequently,

x = - 5 ÷ - 4

x = 5 / 4




x = 1.25
Now substituting this x-value back into the main equation to determine y.
y = - 2x² + 5x + 4
y = - 2(1.25)² + 5(1.25) + 4

y = - 3.125 + 6.25 + 4


y = 7.125


Thus, the vertex (h,k) = (1.25, 7.125)
As observed from the calculations
Ed’s

<span>football attains a higher height.</span>