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2 years ago

Please show work and thank youuu

Mathematics

2 answers:

Papessa [141]2 years ago

8 0

Answer:

x = 8√2

Step-by-step explanation:

As the opposing side of the angle and the hypotenuse are given, take the sine ratio of the angle.

sin 45° = x/16
1/√2 = x/16
x = 16 / √2
x = 16√2 / 2
x = 8√2

Goryan [66]2 years ago

4 0

Answer:

$\sf x=8{\sqrt{2}$

Step-by-step explanation:

Trigonometric ratios

$\sf \sin(\theta)=\dfrac{O}{H}\quad\cos(\theta)=\dfrac{A}{H}\quad\tan(\theta)=\dfrac{O}{A}$

where:

$\theta$ is the angle
O is the side opposite the angle
A is the side adjacent the angle
H is the hypotenuse (the side opposite the right angle)

Therefore, to find x we need to use the sine trig ratio.

Given:

$\theta$ = 45°
O = x
H = 16

Substitute these values into the formula and solve for x:

$\implies \sf \sin(\theta)=\dfrac{O}{H}$

$\implies \sf \sin(45^{\circ})=\dfrac{x}{16}$

$\implies \sf x=16 \sin(45^{\circ})$

$\implies \sf x=16 \cdot \dfrac{\sqrt{2}}{2}$

$\implies \sf x=8{\sqrt{2}$

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(PART-A): s-intercept in this case represents the y-intercept of the graph, whereas the t-intercept in this case represents the x-intercept of the graph.

Always remember that y-intercept represents the value of y where the curve (or line) crosses the y-axis, and x-intercept represents the value of x where the curve (or line) crosses the x-axis.

In the graph attached with the question, at point (0,6) the curve crosses the y-axis. Therefore, the y-intercept (s-intercept) in this case is 6. It means that in year 2000 (t=0), 6 hundred shirts were sold.

However, there is no point on the graph where the curve crosses the x-axis, meaning there is no x-intercept (t-intercept). It means that there is not a single year when the number of shirts sold is 0.

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(PART D): This part is bit tricky. Therefore, read the explanation carefully!

You can see in the graph that number of Shirts sold is in hundreds. It means that 1 unit (of y-axis in a graph) represents 100 shirts. Therefore, as in the question it is mentioned that there are 1000 T-shirts sold, it will become 10 units (since 10*100 = 1000). So, the function g(t) will become the following:

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Why did I add f(t)? Because in the question, the word "and" is underlined. It means that g(t) represents not only 1000 T-shirts (10*100 = 1000) sold at the basketball games each year, but it also has the number of T-shirts sold ONLINE, which is f(t).

Now insert f(t) in (Y) and solve:

$g(t) = f(t) + 10\\g(t) = (1.5)^t + 5+ 10\\g(t) = (1.5)^t + 15$

Hence, g(t) is $(1.5)^t + 15$

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