Dr. Shah visits patients at their homes. The equation y = 150x + 50 represents the amount

Triangle XYZ is an equilateral triangle, meaning the sector's central angle measures 120 degrees, which is equivalent to 2π/3 radians. To find the area of a sector corresponding to a central angle β, we use the formula A = (1/2)r²*β, where β is expressed in radians. For this sector, the area calculation is A = (1/2)*2²*(2π/3) = 4π/3 square units.

d(-3 + x) = kx + 9

• Distribute d within the parentheses:

-3d + dx = kx + 9

• Subtract kx from both sides:

-3d + dx - kx = 9

• Add 3d to both sides:

dx - kx = 9 + 3d

• Factor x from dx - kx:

x(d - k) = 9 + 3d

• Divide both sides by (d - k):

x =

• To further simplify, factor 3 out of the numerator.

x =

Answer:

Step-by-step explanation:

Right Triangles

In a right triangle, one angle measures 90°. This forms a hypotenuse, which is the longest side, alongside two short sides known as legs. These elements are connected to Pythagoras's theorem, and the fundamental trigonometric relationships also apply, including

where a represents the leg opposite and c denotes the adjacent leg.

In this scenario, a statue is observed by a person positioned 50 ft away. The observer looks upwards at an elevation angle of 8° towards the statue's top and then downwards at a 14° angle toward the statue's base. The illustration below depicts the situation.

The statue's height is expressed as h=a+b, where

Therefore,

Step-by-step explanation:

Begin with expressing 492,623 in standard form.

4 hundred thousands + 9 ten thousands + 2 thousands + 6 hundreds + 2 tens + 3 ones.

We can rephrase this in varied forms by shifting a digit to the next lower place value. For instance, shifting the 4 one place right results in 49 ten thousands:

49 ten thousands + 2 thousands + 6 hundreds + 2 tens + 3 ones.

Next, we can move 49 ten thousands one place right to express it as 492 thousands, and shift 6 hundreds right to yield 62 tens.

492 thousands + 62 tens + 3 ones.

Alternatively, we can phrase it as:

4926 hundreds + 23 ones.

Answer: 6.2 m/s

Explanation:

1) This situation involves projectile motion, which follows a parabolic path.

2) Velocity components:

i) Initial velocity is denoted as V₀.

ii) Horizontal velocity component:

V₀x = V₀ cos α

Since horizontal velocity remains constant, Vx equals V₀x.

iii) Vertical velocity component:

V₀y = V₀ sin α

Its change over time is affected by acceleration due to gravity, g ≈ 9.8 m/s².

Vy = V₀y - gt = V₀ sin α - gt

3) Formulas for displacement:

i) Horizontal displacement:

x = V₀ cosα × t

ii) Vertical displacement:

y = V₀ sin α × t - (1/2) g t²

or y ≈ V₀ sin α × t - 4.9 t²

4) Working out the solution:

i) We know x = V₀ cos(32°) t = 2.00 m, because the salmon begins 2.00 m away from the waterfall.

Thus, V₀ = 2 / [cos(32°) × t]

ii) For vertical displacement: y = V₀ sin(32°) t - 4.9 t²

iii) Substituting V₀, y = sin(32°) × 2 / [cos(32°) × t] × t - 4.9 t² = 2 tan(32°) - 4.9 t²

iv) Setting y = 0.55 m (the height of the waterfall) to solve for t:

0.55 = 2 tan(32°) - 4.9 t²

t² = [2 tan(32°) - 0.55] / 4.9 = 0.143 s²

t = √0.143 ≈ 0.38 s

v) Finally, compute V₀:

V₀ = 2 / [cos(32°) × 0.38] = 6.2 m/s