In analytical geometry, there are already derived equations to find the distance of lines and points as well as the angle made between two lines. As special case is when the other line is one of the coordinate axis. Then, the formula can be simplified to

tan θ =m, where m is the slope of the equation

In the next step, we also incorporate operations of calculus. Since the slope is equal to Δy/Δx, this is equivalent to dy/dx in calculus. Therefore, you can find the slope by differentiating the equation in terms of x.

<span>y-2x=7
y = 2x+7
dy/dx = 2 =m

So,

tan </span>θ = 2
θ = tan⁻¹(2)
θ = 63.43°

5 0

3 years ago

Help with this pleaseeee

ELEN [110]

Answer:

(- 3, 37) and (- $\frac{5}{2}$ , $\frac{63}{2}$ )

Step-by-step explanation:

Given the 2 equations

2x² - y + 19 = 0 → (1)

y + 11x = 4 → (2) ← subtract 11x from both sides

y = 4 - 11x → (3)

Substitute y = 4 - 11x into (1)

2x² - (4 - 11x) + 19 = 0

2x² - 4 + 11x + 19 = 0

2x² + 11x + 15 = 0 ← in standard form

(2x + 5)(x + 3) = 0 ← in factored form

Equate each factor to zero and solve for x

2x + 5 = 0 ⇒ 2x = - 5 ⇒ x = - $\frac{5}{2}$

x + 3 = 0 ⇒ x = - 3

Substitute these values into (3) for corresponding values of y

x = - $\frac{5}{2}$ : y = 4 + $\frac{55}{2}$ = $\frac{63}{2}$ ⇒ (- $\frac{5}{2}$ , $\frac{63}{2}$ )

x = - 3 : y = 4 + 33 = 37 ⇒ (- 3, 37 )

4 0

3 years ago

Which type of triangle has special proportions

MrRissso [65]

Answer: right triangle

Step-by-step explanation:

5 0

3 years ago