Can someone Graph y = x + 4

For f (x) = 3x +1 and g(x) = x^2-6, find (g/f)(x)

sp2606 [1]

Answer:

$(g/f) (x) =\frac{x^2-6}{3x+1}$

Step-by-step explanation:

We have the following functions

$f (x) = 3x+1$

$g (x) = x^2-6$

To find $(g/f)(x)$ we must divide the function g(x) with the function f(x)

Then we perform the following operation

$(g/f) (x) =\frac{x^2-6}{3x+1}$

Finally we have that:

$(g/f) (x) =\frac{x^2-6}{3x+1}$

For $x \neq -\frac{1}{3}$

3 0

3 years ago

The curves r1(t) = 4t, t2, t3 and r2(t) = sin(t), sin(5t), 2t intersect at the origin. find their angle of intersection, θ, corr

san4es73 [151]

First get the tangent vectors by differentiating r1 and r2
$r_1 '(t) = (4,2t,3t^2) \\ \\ r_2'(t) = (cos (t), 5 cos(5t), 2)$
Evaluate at t=0
$r_1' = (4,0,0) \\ \\ r_2' = (1,5,2)$

Use identity for angle between 2 vectors:
$u*v = |u| |v| cos \theta$

Evaluate dot product and unit vectors:
$u*v = (4,0,0)*(1,5,2) = 4 \\ \\ |u| = \sqrt{4^2 +0^2+0^2} = 4 \\ \\ |v| = \sqrt{1^2 + 5^2+2^2} = \sqrt{30}$

Sub into identity and solve for theta:
$4 = 4 \sqrt{30} cos \theta \\ \\ cos\theta = \frac{1}{\sqrt{30}} \\ \\ \theta = 79.48$

Answer:
Angle of intersection is about 79 degrees.

5 0

3 years ago

Harris Teeter is selling gala apples for 0.98 per pound Adam purchase 3.5 pounds of the apples how much did she pay for her purc

Schach [20]

Total purchase = (unit cost)(# of pounds purchased)

Here, that total is ($0.98/lb)(3.5 lb) = $3.43 (answer)

8 0

2 years ago

Triangle A B C is shown. Angle A C B is a right angle. The length of the hypotenuse is 20.

kherson [118]

Answer:

The length of BC is needed because it is the side opposite ∠A.

Step-by-step explanation:

Given the right angles triangle as shown in the attachment, we can get sin(A) without using Pythagoras theorem. Instead we will use SOH CAH TOA trigonometry identity.

According to SOH:

Sin(A) = Opposite/Hypotenuse

Sin(A) = |BC|/|AB|

Opposite side of the triangle is the side facing ∠A.

Based on the formula, we will need to get the opposite side of the triangle which is length BC for us to be able to determine sinA since the hypotenuse is given.