Pic below help ASAP (not exam)

What are the coordinates of the hole in the graph of the function f(x) ?

Vinvika [58]

ANSWER

$(3, \infty )$

EXPLANATION

The given function is

$f(x) = \frac{ {x}^{2} - 9}{x - 3}$

When we plug in x=3 into this function, we obtain,

$f(3) = \frac{0}{0}$

This means that the function is discontinuous at x=3.

We need to simplify the function to obtain,

$f(x) = \frac{(x - 3)(x + 3)}{(x - 3)}$

This implies that,

$f(x) = x + 3$

The graph this function is a straight line that is continuous everywhere.

To graph

$f(x) = \frac{ {x}^{2} - 9}{x - 3}$
we draw the graph of

$f(x) = x + 3$
and leave a hole at x=3.

See diagram in attachment.

Hence the coordinates of hole is

$(3, \infty )$

6 0

3 years ago

A ship leaves port at 10 miles per hour, with a heading of N 35° W. There is a warning buoy located 5 miles directly north of th

Leno4ka [110]

The value of the angle subtended by the distance of the buoy from the

port is given by sine and cosine rule.

The bearing of the buoy from the is approximately 307.35°

Reasons:

Location from which the ship sails = Port

The speed of the ship = 10 mph

Direction of the ship = N35°W

Location of the warning buoy = 5 miles north of the port

Required: The bearing of the warning buoy from the ship after 7.5 hours.

Solution:

The distance travelled by the ship = 7.5 hours × 10 mph = 75 miles

By cosine rule, we have;

a² = b² + c² - 2·b·c·cos(A)

Where;

a = The distance between the ship and the buoy

b = The distance between the ship and the port = 75 miles

c = The distance between the buoy and the port = 5 miles

Angle ∠A = The angle between the ship and the buoy = The bearing of the ship = 35°

Which gives;

a = √(75² + 5² - 2 × 75 × 5 × cos(35°))

By sine rule, we have;

$\displaystyle \frac{a}{sin(A)} = \mathbf{ \frac{b}{sin(B)}}$

Therefore;

$\displaystyle sin(B)= \frac{b \cdot sin(A)}{a}$

Which gives;

$\displaystyle sin(B) = \mathbf{\frac{75 \cdot sin(35^{\circ})}{\sqrt{75^2 + 5^2 - 2 \times 75\times5\times cos(35^{\circ}) } }}$

$\displaystyle B = arcsin\left( \frac{75 \cdot sin(35^{\circ})}{\sqrt{75^2 + 5^2 - 2 \times 75\times5\times cos(35^{\circ}) } }\right) \approx 37.32^{\circ}$

Similarly, we can get;

$\displaystyle B = arcsin\left( \frac{75 \cdot sin(35^{\circ})}{\sqrt{75^2 + 5^2 - 2 \times 75\times5\times cos(35^{\circ}) } }\right) \approx \mathbf{ 142.68^{\circ}}$

The angle subtended by the distance of the buoy from the port, C is therefore;

C ≈ 180° - 142.68° - 35° ≈ 2.32°

By alternate interior angles, we have;

The bearing of the warning buoy as seen from the ship is therefore;

Bearing of buoy ≈ 270° + 35° + 2.32° ≈ 307.35°

Learn more about bearing in mathematics here:

brainly.com/question/23427938

5 0

2 years ago

Which numbers belongs in the box?

EleoNora [17]

Answer:

C

Step-by-step explanation:

$42 + 120 = 2 + 160$

3 0

3 years ago

Read 2 more answers

What's the value of x?

8090 [49]

I got 110 but it might be wrong let me check.

5 0

3 years ago

Match the following with their formula.

neonofarm [45]

For simplicity, I’m marking the six different terms on the main part of the image as 1-6 and the six equations/points on the bottom of the image as A-F.

First, we can look at the bottom and see that there are four equations, but A and F are both points. Looking at the terms above, the only ones that are points are 1 and 6. Since the y-intercept is when a function passes through the y-axis, that means that the x value of the point must be 0. Therefore, A matches with 6.

That leaves F to match with 1. The equation (-b/2a) is what is used in a quadratic equation to locate the vertex, so it makes sense that the vertex would be when you put that number into the equation.

Now on to the four different equations. One of the equations, C, is calculating an x value. This means that it has to match with 2 because it’s drawing a line vertically through the point we already determined to be the vertex of a parabola in the above paragraph.

For the three functions that remain, B has no numbers in it, only the standard letters as placeholders for various numbers you would put into a quadratic function. Therefore, it has to match with 3 since it’s just the standard equation.

That leaves us with D and E to match with 4 and 5, meaning that one of them has to be a negative equation and the other has to be a positive equation. This is where you look at the a value in the function. If the a value is positive, then the quadratic opens up (with the tip pointed down) while if the a value is negative, then the quadratic opens down (with the tip pointed up). This means that D matches with 4 and E matches with 5.

In conclusion,
1 = F
2 = C
3 = B
4 = D
5 = E
6 = A

Hope that helped!

3 0

3 years ago