Which of the following is (are) the solution(s) to 9|x-1| = -45

Use the T-table below to determine 3 solutions to this equation: y = 2x

Jet001 [13]

The table is attached as a figure

The given equation is ⇒⇒⇒⇒ y = 2x
To solve this equation, we need to pick numbers from the table then this number will be substituted into the equation to find y
we need 3 solutions . so, we need to pick 3 numbers of x
From the table, let us choose x = 0
y = 2x
y = 2 * (0)
y = 0

From the table, let choose second value of x such as x = 1
y = 2 * (1)
y = 2

From the table, let choose third value of x such as x = -1
y = 2 * (-1)
y = -2

So, the picked three solutions are
y = 0 at x = 0
y = -2 at x = -1
y = 2 at x = 1

3 0

3 years ago

A boat is pulled into a dock by a rope attached to the bow of the boat and passing through a pulley on the dock that is 1 m high

Agata [3.3K]

Answer:

dy/dt = 1.02 m/s

Step-by-step explanation:

First of all, let the distance of the dock above the bow of the boat be represented by x.

Also, let the distance of the boat from the dock be represented by y.

Let z represent the length of the rope.

Now, we can use pythagoras theorem to find a relationship between x, y and z since they form a right angle triangle where the vertical part is the dock, the base represents the water and the hypotenuse represents the rope.

Thus;

x² + y² = z²

Using implicit differentiation, we have;

2x(dx/dt) + 2y(dy/dt) = 2z(dz/dt)

We are given that the dock is 1 meter above the bow. Thus, x = 1

Also, the height is not changing and so dx/dt = 0

We are told the dock is 5 feet away from the boat. Thus, y = 5

dy/dt is is the speed we are looking for which is the rate at which the boat is approaching the dock.

We are not given the value of z but we can find it by using pythagoras theorem since we know the dock is 1 meter above the bow and the boat is 5 m away.

Thus;

z = √(1² + 5²)

z = √26

We are told the rope is being pulled in at the rate of 1 m/s. Thus; dz/dt = 1

Plugging all relevant values into the differentiation equation above gives;

2(1)(0) + 2(5)(dy/dt) = 2(√26)(1)

10(dy/dt) = 2√26

Divide both sides by 10 to get:

dy/dt = (√26)/5

dy/dt = 1.02 m/s

5 0

3 years ago

Between x = 2 and x = 3, which function has a greater average rate of change than y = 13 -x ?

Marrrta [24]

For this case what you should know is that the slope of the line can be calculated as:
Tan x = sin x / cos x
The lines x = 2 and x = 3 have an angle of 90 degrees with respect to the x axis:
Tan 90 = sin 90 / cos 90 = 1/0 = inf
Therefore, both lines have a rate of change that tends to infinity.
answer
Both lines have the same slope (infinity) Both are greater than m = -1

3 0

3 years ago

If two dice are rolled, find the probability of rolling two 6's.

djyliett [7]

Total no. of outcomes when two dice are rolled = 36

No. of outcome when 6 will be on both dice = 1

Probability of rolling two 6's = 1/36

Hope this helps!

8 0

3 years ago

Pls, Help !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

professor190 [17]

I can help you if you still!!!

4 0

2 years ago