Can the product of 2 irrational numbers be rational?

If the image of point J under a 180° rotation about the origin is (-8, 4), what are the coordinates of point J' ?

lesantik [10]

(-4,3) is the correct answer

6 0

3 years ago

Freddie is at chess practice waiting on his opponent's next move. He notices that the 4-inch-long minute hand is rotating around

ale4655 [162]

Answer:

Part 1: $\frac{2\pi}{3}$ radians

Part 2: The minute hand travels $\frac{8\pi}{3}$ inches.

Part 3: The minute hand travels $\frac{3\pi}{4}$ radians.

Part 4: The coordinate point is $(-\frac{\sqrt{2}}{2},\frac{\sqrt{2}}{2})$

Step-by-step explanation:

Part 1:

There are 60 minutes in an hour. 1 hour is 1 revolution (1 circle), which is 360°.

So each minute represents $\frac{360}{60}=6$ degrees

From 3:35 to 3:55 is 20 minutes. Hence, 20 minutes is $6*20=120$ degrees.

To convert from degrees to radians, we multiply the degrees by $\frac{\pi}{180}$

120° is equal to $120*\frac{\pi}{180}=\frac{2\pi}{3}$ radians

Part 2:

We want to find the "arc length" of this.

Formula for arc length is $s=r\theta$

Where,

s is the arc length
r is the radius (here the minute hand was given as 4 inches)
$\theta$ is the angle in radians (we found it to be $\frac{2\pi}{3}$ )

So, $s=r\theta\\s=(4)(\frac{2\pi }{3})=\frac{8\pi}{3}$

The minute hand travels $\frac{8\pi}{3}$ inches.

Part 3:

Here we use the arc length formula where we want to find $\theta$ given that $s=3\pi$ and radius is 4 inches. So we have:

$s=r\theta\\3\pi=(4)(\theta)\\\theta=\frac{3\pi}{4}$

The minute hand travels $\frac{3\pi}{4}$ radians.

Part 4:

The coordinate point associated with a specif radian is given by the formula:

$(x,y)=(cos(\theta)sin(\theta))\\(x,y)=(cos(\frac{3\pi}{4})sin(\frac{3\pi}{4}))\\(x,y)=(-\frac{\sqrt{2}}{2},\frac{\sqrt{2}}{2})$

Thus the coordinate point is $(-\frac{\sqrt{2}}{2},\frac{\sqrt{2}}{2})$

3 0

4 years ago

Read 2 more answers

Choose the correct answers for (a) the total installment price, (b) the carrying charges, and (c) the number of months needed to

Brrunno [24]

Part A:

Given that a dinette table with a cash price of $200 is purchased at $8.50 down and $11.00 per month for 24 months

The total installment price is given by

$P=\$8.50+\$11(24) \\ \\ =\$8.50+\$264=\$272.50$

Part B:

The carrying charges is given by the total installation price minus the cash price.

From part a, we obtained that the total installation price is $272.50 and given that the cash price is $200.

Therefore, the carrying charges is given by

$272.50 - $200.00 = $72.00

Part C:

If the money is to be saved at $11 per month to be able to purchase the table at the cash price, the number of months it will take to be able to save $200 at $11 per month is given by

$\frac{\$200}{\$11} =18.18\, months$

Therefore, it will take 19 months to save the money at the monthly rate needed to buy the item for its cash price.

3 0

3 years ago

Read 2 more answers

A town has a population of 1600 people at time ????=0. In each of the following cases, write a formula for the population P, of

victus00 [196]

Answer:

a) $P(t) =1600 +50t$

b) $P(t) = 1600 (1.05)^t$

Step-by-step explanation:

Assuming the complete question : "A town has a population of 1000 people at time t = 0. In each of the following cases, write a formula for the population, P, of the town as a function of year t. (a) The population increases by 50 people a year. (b) The population increases by 5% a year."

Part a

For this case we can use a linear model in order to estimate the population size since we have a fixed increase each year. So our model would be given by:

$P(t) = P_o + b t$

Where $b =50$ on this case since represent the increase per year of the slope for the linear model. And the initial amount is $P_o = 1600$ , so then the model is:

$P(t) =1600 +50t$

Part b

For this case we have a rate of increase and when we have this the lineal model is not the most appropiate. So then we can use an exponential model given by:

$P(t) =P_o b^{t}$

Where $P_o = 1600$ represent the initial population and for this case b is the rate of increase $b = 1+0.05 = 1.05$ since each year we have an increase of 5% and t is the time. So then the model is given by:

$P(t) = 1600 (1.05)^t$

3 0

3 years ago

How do i solve this: -2x>12 or -2(x+1)< -10. This is a inequality problem

sp2606 [1]

-2x > 12 OR -2(x + 1) < -10
Each inequality is solved separately.
The first one, divide both sides by -2, when you divide by a negative, you change the inequality sign.
So x < 6
For the second inequality, distribute the -2, this gives us -2X -2< -10.
Add 2 to both sides.
-2x < -8
Divide both sides by -2.
When dividing by a negative you change the inequality sign
So x > 4
The answer is:
x < 6 OR x > 4

6 0

4 years ago