A ball, thrown vertically upwards, from the ground, has its height h (in meters) expressed as a function of time t (in seconds), elapsed after the launch, by the law h(t) = 20t - 5t2. According to this information, determine the height at which the ball is 3 seconds after the throw and the maximum height reached by the ball.

Answers

Answer 1

Answer: Height at 3 sec: 15 meters

Max height: 20 meters

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2| x - 3 | > 8, 2| x - 3 | < -8 Sovle the inequality involving absolute value? I don't understand how to get the right answer

Answers

divide both sides by 2

|x-3|>4 and |x-3|<-4
ok so |x-3|<-4 is false, since |x|≥0 always

so we have
|x-3|>4
now assume
x-3>4 and
x-3<-4

x-3>
add 3
x>7

x-3<-4
add 3
x<-1

so
-1>x and x>7

so basically it is all numbers from -∞ to +∞ except from -1 to 7
in interval notaion
(-∞,-1)U(7,∞)

S={x|x<-1 or x>7}

X >7 and X > -1 that would be the answer

The Smith'd CD’s sell for $10 and Arctic Monkeys CD’s sell for $15. If a music store sold 18 CD’s and worth $240, how many of each CD did they sell?

Answers

Answer:

6 Smith'd CDs

12 Arctic Monkeys CDs

Step-by-step explanation:

To solve this problem, we can use a system of equations. Let x be the number of Smith'd CDs sold and y be the number of Arctic Monkeys CDs sold. We know that the total number of CDs sold is 18 and the total sales is $240. We can represent this information in the following system of equations:

x + y = 18

10x + 15y = 240

We can solve this system of equations using elimination. Multiplying the top equation by -10, we get:

-10x - 10y = -180

10x + 15y = 240

Adding the top and bottom equations, we get:

5y = 60

Dividing both sides by 5, we get:

y = 12

Now that we know the value of y, we can substitute it into the top equation to find the value of x:

x + 12 = 18

x = 18 - 12

x = 6

Therefore, the music store sold 6 Smith'd CDs and 12 Arctic Monkeys CDs.

A regular octagon STUVWXYZ is rotated 135 degrees clockwise around its center. Vertex X is carried onto which vertex After the rotation?

Answers

it will be carried onto S

good luck

Final answer:

When a regular octagon is rotated 135 degrees clockwise, vertex X will be carried to the position of vertex S.

Explanation:

When a regular octagon is rotated 135 degrees clockwise around its center, each vertex is carried onto the vertex that is three vertices away in a clockwise direction. The question is asking which vertex the point X will be rotated to after a 135-degree clockwise rotation. Since the octagon is regular, it has 8 equal sections of 45-degrees each. When rotating 135-degrees, we rotate 3 of these 45-degree sections. Therefore, moving clockwise from vertex X, the vertex that will take the position of X after the rotation will be UVWXYZ, i.e., vertex S.