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vlabodo [156]
1 year ago
11

Two water balloons were launched into the air at different moments and collided. the water balloons were modeled by the quadrati

c functions: y = −7x2 26x 3 and y = −6x2 23x 5, where y represents the height in meters and x represents the time in seconds after the launch. what is the time, in seconds, that the balloons collided at the highest point?
Mathematics
1 answer:
DerKrebs [107]1 year ago
5 0

Two water balloons were launched into the air at different moments and collided. the water balloons were modeled by the quadratic functions: y = −7x2 26x 3 and y = −6x2 23x 5, where y represents the height in meters and x represents the time in seconds after the launch. 2.0 seconds is the time, in seconds, that the balloons collided at the highest point

The time in seconds that the balloons collided at the highest point is; B: 2.0 seconds

We are told that the water balloons were modeled by the quadratic functions:

y = -7x² + 26x + 6 and y = -6x² + 25x + 4

where;

y = the height in meters

x = the time in seconds after the launch

The time at which they will collide has to be at the same height.

Thus;

-7x² + 26x + 6 = -6x² + 25x + 4

Rearranging this gives;

x² - x - 2 = 0.

Using an online quadratic equation solver gives us x = 2 or -1. We will take the positive one as x = 2.0 seconds

Learn more about quadratic equations at

brainly.com/question/1214333

#SPJ4

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Consider the points A(5, 3t+2, 2), B(1, 3t, 2), and C(1, 4t, 3). Find the angle ∠ABC given that the dot product of the vectors B
Vilka [71]

Answer:

66.42°

Step-by-step explanation:

<u>Given:</u>

A(5, 3t+2, 2)

B(1, 3t, 2)

C(1, 4t, 3)

BA • BC = 4

Step 1: Find t.

First we have to find vectors BA and BC. We do that by subtracting the coordinates of the initial point from the coordinates of the terminal point.

In vector BA B is the initial point and A is the terminal point.

BA = OA - OB = (5-1, 3t+2-3t, 2-2) = (4, 2, 0)

BC = OC - OB = (1-1, 4t-3t, 3-2) = (0, t, 1)

Now we can find t because we know that BA • BC = 4

BA • BC = 4

To find dot product we calculate the sum of the produts of the corresponding components.

BA • BC = (4)(0) + (2)(t) + (0)(1)

4 = (4)(0) + (2)(t) + (0)(1)

4 = 0 + 2t + 0

4 = 2t

2 = t

t = 2

Now we know that:

BA = (4, 2, 0)

BC = (0, 2, 1)

Step 2: Find the angle ∠ABC.

Dot product: a • b = |a| |b| cos(angle)

BA • BC = 4

|BA| |BC| cos(angle) = 4

To get magnitudes we square each compoment of the vector and sum them together. Then square root.

|BA| = \sqrt{4^2 + 2^2 + 0^2} = \sqrt{20} = 2\sqrt{5}

|BC| = \sqrt{0^2 + 2^2 + 1^2} = \sqrt{5}

2\sqrt{5}\sqrt{5}\cos{(m\angle{ABC})} = 4

10\cos{(m\angle{ABC})} = 4

\cos(m\angle{ABC}) = \frac{4}{10}=\frac{2}{5}

m\angle{ABC} = cos^{-1}{(\frac{2}{5})}

m\angle{ABC} = 66.4218^{\circ}

Rounded to two decimal places:

m\angle{ABC} = 66.42^\circ

3 0
2 years ago
What is the solution to this system of equations?
Ede4ka [16]

Answer:

First choice.

Step-by-step explanation:

You could plug in the choices to see which would make all the 3 equations true.

Let's start with (x=2,y=-6,z=1):

2x+y-z=-3

2(2)+-6-1=-3

4-6-1=-3

-2-1=-3

-3=-3 is true so the first choice satisfies the first equation.

5x-2y+2z=24

5(2)-2(-6)+2(1)=24

10+12+2=24

24=24 is true so the first choice satisfies the second equation.

3x-z=5

3(2)-1=5

6-1=5

5=5 is true so the first choice satisfies the third equation.

We don't have to go any further since we found the solution.

---------Another way.

Multiply the first equation by 2 and add equation 1 and equation 2  together.

2(2x+y-z=-3)

4x+2y-2z=-6 is the first equation multiplied by 2.

5x-2y+2z=24

----------------------Add the equations together:

9x+0+0=18

9x=18

Divide both sides by 9:

x=18/9

x=2

Using the third equation along with x=2 we can find z.

3x-z=5 with x=2:

3(2)-z=5

6-z=5

Add z on both sides:

6=5+z

Subtract 5 on both sides:

1=z

Now using the first equation along with 2x+y-z=-3 with x=2 and z=1:

2(2)+y-1=-3

4+y-1=-3

3+y=-3

Subtract 3 on both sides:

y=-6

So the solution is (x=2,y=-6,z=1).

8 0
3 years ago
What number is 35 percent of 120
KIM [24]
What you would do is multiply for this problem.
you turn 35% into a decimal so the problem would look like 
0.35 x 120 that should equal 42
hope that helps
5 0
3 years ago
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Kenji's town voted on a new speed limit. Of the votes received, 39 were in favor of the new speed limit and 13 were opposed. Wha
Nata [24]

Answer:

75%

Step-by-step explanation:

You need to find the total number of votes first. Just add 13 and 39 which would equal 52.

Then divide the number of people in favour by the total number of voters and multiply by a 100 to find the percentage.

39 + 13 = 52

39/52 = 0.75

0.75 x 100 = 75.0

75%

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3 years ago
michael has 40 coins worth 8.20. consisting of 10 cents and 25 cents . how many of each coins does he have ?
devlian [24]

Answer:

2 dollars I guess l d k

Step-by-step explanation:

pay subcription to get good answer k :)

5 0
3 years ago
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