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Umnica [9.8K]
3 years ago
5

How much times does it take for the first black/clear part to fall through the photo gate timer, starting from the rest? Plastic

strip has 8 black stripes and 8 clear stripes the width of the black/clear pair is 5 cm.
Mathematics
1 answer:
Alik [6]3 years ago
5 0
I can figure out this is a frefall motion.

Starting from rest => Vo = 0

Then, use the equation: d = [1/2]gt^2 => t = √(2d/g)

d = width of a black/clear stripe pair = 5cm = 0.05m

g ≈ 10 m/s^2 (the real value is about 9.81 m/s^2)

t =√(2*0.05m/10m/s^2) =  0.1 s

Answer: approximately 0.1 s
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Solve the rational equation:. x+3/3x-2 minus x-3/3x+2=44/9x^2-4
NISA [10]
\frac{x+3}{3x-2} - \frac{x-3}{3x+2} = \frac{44}{9x^2-4}
\frac{(x+3)(3x+2) - (x-3)(3x-2)}{(3x-2)(3x+2)} = \frac{44}{(3x+2)(3x-2)}

(x+3)(3x+2) - (x-3)(3x-2) = 44
(3x^2 + 11x + 6) - (3x^2 - 11x + 6) = 44
22x = 44
x = 2Substituting x = 2 into the original does not give any extraneous solutions, so this is the answer.
4 0
3 years ago
I have the equations 8x + 3y = 20.50 and 4x + 5y = 22.50<br> How do I solve for x and y?
snow_tiger [21]
8x + 3y = 20.50
-
4x+5y=22.50
=
4x-2y=-2, so you have to divide each number by 2, then
2x-y=-1, so

-y=-1-2x /-1, y=1+2x, then replace it with one original equation like the first one for instance:
8x+3(1+2x)=20.50, then
8x+3+6x=20.50, then
14x=20.50-3
14x=17.5
x=1.25, then solve y:\
y=1+2*(1.25)
y=1+2.5
y=3.5,
So answer is x=1.25, and y=3.5

6 0
4 years ago
Find the equation of the line which passes through (−2, 3) and the point of intersection of the lines x + 2y=0 and 2x − y − 12=0
mote1985 [20]

Answer:

First, let's find where the lines:

x + 2y = 0

2x - y - 12 = 0

intersect.

First, let's isolate the variable y in one side of the equalities.

y = (-x/2)

y = 2x - 12

Now we have:

-(x/2) = 2x - 12

We can solve this for x.

12 = 2*x + x/2 = 2.5*x

12/2.5 = x = 4.8

Then, replacing that value in any of the lines, we can find the value of y.

y = 2*8 - 12 = 2*4.8 - 12 = -2.4

Then those lines intersect in the point (4.8, -2.4)

Now we want to find the line that passes through the points (-2, 3) and (4.8, -2.4)

A linear relationship can be written as:

y = a*x + b

where a is the slope and b is the y-axis intercept.

For a line that passes through the points (x1, y1) and (x2, y2), the slope can be written as:

a = (y2 - y1)/(x2 - x1).

Then, the slope for our line is:

a = (3 - (-2.4))/(-2 - 4.8) = -0.79

And the

y-intercept will be:

y = -0.79*x + b

when x  = -2, y = 3.

3 = -2*-0.79 + b

3 - 2*0.79 = b = 1.42

The line is:

y = -0.79*x + 1.42

3 0
4 years ago
Bryan needs to build a fence around his rectangular vegetable garden. The length will be 2 feet longer than the width. If he use
GalinKa [24]
In order to do this, one side of the rectangle will be x+2, and the other will just be x. The x would be representing the width since the length is the width (x) plus two feet (+2). Next, you have to make an equation. So, since it all has to use 16 feet of fencing, you would set the two sides to be added to equal 16. So, it would be: 16=x+2+x. Then, you reduce that, so it would be: 16=2x+2. After that you just solve for x (which means that you want x by itself on one side of the = ). So, you would subtract 2 from both sides. Since 2-2=0, that would make the "+2" go away; since 16-2=14, that would replace the 16. So, your new equation is: 14=2x. After that you just divide both sides by 2 because 2 divided by 2=0. 14/2=7. So, you would end up getting: 7=x as your final answer.

Now, you just put 7 where x was in the sides. So 2x (which was the length) trims into: 2 times 7, which =14 and the x (which was the width) we already figured out was 7. This, the width would be 7, while the length would be 14.
5 0
3 years ago
Suppose that the average and standard deviation of the fine for speeding on a particular highway are 111.12 and 13.04, respectiv
antoniya [11.8K]

Answer:

3) (98.08, 124.16)

Step-by-step explanation:

The Empirical Rule states that, for a normally distributed random variable:

68% of the measures are within 1 standard deviation of the mean.

95% of the measures are within 2 standard deviation of the mean.

99.7% of the measures are within 3 standard deviations of the mean.

In this problem, we have that:

Mean = 111.12

Standard deviation = 13.04

Calculate an interval that is symmetric around the mean such that it contains approximately 68% of fines.

68% of the fines are within 1 standard deviation of the mean speed. So

From 111.12 - 13.04 = 98.08 to 111.12 + 13.04 = 124.16

The interval notation in the smallest value before the highest value.

So the correct answer is:

3) (98.08, 124.16)

8 0
4 years ago
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