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telo118 [61]
3 years ago
5

A fountain on a lake sprays water in a parabolic arch modeled by the equation y = -0.3x2 + 3x. A beam of light modeled by the eq

uation
-2x + 5.5y = 19.5 passes through the fountain to create a rainbow effect. If the beam cuts the water spray at points A and B, such that point B is at a higher level than point A, what distance from the ground level is point A?
A) 1.66 units
B) 4.15 units
C) 5.44 units
D) 6.14 units
E) 7.13 units
Mathematics
1 answer:
Yakvenalex [24]3 years ago
3 0
Y=-.3x^2+3x 

....

-2x+5.5y=19.5

5.5y=19.5+2x

y=(19.5+2x)/5.5

When the light touches the parabola y=y so

(19.5+2x)/5.5=-.3x^2+3x  multiply both sides by 5.5

19.5+2x=-1.65x^2+16.5x  add 1.65x^2 to both sides

1.65x^2+2x+19.5=16.5x  subtract 16.5x from both sides

1.65x^2-14.5x+19.5=0

Using the quadratic equation for simplicity...

x=(14.5±√81.55)/3.3  we only need the lower point, or the smaller value of x

x≈1.657423  since:

y=(19.5+2x)/5.5

y≈4.15 units


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Answer:

7/12

Step-by-step explanation:

-15/9+9/4

We need to make them have the same denominator:

9x4= 36 so that is our new denominator

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(Sorry if i dont make sense)

Now we have -60/36+81/36 which is equal to 21/36.

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c) P(Y>1)=0.651

Step-by-step explanation:

This a binomial experiment where success is denoted by parts that need rework.

X ∼ B(n, p); n = 20; p = 0.01

The expected value of X is: E(X) = np =20×0.01= 0.2

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Probability function is given by:

\frac{n!}{x!(n-x)!} *p^x*(1-p)^{(n-x)}

P(X≥2)=1-P(X<2)=1-P(X=1)-P(X=0)= 1 - \frac{20!}{1!(20-1)!} *(0.01)^{1}*(1-0.01)^{(20-1)}-\frac{20!}{0!(20-0)!} *(0.01)^{0}*(1-0.01)^{(20-0)}

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b) p=0.04

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P(x>1)= 1 - 0.368 - 0.442=0.190

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In this experiment Y is the number of hours and n= 5 hours.

Then, we check the probability in each hour:

P(Y>1)=1- P(Y=0)

P(Y=0)=\frac{5!}{0!(5-0)!} *(0.19)^{0}*(1-0.19)^{(5-0)}=0.349

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Answer:

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