MATHEMATICS COLLEGE

A Christmas tree is supported by a wire that is 9 meters longer than the height of the tree. The wire is anchored at a point whose distance from the base of the tree is 41 meters shorter than the height of the tree. What is the height of the tree

Answers

Answer 1

Answer:

Answer:

The height of the tree is 80 meters.

Step-by-step explanation:

Let the height of the Christmas tree be x meters.

Then the length of the wire will be, (x + 9) meters.

And the wire will (x - 41) meters away from the base of the tree.

Consider the diagram below.

Use Pythagoras theorem to solve for x as follows:

$AB^(2)=AC^(2)+CB^(2)$

$(x+9)^(2)=x^(2)+(x-41)^(2)\n\nx^(2)+18x+81=x^(2)+x^(2)-82x+1681\n\nx^(2)-100x+1600=0\n\nx^(2) -80x-20x+1600=0\n\nx(x-80)-20(x-80)=0\n\n(x-80)(x-20)=0$

The value of x is either 80 or 20.

If x = 20, then the base CB will be -21. This is not possible as length is always positive.

Thus, the value of x is 80.

Hence, the height of the tree is 80 meters.

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Find the value of h(-67) for the function below
h(x)=-49x-125

Answers

Answer:
h(-67) = 3158
General Formulas and Concepts:
Order of Operations: BPEMDAS
- Substitution and Evaluation
Step-by-Step Explanation:
Step 1: Define
h(x) = -49x - 125
h(-67)

Step 2: Solve
1. Substitute: h(-67) = -49(-67) - 125
2. Multiply: h(-67) = 3283 - 125
3. Subtract: h(-67) = 3158

(g) If each customer takes 3 minutes to check out, what is the probability that it will take more than 6 minutes for all the customers currently in line to check out? The probability that it will take more than 6 minutes for all the customers currently in line to

Answers

The probability that it will take more than 6 minutes for all the customers in line to check out is 0.40.

We are given the probability distribution of x, the number of customers in line at a supermarket express checkout counter.

Moreover, we are given that each customer takes 3 minutes to check out.

It means that if there are 0 customers in line, i.e., x=0, then it will take 0 minutes for all the customers currently in line to check out.

If there is 1 customer in line, i.e., x=1, then it will take 3 minutes for all the customers currently in line to check out.

If there are 2 customers in line, i.e., x=2, then it will take 6 minutes for all the customers currently in line to check out.

If there are 3 customers in line, i.e., x=3, then it will take 9 minutes for all the customers currently in line to check out.

If there are 4 customers in line, i.e., x=4, then it will take 12 minutes for all the customers currently in line to check out.

If there are 5 customers in line, i.e., x=5, then it will take 15 minutes for all the customers currently in line to check out.

From above we note that if there are 3 or more customers in the line, then it will take more than 6 minutes (note that the case of check out time equal to 6 minutes is not included when we want 'more than 6 minutes') for all the customers currently in line to check out.

Thus, required probability is given by:

P(more than 6 minutes for all the customers currently in line to check out) = P(x ≥ 3)

= P(x=3) + P(x=4) + P(x=5)

= 0.20 + 0.15 + 0.05

= 0.40

Therefore, the probability that it will take more than 6 minutes for all the customers in line to check out is 0.40.

To learn more about the probability visit:

brainly.com/question/11234923.

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Final answer:

Without specific information on the total number of customers or the distribution of customers in line, we cannot calculate a specific probability for it to take more than 6 minutes for all customers to check out, given that each customer takes 3 minutes.

Explanation:

The question is about the probability that it will take more than 6 minutes for all the customers in line to check out, given that each customer takes 3 minutes. The time it takes for all the customers to check out is determined by the number of customers in line. If there are two or more customers in line, it will definitely take more than 6 minutes for all of them to check out, because the checkout time is 3 minutes per customer.

So, the question of probability relates to the likelihood of there being two or more customers in line. Without information on the total number of customers, or the distribution of customers in line, we cannot calculate a specific probability.

Please note, this is a practical application of topics in probability and queue theory, involving concepts like mean arrival rate and service rate.

Learn more about Probability here:

brainly.com/question/32117953

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WILL MARK BRAINLIEST PLEASE HELP

Answers

Answer:

1) h = -1/2t^2 +10t

2) h = -1/2(t -10)^2 +72

3) domain: [0, 20]; range: [0, 50]

Step-by-step explanation:

1.) I find it easiest to start with the vertex form when the vertex is given. The equation of the presumed parabolic path for Firework 1 is ...

h = a(t -10)^2 +50

To find the value of "a", we must use another point on the graph. (0, 0) works nicely:

0 = a(0 -10)^2 +50

-100a = 50 . . . . . . subtract 100a

a = -1/2 . . . . . . . . . divide by -100

Then the standard-form equation is ...

h = (-1/2)(t^2 -20t +100) +50

h = -1/2t^2 +10t

2.) The path of Firework 2 is translated upward by 22 units from that of Firework 1.

h = -1/2(t -10)^2 +72

3.) The horizontal extent of the graph for Firework 1 is ...

domain: 0 ≤ t ≤ 20

The vertical extent of the graph for Firework 1 is ...

range: 0 ≤ h ≤ 50

Y=6cosx^2 (derivative)

Answers

dy/dx = d/dx 6cosx^2
= 12cosx d/dx cosx
= 12cosx (-sinx)
= -12cosxsinx

What is the base 10 representation of 11102?

Answers

Answer:

Step-by-step explanation:

The base two number one one one zero is equal to one times eight, plus one times four, plus one times two, plus zero times one, which simplifies to fourteen.

Answer:

1.1102 * 10^4

Step-by-step explanation:

11102

= 1.1102 * 10^4

In a survey of a community, it was found that 85% of the people like winter season and 65% like summer season. If none of them did not like both seasonsi) what percent like both the seasons