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makvit [3.9K]
3 years ago
7

What is the y-value of the point of intersection of y=2sinx-cosx and y=cosx over the interval 0≤x≤pi/2 ? a. 0 b. (square root of

2)/2 c. (square root of 3)/2 d. 1

Mathematics
2 answers:
horsena [70]3 years ago
7 0
We have that

<span>y=2sinx-cosx
y=cosx
</span>over the interval 0≤x≤pi/2-------> 0≤x≤1.57

using a graph tool
see the attached figure

the solution in the given interval is the point (pi/4, 0.707)
the y-value of the point of intersection is 0.707 -----> √2/2

the answer is the option 
<span>b. (square root of 2)/2</span>

Hunter-Best [27]3 years ago
4 0

Answer:

Option b. √2/2 is the correct option.

Step-by-step explanation:

Two functions are given as y = 2sinx - cosx and y = cosx

Now we have to find the point of intersection of two given functions.

So at the point of intersection of these graphs

2 sinx - cosx = cosx

2 sinx = 2 cosx

sinx = cosx

For the given value of x = π/4 sine and cosine functions are equal.

Therefore y value of both the functions

y = cos(π/4) = 1/√2 = √2/2

Therefore over the interval 0≤x≤π/2 value of y coordinate will be √2/2.

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Answer:

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Step-by-step explanation:

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If one-third of a number, x, is greater than five less than twice the number, which of the following is true?
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x= 15/7

Step-by-step explanation:

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Consider the sets A={1,3,5,7} and B={11,13,15,21}.
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4 0
3 years ago
A blind man wanders under a door into an empty room. After running into the walls repeatedly for a while, it stops to think and
Nostrana [21]

From the side where the man is located in the 10' by 12' rectangular room, we have;

A) 0.046

B) The average time to escape in first attempt is approximately 605.02 seconds

<h3>Which concept can be used to find the odds and time of escape?</h3>

A) From The given diagram, we have;

Width of the door = 10 - 6 - 2 = 2

Therefore, the door is 2 feet wide

Distance, d1, from the man to the side of the door closer to him is given by Pythagorean theorem as follows;

  • d1 = √(6² + 7²) = √(85)

From the furthest side of the door to the man, we have;

  • d2 = √(7² + 8²) = √(113)

According to the law of cosines, we have;

2² = 85+113 - 2×√(85)×√(113) cos(A)

Where angle <em>A </em>is the angle formed by the lines from the man to the closer and farther sides of the door.

2×√(85)×√(113) cos(A) = 85+113 - 2²

A = arccos((85+113 - 2²)/(2×√(85)×√(113)))

A = arccos (194/(2×√(9605)) ≈ 8.213°

The angle of the possible directions in which the man can turn is 180°.

Therefore;

The probability, <em>P(</em><em>E)</em>, of escaping in the first move is therefore;

  • P(E) = 8.213°/180° ≈ 0.046

B) Given that the man escapes in the first move, the shortest and longest distances the man moves are;

d1 = √(85) and d2 = √(113)

Speed of the man, <em>v </em>= 0.5 cm/sec

Therefore by unit conversion function of a graphing calculator;

  • v = (25/1524) ft./sec

The times taken are;

t1 = √(85)/(25/1524) ≈ 562.023

t2 = √(113)/(25/1524) ≈ 648.014.

Average time, <em>t </em>= (t1 + t2)/2

Which gives;

t = (562.023 + 648.014)/2 ≈ 605.02

The average time it takes the man to escape in first move is <em>t </em><em>≈</em> 605.02 seconds.

Learn more about Pythagorean theorem and probability here:

brainly.com/question/27180985

brainly.com/question/654982

brainly.com/question/24756209

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3 0
1 year ago
Sam's Club has a special that charges $2.49 per case of water. Vinny wants to pay that price, but needs to purchase a membership
castortr0y [4]

Answer: $50 + $2.49x = $67.43

Step-by-step explanation:

Let the case of water bought be represented by x.

We are informed that Sam's Club has a special that charges $2.49 per case of water and that Vinny wants to pay that price, but needs to purchase a membership first, which costs $50 and that Vinny eventually spent $67.43.

The equation that represents the number of cases of water that Vinny bought at Sam's club will be:

$50 + $2.49x = $67.43

8 0
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