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Bumek [7]
3 years ago
10

How would you do this question?

Mathematics
1 answer:
diamong [38]3 years ago
8 0

Answer:

1) ∫ x² e^(x) dx

4) ∫ x cos(x) dx

Step-by-step explanation:

To solve this problem, eliminate the choices that can be solved by substitution.

In the second problem, we can say u = x², and du = 2x dx.

∫ x cos(x²) dx = ∫ ½ cos(u) du

In the third problem, we can say u = x², and du = 2x dx.

∫ x e^(x²) dx = ∫ ½ e^(u) du

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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

#SPJ1

3 0
1 year ago
If 25% more than a number is 325 what is 20% less than the number
Verdich [7]
Let the number be x.  Then 1.25x = 325, or x = 260.  

20% less than 260 is 0.80(260) = 208
7 0
2 years ago
—7m&lt;28 solve please hurry
mario62 [17]

Answer:

the answer is -4

Step-by-step explanation:

step 1: -7m<28

step 2: -7m÷ (-7)>28÷(-7)

step 3: m>28÷(-7)

step 4: m>-28÷7

step 5: m>-4

8 0
2 years ago
Please help with 11 and 12
larisa [96]
11.k>-3(4r+3)/4r-5
12.k<(2x+2)/x+3
7 0
3 years ago
A small pizza has an 8-in. Diameter a large pizza has a 15-in. Diameter. The pizzeria charges the same price per square inch for
vlabodo [156]

The cost of large pizza is $24.62, a small pizza has an 8-in. diameter a large pizza has a 15-in. diameter the pizzeria charges the same price per square inch for both pizzas and the small pizza cost $7.

Step-by-step explanation:

The given is,

                A small pizza has an 8-inches in diameter

                A large pizza has a 15-inches in Diameter

                The small pizza cost $7

Step:1

                Area of smaller pizza,

                                        Area, A_{S} = \pi  r^{2}...................................(1)

                 Where, r - Radius of small pizza

                 From given, r=\frac{d}{2}

                                         = \frac{8}{2}

                                       r = 4 inches

                  Equation (1),

                                    A_{S} = \pi  4^{2}

                                          =(3.14)(16)                             ( ∵ \pi=3.14 )

                                          = 50.24 Square inches

Step:2

              Area of smaller pizza,

                                        Area, A_{L} = \pi  r^{2}...................................(1)

                 Where, r - Radius of small pizza

                 From given, r=\frac{d}{2}

                                         = \frac{15}{2}

                                       r = 7.5 inches

                  Equation (1),

                                    A_{S} = \pi  7.5^{2}

                                          =(3.14)(56.25)                             ( ∵ \pi=3.14 )

                                          = 176.625 Square inches

Step:3

            Cost of pizza per square meter,

                                                = \frac{Cost of small pizza}{Area of small pizza}

                                                =\frac{7}{50.24}

                                                = $ 0.1393 per square meter

                Cost of Larger pizza = Area of Larger pizza × Cost per square meter

                                                = (176.625)(0.139331)

                                                = $24.62

Result:

          The cost of large pizza is $24.62, a small pizza has an 8-in. diameter a large pizza has a 15-in. diameter the pizzeria charges the same price per square inch for both pizzas and the small pizza cost $7.

         

                                             

6 0
3 years ago
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