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3 years ago

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

You might be interested in

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 A 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, P(E), 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, v = 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, t = (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 t ≈ 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<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:

6 0

3 years ago