All categories

2 years ago

Sketch the region of integration for the following integral. ∫π/40∫6/cos(θ)0f(r,θ)rdrdθ

Mathematics

1 answer:

solong [7]2 years ago

3 0

Answer:

The graph is sketched by considering the integral. The graph is the region bounded by the origin, the line x = 6, the line y = x/6 and the x-axis.

Step-by-step explanation:

We sketch the integral ∫π/40∫6/cos(θ)0f(r,θ)rdrdθ. We consider the inner integral which ranges from r = 0 to r = 6/cosθ. r = 0 is located at the origin and r = 6/cosθ is located on the line x = 6 (since x = rcosθ here x= 6)extends radially outward from the origin. The outer integral ranges from θ = 0 to θ = π/4. This is a line from the origin that intersects the line x = 6 ( r = 6/cosθ) at y = 1 when θ = π/2 . The graph is the region bounded by the origin, the line x = 6, the line y = x/6 and the x-axis.

You might be interested in

In ΔFGH, f = 37 cm, ∠F=28° and ∠G=124°. Find the length of g, to the nearest 10th of a centimeter.

MatroZZZ [7]

Answer:

65.3 cm

Step-by-step explanation:

The law of sines can be used for this.

g/sin(G) = f/sin(F)

g = (37 cm)sin(124°)/sin(28°) ≈ 65.3 cm . . . . multiply by sin(G)

The length of g is about 65.3 cm.

6 0

2 years ago

You just found a positive trend line showing a strong relationship between homework scores and test scores for five students. Ex

Scrat [10]

The positive trend among the homework scores and the test scores would reveal that if a student does well in homework, he is likely to do well in exams. This can be explained in the sense that the homework will serve as the practice for the student before finally taking the exam.

8 0

2 years ago

Read 2 more answers

Point T, the midpoint of segment RS, can be found using the formulas x = (6 – 2) + 2 and y = (4 – 6) + 6. What are the coordinat

Fiesta28 [93]

Question:

Point T, the midpoint of segment RS, can be found using the formulas x = (1/2) (6 – 2) + 2 and y = (1/2) (4 – 6) + 6. What are the coordinates of point T?

Answer:

$T(4,5)$

Step-by-step explanation:

Given

$x = \frac{1}{2}(6 - 2) + 2$

$y = \frac{1}{2}(4 - 6) + 6$

Required

Determine the coordinates of T

The coordinates of T can be represented as $T(x,y)$

To do this, we simply solve for x and y

$x = \frac{1}{2}(6 - 2) + 2$

Solve 6 - 2

$x = \frac{1}{2}*4 + 2$

Solve 1/2 * 4

$x = 2 + 2$

$x = 4$

$y = \frac{1}{2}(4 - 6) + 6$

Solve 4 - 6

$y = \frac{1}{2}*-2 + 6$

Solve 1/2 * -2

$y = -1 + 6$

$y = 5$

Hence, the coordinates of T(x,y) is:

$T(x,y) = T(4,5)$

5 0

1 year ago

Read 2 more answers

Nathan is out rafting. He rafts 16 miles with the river current. At the end of 16 miles, he turns around and rafts the same dist

Novosadov [1.4K]

S = d/t

st = d

t = d/s

The time going is t1.
The time returning is t2.
The total time is 4 hours, so we have t1 + t2 = 4

The speed of the current is c.
The speed going is 9 + c.
The speed returning is 9 - c.

t1 = 16/(9 + c)

t2 = 16/(9 - c)

t1 + t2 = 16/(9 + c) + 16/(9 - c)

4 = 16/(9 - c) + 16/(9 + c)

1 = 4/(9 - c) + 4/(9 + c)

(9 + c)(9 - c) = 4(9 - c) + 4(9 + c)

81 - c^2 = 36 - 4c + 36 + 4c

81 - c^2 = 72

c^2 = 9

c^2 - 9 = 0

(c + 3)(c - 3) = 0

c + 3 = 0 or c - 3 = 0

c = -3 or c = 3

We discard the negative answer, and we get c = 3.

The speed of the current is 3 mph.

7 0

2 years ago

Read 2 more answers

Becky is an experienced swimmer. The table contains data on her times in the 100-meter freestyle event for each year over the pa

Sauron [17]

Correlation coefficient (r) = [nΣxy - (Σx)(Σy)] / [sqrt(nΣx^2 - (Σx)^2)sqrt(nΣy^2 - (Σy)^2)]
Σx = 21 => (Σx)^2 = 21^2 = 441
Σy = 671 => (Σy)^2 = 671^2 = 450,241
Σx^2 = 1 + 4 + 9 + 16 + 25 + 36 = 91
Σy^2 = 98^2 + 101^2 + 109^2 + 117^2 + 119^2 + 127^2 = 75,665
Σxy = 1(98) + 2(101) + 3(109) + 4(117) + 5(119) + 6(127) = 2,452
r = [6(2,452) - 21(671)] / [sqrt(6(91) - 441)sqrt(6(75,665) - 450,241)] = 621/sqrt(105)sqrt(3749) = 0.99

option b is the correct answer.

5 0

2 years ago