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2 years ago

Find the integral of 1/sqrt(x^2-9)

1 answer:

6 0

Let x = 3secβ, then dx = 3secβtanβ

∫dx/√(x²-9) = ∫[(3secβtanβ)/(3tanβ)]dβ
                 = ∫secβdβ
                 = ln |tanβ - secβ| + c
                 = ln |√(x² - 9)/3 - x/3| + C
                 = ln |√(x² - 9)/x| + C

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A class of 40 students has 11 students who ride the bus and 10 students who are in the band. Three of the students who ride the

Alexxandr [17]

The denominator is 40
10-3=7 (number of students in the band who do not ride the bus)
7/40=0.175
0.174*100=17.5% chance
Hope this helps!

8 0

2 years ago

Sophie gets an allowance of $15.00 each month plus an extra $2.00 for each chore she completes around the house. Which of the fo

Alex Ar [27]

Answer:

Linear equation

Step-by-step explanation:

f(x) = 2x + 15

Linear because constant increase

6 0

2 years ago

(4) A spherical balloon is being inflated so that its diameter is increasing at a constant rate of 6 cm/min. How quickly is the

fredd [130]

In terms of its radius $r$ , the volume of the balloon is

$V(r)=\dfrac{4\pi}3r^3$

The diameter $d$ is twice the radius, so that in terms of its diameters, the balloon's volume is given by

$V(d)=\dfrac{4\pi}3\left(\dfrac d2\right)^3=\dfrac\pi6d^3$

Differentiate both sides with respect to time $t$ :

$\dfrac{\mathrm dV}{\mathrm dt}=\dfrac\pi2d^2\dfrac{\mathrm dd}{\mathrm dt}$

The diameter increases at a rate of $\frac{\mathrm dd}{\mathrm dt}=6\frac{\rm cm}{\rm min}$ . When the diameter is $d=50\,\mathrm{cm}$ , we have

$\dfrac{\mathrm dV}{\mathrm dt}=\dfrac\pi2(50\,\mathrm{cm})^2\left(6\frac{\rm cm}{\rm min}\right)=7500\pi\dfrac{\mathrm{cm}^3}{\rm min}$

or about 23,562 cc/min (where cc = cubic centimeters)

5 0

3 years ago

Help me pls ill give brainly <br> 64−(3y+8y+y)÷40=37

Solnce55 [7]

64 - (3y + 8y + y) / 40 = 37

Simplify 3y + 8y + y

64 - 12y / 40 = 37

Add 12y / 40 to both sides and subtract 37

27 = 12y / 40

Multiply both sides by 40

1080 = 12y

Divide both sides by 12

90 = y

6 0

3 years ago

Read 2 more answers

Help anyone can help me do the question,I will mark brainlest.

Marrrta [24]

Part (a)

The radius is r = 42 because OA = 42.

The circumference, aka distance around the circle, is

C = 2*pi*r

C = 2*(22/7)*42

C = 264

We're told that arc AB is 110 mm which is 110/264 = 5/12 of the full distance around the circle.

So we'll apply 5/12 to the full rotation 360 to get (5/12)*360 = 150

<h3>Answer: 150 degrees</h3>

==============================================================

Part (b)

Compute the area of the full circle

A = pi*r^2

A = (22/7)*(42)^2

A = 5544

Then take 5/12 of this because we only want 5/12 of the full circle area (to get the area of the shaded pizza slice)

(5/12)*(5544) = 2310

<h3>Answer: 2310 square mm</h3>

==============================================================

Side note: Both answers are approximate because pi = 22/7 is approximate.

5 0

2 years ago