ravin has to see the doctor at 10:05 am. He gets to the doctor’s clinic at9:52 am. How many minutes early is he?

The volume V determined by the cylindrical shells is  [tex]\frac{65\pi }{6}[/tex]  cube units

Given data:

The cylindrical shells method involves integrating the volume of infinitesimally thin cylindrical shells formed by revolving a vertical strip of the region about the specified axis.

Step 1: Visualize the region and the axis of rotation.

The region bounded by the curves [tex]x = 5y^2[/tex] , y ≥ 0, and x = 5 is the region in the first quadrant between the parabola x = 5y^2 and the line x = 5. The axis of rotation is the line y = 2.

Step 2: Set up the integral for the volume.

We will integrate the volume of cylindrical shells from y = 0 to y = a, where a is the y-coordinate of the point of intersection between x = 5y^2 and x = 5. To find this point of intersection, we equate the two equations:

[tex]5y^2 = 5[/tex]

[tex]y^2 = 1[/tex]

y = ±1

dV = circumference * height * dx

Now, the radius of each cylindrical shell is the distance from the axis of rotation (y = 2) to the curve [tex]x = 5y^2[/tex]. The radius is given by r = 2 - y.

The height is given by  [tex]h = 5y^2 - 5[/tex].

The circumference of each cylindrical shell is given by 2πr, where r is the distance between the line y = 2 and the curve, which is x.

Therefore, the circumference is 2πx.

Substituting the height and circumference into the integral:

[tex]V = \int\limits^1_0 {2 \pi (2 - y)(5y^2 - 5) dy[/tex]

On solving the integral:

[tex]V =-10 \pi \int\limits^0_1 { (2 - y)(y^2 - 1) dy[/tex]

On simplifying:

[tex]V=-10\pi (\frac{-13}{12})[/tex]

Hence, the value of integral is  [tex]\frac{65\pi }{6}[/tex]  cube units and the graph is attached below.

To learn more about definite integral click :

https://brainly.com/question/14279102

#SPJ12

Check the picture below.

well, we know the angle's cosine and sine or namely adjacent and opposite sides, let's get the hypotenuse.

[tex]\textit{using the pythagorean theorem} \\\\ c^2=a^2+b^2 \qquad \begin{cases} c=hypotenuse\\ a=\stackrel{adjacent}{1}\\ b=\stackrel{opposite}{-8}\\ \end{cases} c=\sqrt{1^2+(-8)^2}\implies c=\sqrt{65} \\\\[-0.35em] ~\dotfill\\\\ csc(\theta )=\cfrac{\stackrel{hypotenuse}{\sqrt{65}}}{\underset{opposite}{-8}}\implies csc(\theta )=-\cfrac{\sqrt{65}}{8}[/tex]

Answer:

A compass is used to draw arcs is the answer.

Answer: Intersecting arcs are created and connected.

Step-by-step explanation:

Intersecting arcs are created and connected.

Answer:

y= 18

z= 22.5

x= 37.5

Similar right triangles

Answer:

2

Step-by-step explanation:

3.60+3.60=7.20 thats correct

Answer:

540 SUV's

Step-by-step explanation:

Sales percentage of non SUV's = 100 - 60 = 40%

Let total cars be x

40% of x = 360

[tex]\dfrac{40}{100}*x=360\\\\\\x=360*\dfrac{100}{40}\\\\\\x = 900[/tex]

Number of SUV's = Total cars -   number of non SUV's

                             = 900 - 360

                              = 540

anwer 2(4x-1)

Distribuye

Distribuye 8 ( − 5 ) + 3 8 {\color{#c92786}{8(x-5)}}+38 8 − 4 0 + 3 8 Suma los números 8 − 4 0 + 38 − 2Factoriza por agrupamiento Factoriza por agrupamiento 8 ( − 5 ) + 3 8 8(x-5)+38 2 ( 4 − 1 )

Answer:

Infinitely many solutions!

Step-by-step explanation:

Using PEMDAS rules, let's distribute the 8 to (x - 5)

Now the equation looks like: 8x - 40 + 38 = 8x - 2

We combine like terms, so -40 + 38 would be -2

Now the equation would look like 8x - 2 = 8x - 2

Let's add 2 on the other side to try and get x by itself

8x = 8x - 2 (+2) Which brings the equation to 8x = 8x

Technically speaking, you can stop here because the statement is true. No matter what x equals, the statement would be true. Therefore infinitely many solutions would be your answer. You can plug in any number for x and the equation would still be correct.

Answer:

[tex]4\sqrt{3} -3\sqrt{2} (or) 2.68556[/tex]

Step-by-step explanation:

first you're going to simplify the radical expression:

[tex]-\sqrt{12}[/tex] becomes [tex]-2\sqrt{3}[/tex]

[tex]\sqrt{18}[/tex] becomes [tex]3\sqrt{2}[/tex]

[tex]2\sqrt{27}[/tex] becomes [tex]6\sqrt{3}[/tex]

your equation should now be [tex]-2\sqrt{3} -3\sqrt{2} +6\sqrt{3}[/tex]

next you're going to collect like terms [tex]-2\sqrt{3} +6\sqrt{3} =4\sqrt{3}[/tex]

so your final answer is [tex]4\sqrt{3} -3\sqrt{2}[/tex]

Answer:

1.02c

Step-by-step explanation:

Answer:

X=16

Step-by-step explanation:

52/13=4

4 = how much the shape was dialated

And so you would multiply 4 by 4 to get the corresponding side which is X

The amount of water in the pond per hour is 300 liters per hour

From the graph, we have the following points:

(x,y) = (0,100) and (1,400)

This means that:

The amount of water per hour is the calculated using:

Rate = (y2 - y1)/(x2 - x1)

Substitute known values

Rate = (400 - 100)/(1 - 0)

Evaluate the quotient

Rate = 300

Hence, the amount of water in the pond per hour is 300 liters per hour

Read more about linear functions at:

https://brainly.com/question/14323743

Step-by-step explanation:

first let's get the original line in slope intercept form.

the vegetal slope intercept form is

y = ax + b

a is the slope, b is the y-intercept.

2x + y = 5

y = -2x + 5

there !

a line parallel to this line must have the same slope (-2).

but it will intersect with the y-axis at a different point.

the y-intersect is the y value when x = 0.

the given point (0, 1) is already that y-intersect (because x=0).

so, the desired parallel line function is

y = -2x + 1

if we had a different point of the line, e.g. (4, -7), we would go back to the general equation

y = ax + b

put in the slope we know (-2)

y = -2x + b

and then put in the x and y cakes if the point and calculate b

-7 = -2×4 + b

-7 = -8 + b

b = 1

and then we get again

y = -2x + 1

Answer:

0.4

Step-by-step explanation:

0.43118 to 1 significant figure will remove all but one digit of information.

Answer:

B

Step-by-step explanation:

pretty sure im on the same part as u

Answer:

Step-by-step explanation:

Hence, the expression is 46k - 32.

Hi!

First, let's distribute -8:

-8(-5k+4)+6k

[tex]\rm{40k-32+6k[/tex]

Combine Like Terms:

[tex]\rm{46k-32[/tex] (Answer)

Hope it helps!

~Misty~

Answer:

the answers is 530000 millimeters

Answer:

$212.5

Step-by-step explanation:

10%= 25 (because 250/10)

5%= 12.5
15%= 37.5

250-37.5= $212.5

Answer:

Hence the price of the phone with a discount coupon will be $212.5

Step-by-step explanation:

[tex]Solution,\\\\MP=250\\\\Discount=15percent\\\\Now ,\\\\Discount amount=Discount percent*MP\\\\Discount amount=15/100*250\\\\Discount amount=37.5\\\\SP=MP-Discount\\\\SP=250-37.5\\SP=212.5[/tex]

Answer:

mode = 11.18 (non recurring)

Step-by-step explanation:

hope this answer helps you! and sorry if it looks messy

Answer:The area of a triangle is defined as the total space occupied by the three sides of a triangle in a 2-dimensional plane.

Step-by-step explanation:The basic formula for the area of a triangle is equal to half the product of its base and height, i.e., A = 1/2 × b × h.

Answer:

D

Step-by-step explanation:

The slope is -100/3 and the y intercept is 450

Answer:

letter D

Step-by-step explanation:

hope it helps alot

Answer:

A & D are correct

Step-by-step explanation:

to solve for 'x':

4x + 16 = 180

4x = 164

x = 41

m∡A =  2(41)+1 = 83°

m∡B = 41°

m∡C = 41+15 = 56°

Answer:

w = 4

Step-by-step explanation:

The sum of the 3 angles in a triangle = 180°

sum the 3 angles and equate to 180

13w + 18w + 56 = 180

31w + 56 = 180 ( subtract 56 from both sides )

31w = 124 ( divide both sides by 31 )

w = 4

Answer:

[tex]Solution,\\When,b=2\\Now, b*5=2*5=10[/tex]

Step-by-step explanation:

Answer:

12 hours(105km)

13.64 hours (120 km)

16 hours (141 km)

40 hours ( 352km)

Answer:

12 hours ( 105 km )

13.64 hours ( 120 km )

16 hours ( 141 km )

40 hours ( 352 km ) .

The area of the shaded region /ACDEH/ is 325.64cm²

Step 1 - Collect all the facts

First, let's examine all that we know.

Please note that the shaded region comprises a rectangle /ADEH/ and a scalene triangle /ACD/.

So to get the area of the entire region, we have to solve for the area of the Scalene Triangle /ACD/ and add that to the area of the rectangle /ADEH/

Step 2 - Solving for /ACD/

The formula for the area of a Scalene Triangle is given as:

A = [tex]\sqrt{S(S-a)(S-b)(S-c) square units}[/tex]

This formula assumes that we have all the sides. But we don't yet.

However, we know the side /CD/ is 10cm. Recall that side /CD/ is one of the sides of the octagon ABCDEFGH.

This is not enough. To get sides /AC/ and /AD/ of Δ ACD, we have to turn to another triangle - Triangle ABC. Fortunately, ΔABC is an Isosceles triangle.

Step 3 - Solving for side AC.

Since all the angles in the octagon are equal, ∠ABC = 135°.

Recall that the total angle in a triangle is 180°. Since Δ ABC is an Isosceles triangle, sides /AB/ and /BC/ are equal.  

Recall that the Base angles of an isosceles triangle is always equal. That is ∠BCA and ∠BAC are equal. To get that we say:

180° - 135° = 45° [This is the sum total of ∠BCA and ∠BAC. Each angle therefore equals

45°/2 = 22.5°

Now that we know all the angles of Δ ABC and two sides /AB/ and /BC/, let's try to solve for /AC/ which is one of the sides of Δ ACD.

According to the Sine rule,

[tex]\frac{Sin 135}{/AC/}[/tex] = [tex]\frac{Sin 22.5}{/AB/}[/tex] = [tex]\frac{Sin 22.5}{/BC/}[/tex]

Since we know side /BC/, let's go with the first two parts of the equation.

That gives us [tex]\frac{0.7071}{/AC/} = \frac{0.3827}{10}[/tex]

Cross multiplying the above, we get

/AC/ = [tex]\frac{7.0711}{0.3827}[/tex]

Side /AC/ = 18.48cm.

Returning to our Scalene Triangle, we now have /AC/ and /CD/.

To get /AD/ we can also use the Sine rule since we can now derive the angles in Δ ABC.

From the Octagon the total angle inside /HAB/ is 135°. We know that ∠HAB comprises  ∠CAB which is 22.5°, ∠HAD which is 90°. Therefore, ∠DAC = 135° - (22.5+90)

∠DAC = 22.5°

Using the same deductive principle, we can obtain all the other angles within Δ ACD, with ∠CDA = 45° and ∠112.5°.

Now that we have two sides of ΔACD and all its angles, let's solve for side /AD/ using the Sine rule.

[tex]\frac{Sin 112.5}{/AD/}[/tex] = [tex]\frac{Sin 45}{18.48}[/tex]

Cross multiplying we have:

/AD/ = [tex]\frac{17.0733}{0.7071}[/tex]

Therefore, /AD/ = 24.15cm.

Step 4 - Solving for Area of ΔACD

Now that we have all the sides of ΔACD, let's solve for its area.

Recall that the area of a Scalene Triangle using Heron's formula is given as

A = [tex]\sqrt{S(S-a)(S-b)(S-c) square units}[/tex]

Where S is the semi-perimeter given as

S= (/AC/ + /CD/ + /DA/)/2

We are using this formula because we don't have the height for ΔACD but we have all the sides.

Step 5 - Solving for Semi Perimeter

S = (18.48 + 10 + 24.15)/2

S = 26.32

Therefore, Area =  [tex]\sqrt{26.32(26.32-18.48)(26.32-10)(26.32-24.15)}[/tex]

A = [tex]\sqrt{26.32 * 7.84*16.32 * 2.17)}[/tex]

A = [tex]\sqrt{7,307.72}[/tex] Square cm.

A of ΔACD = 85.49cm²

Recall that the shape consists of the rectangle /ADEH/.

The A of a rectangle is L x B

A of /ADEH/ = 240.15cm²

Step 6 - Solving for total Area of the shaded region of the Octagon

The total area of the Shaded region /ACDEH/, therefore, is 240.15 + 85.49

= 325.64cm²


See the link below for more about Octagons:
https://brainly.com/question/4515567

Answer:

80x

hope it helpss.....