Find the volume of the cylinder. Round your answer to the nearest tenth.
8 m
10 m

Answer:

[tex] \rm\displaystyle \displaystyle \displaystyle θ= {60}^{ \circ} , {300}^{ \circ} [/tex]

[tex] \rm \displaystyle a = - \frac{ \sqrt{3} }{2} - 1, \frac{\sqrt{3}}{2} - 1[/tex]

Step-by-step explanation:

we are given two coincident points

[tex] \displaystyle P( \sin(θ)+2, \tan(θ)-2) \: \text{and } \\ \displaystyle Q(4 \sin ^{2} (θ)+4 \sin(θ) \cos(θ)+2a \cos(θ), 3 \sin(θ)-2 \cos(θ)+a)[/tex]

since they are coincident points

[tex] \rm \displaystyle P( \sin(θ)+2, \tan(θ)-2) = \displaystyle Q(4 \sin ^{2} (θ)+4 \sin(θ )\cos(θ)+2a \cos(θ), 3 \sin(θ)-2 \cos(θ)+a)[/tex]

By order pair we obtain:

[tex] \begin{cases} \rm\displaystyle \displaystyle 4 \sin ^{2} (θ)+4 \sin(θ) \cos(θ)+2a \cos(θ) = \sin( \theta) + 2 \\ \\ \displaystyle 3 \sin( \theta) - 2 \cos( \theta) + a = \tan( \theta) - 2\end{cases}[/tex]

now we end up with a simultaneous equation as we have two variables

to figure out the simultaneous equation we can consider using substitution method

to do so, make a the subject of the equation.therefore from the second equation we acquire:

[tex] \begin{cases} \rm\displaystyle \displaystyle 4 \sin ^{2} (θ)+4 \sinθ \cos(θ)+2a \cos(θ )= \sin( \theta) + 2 \\ \\ \boxed{\displaystyle a = \tan( \theta) - 2 - 3 \sin( \theta) + 2 \cos( \theta) } \end{cases}[/tex]

now substitute:

[tex] \rm\displaystyle \displaystyle 4 \sin ^{2} (θ)+4 \sin(θ) \cos(θ)+2 \cos(θ) \{\tan( \theta) - 2 - 3 \sin( \theta) + 2 \cos( \theta) \}= \sin( \theta) + 2 [/tex]

distribute:

[tex]\rm\displaystyle \displaystyle 4 \sin ^{2}( θ)+4 \sin(θ) \cos(θ)+2 \sin(θ ) - 4\cos( \theta) - 6 \sin( \theta) \cos( \theta) + 4 \cos ^{2} ( \theta) = \sin( \theta) + 2 [/tex]

collect like terms:

[tex]\rm\displaystyle \displaystyle 4 \sin ^{2}( θ) - 2\sin(θ) \cos(θ)+2 \sin(θ ) - 4\cos( \theta) + 4 \cos ^{2} ( \theta) = \sin( \theta) + 2 [/tex]

rearrange:

[tex]\rm\displaystyle \displaystyle 4 \sin ^{2}( θ) + 4 \cos ^{2} ( \theta) - 2\sin(θ) \cos(θ)+2 \sin(θ ) - 4\cos( \theta) + = \sin( \theta) + 2 [/tex]

by Pythagorean theorem we obtain:

[tex]\rm\displaystyle \displaystyle 4 - 2\sin(θ) \cos(θ)+2 \sin(θ ) - 4\cos( \theta) = \sin( \theta) + 2 [/tex]

cancel 4 from both sides:

[tex]\rm\displaystyle \displaystyle - 2\sin(θ) \cos(θ)+2 \sin(θ ) - 4\cos( \theta) = \sin( \theta) - 2[/tex]

move right hand side expression to left hand side and change its sign:

[tex]\rm\displaystyle \displaystyle - 2\sin(θ) \cos(θ)+\sin(θ ) - 4\cos( \theta) + 2 = 0[/tex]

factor out sin:

[tex]\rm\displaystyle \displaystyle \sin (θ) (- 2 \cos(θ)+1) - 4\cos( \theta) + 2 = 0[/tex]

factor out 2:

[tex]\rm\displaystyle \displaystyle \sin (θ) (- 2 \cos(θ)+1) + 2(- 2\cos( \theta) + 1 ) = 0[/tex]

group:

[tex]\rm\displaystyle \displaystyle ( \sin (θ) + 2)(- 2 \cos(θ)+1) = 0[/tex]

factor out -1:

[tex]\rm\displaystyle \displaystyle - ( \sin (θ) + 2)(2 \cos(θ) - 1) = 0[/tex]

divide both sides by -1:

[tex]\rm\displaystyle \displaystyle ( \sin (θ) + 2)(2 \cos(θ) - 1) = 0[/tex]

by Zero product property we acquire:

[tex] \begin{cases}\rm\displaystyle \displaystyle \sin (θ) + 2 = 0 \\ \displaystyle2 \cos(θ) - 1= 0 \end{cases}[/tex]

cancel 2 from the first equation and add 1 to the second equation since -1≤sinθ≤1 the first equation is false for any value of theta

[tex] \begin{cases}\rm\displaystyle \displaystyle \sin (θ) \neq - 2 \\ \displaystyle2 \cos(θ) = 1\end{cases}[/tex]

divide both sides by 2:

[tex] \rm\displaystyle \displaystyle \displaystyle \cos(θ) = \frac{1}{2}[/tex]

by unit circle we get:

[tex] \rm\displaystyle \displaystyle \displaystyle θ= {60}^{ \circ} , {300}^{ \circ} [/tex]

so when θ is 60° a is:

[tex] \rm \displaystyle a = \tan( {60}^{ \circ} ) - 2 - 3 \sin( {60}^{ \circ} ) + 2 \cos( {60}^{ \circ} ) [/tex]

recall unit circle:

[tex] \rm \displaystyle a = \sqrt{3} - 2 - \frac{ 3\sqrt{3} }{2} + 2 \cdot \frac{1}{2} [/tex]

simplify which yields:

[tex] \rm \displaystyle a = - \frac{ \sqrt{3} }{2} - 1[/tex]

when θ is 300°

[tex] \rm \displaystyle a = \tan( {300}^{ \circ} ) - 2 - 3 \sin( {300}^{ \circ} ) + 2 \cos( {300}^{ \circ} ) [/tex]

remember unit circle:

[tex] \rm \displaystyle a = - \sqrt{3} - 2 + \frac{3\sqrt{ 3} }{2} + 2 \cdot \frac{1}{2} [/tex]

simplify which yields:

[tex] \rm \displaystyle a = \frac{ \sqrt{3} }{2} - 1[/tex]

and we are done!

disclaimer: also refer the attachment I did it first before answering the question

Answer:

[tex]y=\frac{4}{3}x -8[/tex]

Step-by-step explanation:

So first find the slope of the given line

-2 - 4 = -6

4 + 4 = 8

-6 ÷ 8 = [tex]-\frac{3}{4}[/tex]

The slope of a line perpendicular to another line is the opposite reciprocal of the given slope.

The opposite reciprocal of [tex]-\frac{3}{4}[/tex] is [tex]\frac{4}{3}[/tex]

So now all we need to finish the slope intercept form y = mx + b is b, which is the y intercept.

[tex]y=\frac{4}{3}x+b[/tex]

Now that they give us the X intercept, you can plug in the values (6, 0).

[tex]0=8+b[/tex]

b = -8

Answer:

37 inches

Step-by-step explanation:

to get 37 inches, you need to add 24 and 13. so 24+13 would equal 37.

Answer:

8 months and $320

Step-by-step explanation:

To find when 30m + 80 = 40m, isolate m.

30m + 80 = 40m

Subtract 40m from both sides.

-10m + 80 = 0

Subtract 80 from both sides.

-10m = -80

Divide both sides by -10

m = 8

To find the cost, substitute 8 as m in one of the equations.

40(8) = 320

Answer:

1/14

Step-by-step explanation:

There is only 1 common multiple of 4 and 6 between 1 and 14.

So the probability is:

[tex]P = \frac{1}{14}[/tex]

Answer:

5/14

Step-by-step explanation:

the multiples of 6 are 6 and 12. the multiples of 4 are 4,8,12(but its the same as 4 so we don't add that one), and 14. Add 2 and 3 and you get 5.

The total is 14 so it ends up being a 5/14 chance.

Answer: 22 batches of chocolate chip cookies

Step-by-step explanation:

A batch of cookies can take 0.25 cups of sugar to make.

You instead have 5.50 cups of sugar.

The number of batches that can be made is:

= Total amount of sugar available / Amount of sugar required for one batch

= 5.50 / 0.25

= 22 batches of chocolate chip cookies

Answer:

A translation of 5 units to the right, followed by a reflection across the x axis.

Answer:answer is 2.5v+5<5v A.k.a:A

Step-by-step explanation:

Answer:

10,000 * (0.5)^x/19 ; 19.53125

Step-by-step explanation:

Sorry, Im not good at chemistry, but I think this is how you do it.

Part 1: 10,000 * (0.5)^x/19 x=time

Part 2: 10,000 * (0.5)^171/19 = 10,000 *(0.5)^9 = 19.53125

Answer:

1.86

Step-by-step explanation:

Since decimals are the same as fractions, we can convert 4/5 to .80. And since "of" means multiply, we can convert .80 of 9.3 to:

.8 x 9.3 = 7.44

This is the amount of pears, so we subtract:

9.3 - 7.44 = 1.86

The weight of the apples is 1.86.

Answer:

What?

Step-by-step explanation:

G8ve me more info and Ill answer again

Answer:

There is a little over 1 gallon

Step-by-step explanation:

Answer:

400 & 2

Step-by-step explanation:

Alright, so for the first question you do 14 + 6 which = 20 and if you do 20 × 20, it equals 400.

And for the second one 14 - 12= 2.

Answer:

71

Step-by-step explanation:

ndndnrbrjen3n3nn3b2n2b2b

Answer:

8 1/3 or 8.33 yards per second

Step-by-step explanation:

100/12 = 8 1/3

Answer:

m<BAC = 34

Step-by-step explanation:

It is given that (<BOC) is a central angle with a degree measure of (68). A central angle is an angle whose vertex is the center of the circle. (<BAC) is an inscribed angle, an angle whose vertex is on the circumference (perimeter) of the circle. Arc (BC) connects the ends of both of these angles.

The central angle theorem states that the measure of the central angle is equivalent to its surrounding arc. Using this theorem, one can state the following,

m<BOC = BC = 68

The inscribe angle theorem states that the measure of the arc surrounding the inscribed angle is twice the measure of the inscribed angle. Applying this theorem, one can state the following,

2(m<BAC) = (BC)

2 (m<BAC) = 68

m<BAC = 34

Answer:

-|7|, |4|, |2-9|, |6+4|

Step-by-step explanation:

I think this is correct

Answer:

Taking 45 degree as reference angle

Then using sine rule

sin 45=

p/h

replacing the value of sin 45 degree by 1/root 2.so

1/root 2=9/c

doing cross multiplication

9*root 2=1*c

9 root 2 =c

therefore the value of c is 9 root 2

Step-by-step explanation:

Answer:

D. and F.

Step-by-step explanation:

Answer:

The angle between the two blades is 120 degree.

Step-by-step explanation:

number of blades = 3

The blades are equally spaced.

The total angle around a circle is 360 degree.

So, the angle between the two blades is given by

[tex]\theta =\frac{360}{n}\\\theta =\frac{360}{3} = 120^{o}[/tex]

Answer:

The first ">" should be underlined in the equation.

..

The rules for solving inequalities are the same as those used for solving regular equations except for one important rule, that is, when you multiply both sides of an inequality by -1, the inequality sign reverses.

..

5-4x≥17

-4x≥12

-x≥3

Step-by-step explanation:

Answer:

hope it helps.

Answer:

x=0, y=-2

Step-by-step explanation:

6x0=0

2(-2)=-4

so, -4=-4 so it is determined true

Then 0-2(-2), -2(-2)=4

subtract 0 from 4 which is 4

so, 4=4, so it is determined true

Answer:

Its A let me know if im wrong!

Answer:

Fourth option is most suitable here.

Answer:

hope this helps

Step-by-step explanation:

31 divided by 2 = 15.5 then do 15.5 x 15.5= 240.25 then you do 240.25 x 3.14 = 754.385

Answer:

m=  1/2

y=1

Step-by-step explanation:

you go up 2 over 4 but you simplify it to 1/2

you then go to the first point for y intercept, which is 1 (because it follow the patteren)

Answer:

Step-by-step explanation:

Use the volume of a sphere formula and then multiply it by .5 to get half of it, since a hemisphere is half of a sphere. Doing that gives us the formula:

[tex]V=\frac{4}{3}\pi r^3\frac{1}{2}[/tex] which simplifies to

[tex]V=\frac{2}{3}\pi r^3[/tex] . Now, filling in what we were given:

[tex]45729=\frac{2}{3}\pi r^3[/tex] which simplifies a bit to

[tex]137187=2\pi r^3[/tex]. We divide by 2π to get

[tex]2183.98918=r^3[/tex] and take the cubed root on your calculator to get that

r = 27.9"

[tex]Volume= 45729in^3\\\\[/tex]

[tex]Radius=r[/tex]

[tex]2/3\pi r^3=45729[/tex]

[tex]r^3=3*45729\\~~~~------\\~~~~~~2*3.14[/tex]

[tex]r^3=21845.06[/tex]

[tex]r=27.95~in[/tex]

hope it helps...

have a great day!!

Number of years to make a worth of $45000 with Depreciation rate of 12% and Total worth $45000 is 4 years

Years= 4 year

The term depreciation refers to an accounting method used to allocate the cost of a tangible or physical asset over its useful life. Depreciation represents how much of an asset's value has been used. It allows companies to earn revenue from the assets they own by paying for them over a certain period of time.

Given that:

limousine costs $75000

Depreciation rate = 12% per year= 0.12

Total worth= $45000

By using the formula for year we have

total worth = cost of object [tex](1- Depreciation \;rate)^{year}[/tex]

45000= 75000x [tex](1-0.12)^{year}[/tex]

0.6= [tex](0.88)^{year}[/tex]

Now taking log on both side we have

log 0.6= year x  log0.88

-0.2218 = year x -0.05551

year= 4.049

year≈ 4 year(rounding off nearest year)

Learn more about depreciation here:

https://brainly.com/question/14682335

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