A cylinder has a volume of 675.1 cubic centimeters. The diameter of the cylinder is 10 cm. What is the height of the cylinder? (Assume = 3.14)

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

Explanation:

Note that m + 1/m and m^2 + 1/(m^2) are very similar. If we square (m + 1/m), then we end up with something in the form (a+b)^2 = a^2 + 2ab + b^2, where a = m and b = 1/m. The 2ab portion is equal to 2*m*(1/m) = 2 which allows us to isolate m^2 + 1/(m^2) fully.

The steps below show this

[tex]m + \frac{1}{m} = \sqrt{71}\\\\\left(m + \frac{1}{m}\right)^2 = \left(\sqrt{71}\right)^2\\\\m^2 + 2*m*\frac{1}{m} + \frac{1}{m^2} = 71\\\\m^2 + 2 + \frac{1}{m^2} = 71\\\\m^2 + 2 + \frac{1}{m^2} - 2 = 71-2\\\\m^2 + \frac{1}{m^2} = 69\\\\[/tex]

-------------

Alternatively, you can isolate m in the equation [tex]m + \frac{1}{m} = \sqrt{71}[/tex] to get two irrational solutions. Plug either solution into m^2 + 1/(m^2) and you should get the same result as above.

Answer:

50mph

Step-by-step explanation:

Speed=v

time=t

distance=s

v=s/t

v=300m/6h

v=50mph

Let me know if my answer is wrong.

Hope this helps :) ❤❤❤

Answer:

[tex]\boxed{Speed = 50 miles/hr}[/tex]

Step-by-step explanation:

Given:

Distance = S = 300 miles

Time = t = 6 hours

Required:

Average Speed = v = ?

Formula:

Average Speed = Total Distance Covered / Total Time Taken

Solution:

v = S/t

v = 300 miles / 6 hours

v = 50 miles/hr

Answer:

150 I believe but don't quote me on that

Answer:

a. 51

Step-by-step explanation:

[tex]t_{n} =a+(n-1)d[/tex]

201 = 1 + (n - 1)4

200 = (n - 1)4

50 = n - 1

51 = n

Answer:

C) g(x) is stretched vertically by a factor of 3 and translated to the right 7 units compared to ƒ(x).

Step-by-step explanation:

Notice that by transforming  [tex]f(x)=log_5\,(x)[/tex]  into [tex]g(x)=3\,log_5\,(x-7)[/tex] we have performed the following transformations:

a) a horizontal shift to the right 7 units by subtracting 7 from the x-variable, and

b) stretching the full function vertically by a factor of 3, by multiplying the full function by 3.

Therefore, our answer matches answer C in the list of possible options

Answer:

The distance of the midpoint of AB = 4 cm

The distance of the midpoint of CD = 28 cm

Step-by-step explanation:

The given information are;

Segment AD = 36

Point C and point B are points on AD such that AB:BC:CD = 2:3:4

Which gives;

The proportion of AB in AD = 2/(2+3+4) = 2/9

The length of AB = 2/9×36 = 8 cm

The proportion of BC in AD = 3/(2+3+4) = 3/9

The length of AD = 3/9×36 = 12 cm

The proportion of CD in AD = 3/(2+3+4) = 4/9

The length of AD = 4/9×36 = 16 cm

The coordinate of the midpoint of AB = 8/2 = 4 cm from A

The distance of the midpoint of AB = 4 cm

The coordinate of the midpoint of CD = 8 + 12 + 16/2 = 28 cm from A

The distance of the midpoint of CD = 28 cm.

Answer: the elementary 45

Step-by-step explanation: if you need anything else let me know

Explanation:

OQ = 10 is the radius, and so is segment RO. Both are the same length as they are the radii of the same circle. Triangle ORP has a leg of RO = 10 and a hypotenuse of PO = 26. The unknown side is PR = x.

Use the pythagorean theorem. We can use this theorem because the tangent formed (at point R) creates a 90 degree angle.

a^2 + b^2 = c^2

(PR)^2 + (RO)^2 = (PO)^2

x^2 + 10^2 = 26^2

x^2 + 100 = 676

x^2 = 676 - 100

x^2 = 576

x = sqrt(576) ... apply square root

x = 24

Answer:

..

-10 + 8× 119

= -10 + 952

= 942. .....

Answer:

236 (i think)

Step-by-step explanation:

cuz 0-10= -10+8= -2 X 119=236   (sorry if you cant read this my keyboard sucks

Answer:

[tex]\large \boxed{\sf \ \ 35.805 \ \ }[/tex]

Step-by-step explanation:

Hello,

First of all we need to find the intersection points of y = 12 and

[tex]y=f(x)=e^x+e^{-x}[/tex]

We need to solve the following equation.

[tex]e^x+e^{-x}=12\\\\\text{*** We multiply by }e^x\text{ both side ***}\\\\\left(e^x\right)^2+1=12e^x\\\\\text{*** Let's note } X =e^x\text{, it comes *** }\\\\X^2-12X+1=0[/tex]

[tex]\Delta=b^2-4ac=12^2-4=140=2^2\cdot 35\\\\X_1=\dfrac{12-2\sqrt{35}}{2}=6-\sqrt{35}\\\\X_2=\dfrac{12+2\sqrt{35}}{2}=6+\sqrt{35}\\[/tex]

And, we take the greater solution to solve:

[tex]X=e^x=6+\sqrt{35}<=>\boxed{x=ln(6+\sqrt{5})}[/tex]

Let's note it a.

Let's compute the integral.

We need to compute the following (because 12-f(x) is pair the integral that we are looking for is)

[tex]\displaystyle 2\int\limits^a_{0} {\left(12-(e^x+e^{-x})\right)} \, dx =12*(2a)-2\int\limits^a_{0} {(e^x+e^{-x})} \, dx \\\\=24a-2[e^x-e^{-x}]_{0}^a=24a-2(e^a-e^{-a})[/tex]

We can replace a by the value we already found.

[tex]24\cdot ln(6+\sqrt{35})-2\left( 6+\sqrt{35}-\dfrac{1}{6+\sqrt{35}}\right)\\\\=24\cdot ln(6+\sqrt{35})-2\left(6+\sqrt{35}-\dfrac{\sqrt{35}-6}{(\sqrt{35}-6)(\sqrt{35}+6)}\right)\\\\=24\cdot ln(6+\sqrt{35})-2\left(\dfrac{29*6+29*\sqrt{35}-\sqrt{35}+6}{29}\right)\\\\\\=24\cdot ln(6+\sqrt{35})-2\left(\dfrac{180+28\sqrt{35}}{29}\right)\\\\[/tex]

= 59.46933...-26.66432...=35.8050...

So the answer is [tex]\boxed{\sf \ \ 35.805 \ \ }[/tex]

Hope this helps.

Do not hesitate if you need further explanation.

Thank you

Answer:choice one

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

I did the test

Answer:

I need the numbers

Step-by-step explanation:

Answer:

m∠MNP = (x – y)

m∠MNP = (x + y)

m∠MNP = (z + y)

m∠MNP = (z – y)

Answer:

I plotted them for you!

The first dot (closest to the left) is 1 1/3 and the one closest to the right is 2 7/9 :)

Step-by-step explanation:

Hope this helped :) good luck!

Answer:

(-6,6), (0,12), (4,8)

Step-by-step explanation:

To dilate an object, we need to multiply the x and y values by the given scale factor.

In this case the scale factor is 2 --> 2(x, y)

Before-> After dilation

2(-3,3) = (-6,6)

2(0,6) = (0,12)

2(2,4) = (4,8)

Please leave a 'thanks' if this helps!

Answer:

x ≤ -1

Step-by-step explanation:

Answer:

Step-by-step explanation:

Slope intercept form :  y - y1 = m(x -x1)

m = 3/2

(x1, y1) = (6, 1)

[tex]y - 1 = \frac{3}{2}(x - 6)\\\\y -1 = \frac{3}{2}*x -\frac{3}{2}*6\\\\y-1=\frac{3}{2}x-3*3\\\\y-1=\frac{3}{2}x-9\\\\y=\frac{3}{2}x-9+1\\\\y=\frac{3}{2}x -8[/tex]

Answer:

y=3/2 x  -8

Step-by-step explanation:

The slope should be in front of the x and the y intercept should be right after the x to create the slope intercept form. I used a graphing calculator which continued the line of 6,1 with a slope of 3/2 and then got

y=3/2x-8

Answer:

B. AD = sqrt(CD * BD)

Step-by-step explanation:

By the right triangle altitude theorem,

CD/AD = AD/BD

AD^2 = CD * BD

AD = sqrt(CD * BD)

Answer: B. AD = sqrt(CD * BD)

Answer:

B

Step-by-step explanation:

[tex]$\frac{CD}{AD} =\frac{AD}{BD} $[/tex]

[tex]AD^2=CD \cdot BD[/tex]

[tex]AD=\sqrt{CD \cdot BD}[/tex]

In this question, you are clearly supposed to use the geometric mean theorem or known as the right triangle altitude theorem. But note that there are other approaches to find the height of the triangle.

Using Pythagorean theorem:

[tex]AD^2+CD^2=AC^2 \Rightarrow AD=\sqrt{AC^2-CD^2}[/tex]

Also,

[tex]AD=AC\sin(c)[/tex]

Hey there! I'm happy to help!

First, we arrange the numbers from least to greatest.

26,29,31,31,32,37,43

The median here is 31 because it is the middle number. The three numbers before it is one half of it and the last 3 numbers are their own half, because you cannot split the 31 between the two halves.

Now, we want to find the first quartile. This is basically the media of the first half of numbers. So, our first half consists of 26,29, and 31.

The middle number of this first half is 29.

So, our Q1 (first quartile) is 29.

Now, for the third quartile. We do the exact same thing here but with the second half.

32,37,43

Looking at this, our Q3 is 37

The interquartile range is how far apart Q1 and Q3 are, so to find it, we subtract our Q1 from the Q3.

37-29=48

Therefore, our IQR is 8.

Congratulations! Now you can find the IQR of a data set! Have a wonderful day! :D

Answer:

8

Step-by-step explanation:

You first put the numbers in order. Then you find the median(in this case, 31) and after that you find the Q1 and Q3(think of Q1 as the median of the lower half and Q3 as the mdian of the upper half.) Subtract Q1 from Q3, in this case, 37-29=8. 8 is the IQR or the interquratile range.

Answer:

First person ate 2.1 pounds and second person ate 4.8 pounds

Step-by-step explanation:

First we find the common denominator. So 3/5=12/20. 12/20+3/20+15/20. That means that 5/20=1.5 lb. So 1/20=.3 pounds. So person number one ate .9+1.2=2.1 pounds of candy and person number two ate 4.5+.3=4.8

Answer:

1. Multiply the first equation by 3

3(x + y ) = 3(-2)

3x + 3y - 6

2. Add 3x + 3y = - 6 ( obtained in step 1) to

2x - 3y = - 9 (given) and solve for x

3. x = - 3

4. Substitute the value of x in the first equation

( x + y = - 2) to get y = - 1

5. The solution for the linear system of equations is ( - 3 , 1)

Hope this helps you

Answer:

one cocoa pod makes 5/6 bar

to make 35 bars, he needs

35 / (5/6) = 35 * 6/5 = 42 pods

Monday - Friday is 5 days

42/5 = 8.4

Amount of the job done after 2 hours:

2(1/6 + 1/8)

2(4/24 + 3/24)

2(7/24)

7/12 (amount of job finished)

.

amount of job left to do:

1 - 7/12

12/12 - 7/12

5/12 (remaining)

.

Let x = time (hours) slower press takes to finish job

then

x(1/6) = 5/12

multiplying both sides by 6:

x = 5/12 *6

x = 5/2 hours

or

x = 2 hours and 30 minutes

The slower press (8-hour press), will take h 3 hours, 20 minutes to complete the job

Answer:

vertex (-4,-1)

2nd point ( 0,31)

Step-by-step explanation:

f(x) = 2x^2 + 16x + 31

First find the vertex

The x coordinate of the vertex is -b/2a  where ax^2 +bx +c

-16/ 2(2) = -16/4 = -4

Substitute into the function

f(-4) = 2 ( -4)^2 +16(-4) +31

       = 2 *16-64 + 31

       = 31 -64 +31

       = -1

The vertex is at ( -4,-1)

Another point can be x=0

f(0) = 0+16(0)+31

     = 31

( 0,31)

Answer:

0.53 is the right answer

Answer:

variation constant = k = 8

equation of variation : y = 8x

Step-by-step explanation:

Any relationship of variation can be written as y = kx

where k is the variation constant.

_______________________________________

Let the equationof relation between y and x be y =kx here as well

given

y = 16 when x = 2

substituting this value in the equation y = kx

16 = k*2

=> k = 16/2 = 8

Thus,

variation constant = k = 8

equation of variation : y = 8x

Answer:

v = 7

Step-by-step explanation:

a. v = 5x + 2y

= 5 × 3 + 2 × -4

= 15 + -8

= 7

Sorry I know only the A one anyways , hope this helps :)

Answer:

Step-by-step explanation:

a  v = 5x+ 2y = 5*3 + 2*-4 = 7

b 3p(p+5) = 3p^2 =15p

c 4k = 44

k=44/4 =11

i hope the person who had deleted my answer this much explanation is only required if not please say so that I can correct myself by ellaborating ...

The correct option is A. The equation in point-slope form for the line perpendicular to y = -2x + 8 and passing through (-3, 9) is: y - 9 = 1/2(x + 3).

To find the equation of a line perpendicular to y = -2x + 8 that passes through the point (-3, 9), we need to determine the slope of the perpendicular line.

The given equation is in slope-intercept form, y = mx + b, where m represents the slope. In this case, the slope of the given line is -2.

Since the perpendicular line has a slope that is the negative reciprocal of -2, we can determine its slope as 1/2.

Now that we have the slope (1/2) and a point (-3, 9) on the line, we can use the point-slope form of a line to write the equation:

y - y₁ = m(x - x₁)

where (x₁, y₁) is the given point and m is the slope.

Plugging in the values, we get:

y - 9 = 1/2(x - (-3))

Simplifying:

y - 9 = 1/2(x + 3)

Rearranging to match the given options:

y - 9 = 1/2(x) + 3/2

The equation in point-slope form for the line perpendicular to y = -2x + 8 and passing through (-3, 9) is:

y - 9 = 1/2(x + 3)

Therefore, the correct option is A.

Learn more about equation here

https://brainly.com/question/17126696

#SPJ2

Complete question is below

Identify an equation in point-slope form for the line perpendicular to

y=-2x+ 8 that passes through (-3,9).

A. y - 9 = 1/2(x+3)

B. y+3 = 3(x-9)

C. y - 9 = (x + 2)

D. y + 9 = 1/2(x – 3)

Answer:

Rotation

Step-by-step explanation:

when you rotate a point it swaps the numarical values x⇄y as well as in some cases it changes its the symbol from negative to positive depending on the quadrant, in this case, it started in quadrant one and ended in quadrant three.

The mass of water will be - 3785.41 grams.

We have density of water is 1.00 g/ml.

We have to determine the mass in grams of 1.00 gal of water.

The relation between Mass (m) and Density (ρ) is -

m = ρV

where -  V is the volume of object.

According to the question -

Density of water -  1.00 g/ml

Volume of water -  1 gallon = 3785.41 ml

m = ρV

m = 1 x 3785.41 = 3785.41 grams.

Hence, the mass of water will be - 3785.41 grams.

To solve more questions on Mass and Density, visit the link below -

https://brainly.com/question/24641072

#SPJ2