Ten turns of a wire are helically wrapped around a cylindrical tube with outside circumference 4 inches and length 9 inches. The ends of the wire coincide with ends of the same cylindrical element. Find the length of the wire. (a) 41 inches (b)36 inches (c) 40 inches (d) 90 inches

Answers

Answer 1

Answer:

b) 36 inches

Step-by-step explanation:

Length  of the  wire = Outside circumference of the cylindrical tube * length of the cylinder

= 4 * 9

= 36 inches

Length of the wire will be same to the surface area of the cylinder

Surface area of cylinder = circumference * length


Related Questions

The nth term of a geometric sequence is a sub n =a sub 1 times r ^n-1 , where a sub 1 is the first term and r is the common ratio. Identify a sub 1 and r for each geometric sequence.

Answers

Answer/Step-by-step explanation:

Common ratio of a sequence can be gotten by dividing any of the consecutive term in a sequence, by the term before it.

Thus,

For the sequence, [tex] 3, 9, 27. . . [/tex] : [tex] a_1 = 3 [/tex]

[tex] r = \frac{9}{3} = 3 [/tex]

For the sequence, [tex] 8, 4, 2, 1. . . [/tex] : [tex] a_1 = 8 [/tex]

[tex] r = \frac{4}{8} = \frac{1}{2} [/tex]

For the sequence, [tex] -16, 64, -256 . . [/tex] : [tex] a_1 = -16 [/tex]

[tex] r = \frac{64}{-16} = -4 [/tex]

Convert 125 degrees into radians. (NEED ASAP)

Answers

Answer:

[tex]\boxed{\frac{25\pi }{36}}[/tex]

Step-by-step explanation:

Use the formula to convert from degrees to radians: [tex]x * \frac{\pi }{180}[/tex], where x is the value in degrees.

[tex]125 * \frac{\pi }{180}[/tex] = [tex]\frac{125\pi }{180}[/tex]

Then, simplify your fraction ⇒ [tex]\frac{125\pi }{180} = \boxed{\frac{25\pi}{36} }[/tex]

Kite A B C D is shown. Lines are drawn from point A to point C and from point B to point D and intersect. In the kite, AC = 10 and BD = 6. What is the area of kite ABCD? 15 square units 30 square units 45 square units 60 square units

Answers

Answer:

[tex]30 u^{2}[/tex]

Step-by-step explanation:

The computation of the area of kite ABCD is shown below:

Given data

AC = 10 ;

BD = 6

As we can see from the attached figure that the Kite is a quadrilateral as it involves two adjacent sides i.e to be equal

Now the area of quadrilateral when the diagonals are given

So, it is

[tex]\text { area of kite }=\frac{1}{2} \times d_{1} d_{2}[/tex]

where,

[tex]d_{1}=10\ and\ d_{2}=6[/tex]

So, the area of the quadrilateral is

[tex]=\frac{1}{2}(10)(6)\\\\=30 u^{2}[/tex]

Answer:

C

Step-by-step explanation:

I just took the test

Write 2(6² + 4²) as the sum of two perfect square.

Answers

Answer 114
2(6*6+4*4)=2(36+16)=2*52=114

sin theta=-1/2 then cos theta=​

Answers

Answer:

cos 30°= 0.866

Step-by-step explanation:

Step one:

Applying the SOH CAH TOA principle

assuming all dimensions are in cm

Step two:

Given data

opposite= 1 cm

hypotenuse= 2 cm

we can now solve for θ

Sin(θ)= opp/hyp

Sin(θ)= 1/2

Sin(θ)= 0.5

θ= sin-1 0.5

θ= 30°

hence  from tables cos 30°= 0.866

I REALLY NEED HELP! PLEASE help me...

Answers

Answer:

A. The domain is (1,∞), and the range is (-7,∞)

Step-by-step explanation:

Well lets graph it first,

Look at the image below ↓

By looking at the image we move it 3 units right and 3 units down.

Then it will be located at the point (1,-7).

Meaning for the domain it starts at 1 and goes on for infinity.

And For the range it starts down at -7 and goes down for infinity.

Thus,

the correct answer is choice A.

Hope this helps :)

Answer:

A

Step-by-step explanation:

Solution:-

- First we will go through the guidelines that are followed when a given function [ f ( x ) ] is translated in a cartesian coordinate system domain.

Horizontal shifts:

Left shift: f ( x ) - > f ( x + a ). Right Shift: f ( x ) - > f ( x - a )    

Where, the constant ( a ) denotes the magnitude of shift  

Vertical shifts:

Up shift: f ( x ) - > f ( x ) + bDown Shift: f ( x ) - > f ( x ) - b    

Where, the constant ( b ) denotes the magnitude of shift  

- The generalized form of a translated function is defined by the combination of both horizontal and vertical shifts as follows:

                    General: f ( x ) -> f ( x ± a ) ± b

Where, (a) and (b) are constants of respective translation shifts.

- We are given a function H ( x ) is to be translated 3 units to right and 3 units down. Use the above guidelines to determine the translated function H* ( x ) as follows:

                    [tex]H ( x ) = \sqrt{x+2} - 4\\\\H^* ( x ) = H ( x - 3 ) - 3[/tex]

- Substitute ( x - 3 ) in place of all ( x ) in the given function H ( x ) and subtract ( 3 ) from H ( x ) as follows:

                   [tex]H^* ( x ) = \sqrt{x-3 + 2} -4 - 3\\\\H^* ( x ) = \sqrt{x-1} -7\\[/tex]

- Now we will look for any transcendental functions in the translated function H*(x). These are " Radicals, fractions, Logs, trigonometric ratios "

- We have a radical - > " square root " in H* ( x ). To find the domain of H*(x) we need to determine for what real values of x is the function H*(x) is defined.

- The square root exist for all only positive numbers. So the terms under the square root must be positive; hence,

                     [tex]x - 1 \geq 0\\\\x \geq 1[/tex]

- Since the square root is the only transcendental in the given function H*(x) we have a one sided closed interval for the domain of the translated function.

                    Domain: [ 1 , ∞ )       ... Answer  

- The range of the function is the corresponding output of function H*(x) for the domain established above. We can determine this by plugging in the end-points of the defined domain in the translated function H*(x) as follows:

                    [tex]H^* ( 1 ) = \sqrt{1 - 1} - 7 = -7\\\\H^* ( inf ) = \sqrt{inf - 1} - 7 = inf - 7 = inf\\\\[/tex]

Therefore the range of the function is also a one sided closed interval bounded by x = 1.

                    Range: [-7 , ∞ )       ... Answer

How many solutions does this system have? 6 x + 3 y = negative 12. y = negative 2 x + 4. one two an infinite number no solution

Answers

Answer:

work is shown and pictured

Write two equivalent expressions using the commutative property that can be used to find the total number of points Dean Scored on his math test

Answers

Answer:

2

Step-by-step explanation:

pyramid.
In the adjoining solid, a square based pyramid is
situated on the top of a square based cuboid so that
the total height of the solid is 15 cm. If the volume
of the pyramid and cuboid are 300 cm and 600 cm
respectively, find the height of the pyramid.
15 cm
adean of the same
The heich​

Answers

Answer:

9 cm.

Step-by-step explanation:

Let the height of the pyramid be h cm, then the height of the cuboid is (15 - h) cm.

Volume of the pyramid:

= 1/3 * h * s^2      where s is the length of a side of the square base.

= hs^2/3 cm^3

Volume of the cuboid:

= s^2(15 - h).

So we have:

hs^2/ 3 = 300.......................(1)

s^2(15 - h) = 600..................(2)

From  equation (1) :

h s^2 = 900

s^2 = 900/h

Now substitute for s^2 in  equation (2) :

(900/h)(15 - h) = 600

Multiply through by h:

900(15 - h) = 600h

13500 - 900h = 600h

1500h = 13500

h = 9 cm (answer).

If the total height of the solid is 15 cm. If the volume of the pyramid and cuboid are 300 cm and 600 cm respectively, then height of pyramid is 9cm.

What is Three dimensional shape?

a three dimensional shape can be defined as a solid figure or an object or shape that has three dimensions—length, width, and height.

Let the height of the pyramid be h cm, then the height of the cuboid is (15 - h) cm.

Volume of the pyramid:

300= 1/3 ×h×s²  

300= hs²/3

hs²=900

Volume of the cuboid:

600= s² (15 - h).

600=15s²-hs²

600=15s²-900

600+900=15s²

1500=15s²

100=s²

s=10

Now substitute s value in hs²=900

h(100)=900

Divide both sides by 100

h=9cm

Hence height of the pyramid is 9cm.

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if p(x) = x+ 7/ x-1 and q (x) = x^2 + x - 2, what is the product of p(3) and q(2)? a. 50 b. 45 c. 40 d. 20 e. 6

Answers

Answer:

d. 20

Step-by-step explanation:

To answer the question given, we will follow the steps below:

we need to first find p(3)

p(x) = x+ 7/ x-1

we will replace all x by 3 in the equation above

p(3) = 3+7 / 3-1

p(3) = 10/2

p(3) = 5

Similarly to find q(2)

q (x) = x^2 + x - 2,

we will replace x by 2 in the equation above

q (2) = 2^2 + 2 - 2

q (2) = 4 + 0

q (2) = 4

The product of p(3) and q(2)   =   5 × 4   = 20

Write an expression for the volume and simplify your answer. 3x x+1 x+4

Answers

Answer:

volume=3x³+15x²+12x

Step-by-step explanation:

v= l*w*h =(3x )(x+1) (x+4)

v=3x(x²+5x+4)

volume=3x³+15x²+12x

A constant force of 85 N accelerates towards a 10 kg box from a speed of 3.0 m/s to a speed of 7.0 m/s as it goes 14 m along a horizontal floor. What is the coefficient of friction between the box and the floor?

Answers

Answer:

Step-by-step explanation:

Let us find the acceleration of box .  

v² = u² + 2as

Putting the values

7² = 3² + 2 a x 14

a = 1.43 m /s²

If coefficient of friction be μ

force of friction = μ mg

= μ x 10 x 9.8

= 98μ

Net force pushing the box

= 85 - 98μ

Applying newton's second law

85 - 98μ = 10 x 1.43

98μ = 85 - 14.3

μ = .72

Heather used a graphing utility to find the equation of the line of best fit in this scatter plot. VA PW1ALG131_Using Models from Data After reading equation of the line from the graphing utility, Heather wrote in her notebook that the line of best fit is represented by the equation y = 0.77x + 1.34. Heather likely an error when writing the equation of the line in her notebook because the slope and the y-intercept of the equation she recorded.

Answers

The answers are did not make, and both the slope and the y-intercept match if the line of the best fit is represented by the equation y = 0.77x + 1.34

What is the line of best fit?

A mathematical notion called the line of the best fit connects points spread throughout a graph. It's a type of linear regression that uses scatter data to figure out the best way to define the dots' relationship.

We have a line of best fit:

y = 0.77x + 1.34

Here the slope of the line is 0.77 and y-intercept is 1.34

From the graph and line of best fit, we can say heather did not make an error when writing the equation of the line in her notebook because both the slope and the y-intercept match the slope and the y-intercept of the equation she recorded

Thus, the answers are did not make, and both the slope and the y-intercept match if the line of the best fit is represented by the equation y = 0.77x + 1.34

Learn more about the line of best fit here:

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Answer:

Heather likely did not make an error when writing the equation of the line in her notebook because both the slope and the y-intercept match the slope and the y-intercept of the equation she recorded.

Write the following as an inequality:
y is no greater than 4 but more than -2.

Answers

Answer:

4>Y>-2 :) ..............

Answer:

[tex]\boxed{-2 < y \leq 4}[/tex]

Step-by-step explanation:

For y is no greater than 4, it would be either less than or equal to 4. So, the inequality for it would be:

y ≤ 4

Now, the inequality for y more than -2:

-2 < y

Combining the inequality:

-2 < y ≤ 4

What is 1/9 of 63% of 6000?

Answers

Answer:

420

Step-by-step explanation:

To find 63% of 6000, we can do 0.63 * 6000 = 3780 because 63% = 0.63.

1/9th of that is 1/9 * 3780 = 420.

Answer:

420

Step-by-step explanation:

Let's first start by finding 63% of 6000 so we can later find 1/9 of that number.

We can set up a percentage proportion.

[tex]\frac{x}{6000} = \frac{63}{100}[/tex]

[tex]6000\cdot63=378000\\378000\div100 = 3780[/tex]

Now to find 1/9 of 3780.

[tex]\frac{1}{9} \cdot \frac{3780}{1}\\\\\frac{3780}{9} = 420[/tex]

So, the answer is 420.

Hope this helped!

Use the first three terms of the binomial theorem to approximate 3.5^6.

Answers

Answer:

2065.5

Step-by-step explanation:

You have to approximate the following calculation 3.5^6

The binomial theorem is given by:

[tex](a+b)^n=\Sigma_{k=0}^{k=n}\left[\begin{array}{c}n&k\end{array}\right] a^{n-k}b^k[/tex]      (1)

You can express the number 3as follow:

[tex]3.5^6=(3+0.5)^6=(3+\frac{1}{2})^6[/tex]          (2)

by comparing the equation (1) with the equation (2) you have

a = 3

b = 1/2

To calculate the first three terms of the binomial theorem you use k=3. You replace the values of a, b, n and k in the equation (1):

[tex](3+\frac{1}{2})^6=\Sigma_{k=0}^{k=6}\left[\begin{array}{c}6&k\end{array}\right] (3)^{6-k}b^k[/tex]

You only take the first three terms:

[tex](3+\frac{1}{2}^6)\approx(1)(3)^6(\frac{1}{2})^0+(6)(3)^5(\frac{1}{2})^1+\frac{6\cdot 5}{1\cdot 2}(3)^4(\frac{1}{2})^2\\\\(3+\frac{1}{2}^6)\approx729+729+\frac{1215}{2}=2065.5[/tex]

By using the first three terms of bynomial theorem you obtain 2065.5

A steady stream of water flows into a partially-filled rectangular tank. After 6 minutes, there are 87 gallons of water in the tank. After 21 minutes, there are 222 gallons. Write an equation to represent the volume of water in the tank y after x minutes. How much water was in the tank to begin?

Answers

Answer: y=9x+33

33 gallons of water to begin with.

Step-by-step explanation:

So we essentially are given two coordinates: (6,87) and (21,222). To find an equation, we simply need to find the slope and y-intercept. We know it's a linear equation because it's a steady stream, meaning a constant slope.

The slope is:

So, the rate at which the stream flows is 9 gallons per minute.

Now, let's find the initial amount of water. To do this, we can use point-slope form. Pick either of the two points. I'm going to use (6,87).

So, there were 33 gallons of water in the tank to begin with.

Answer:

There were 33 gallons.

Step-by-step explanation:

Please help me!!!! I really need help!!

Answers

Answer:

A. 25°

Hope it helped

Write 10:5 as a ratio in its simplest form

Answers

Answer:

its simplest form for the question is 2:1

Question 5 of 10
Which of the following is the converse of the statement "If it is summer, then
it is warm outside"?
A. If it is warm outside, then it is summer.
B. If it is not warm outside, then it is summer.
O
C. If it is warm outside, then it is not summer.
D. If it is not warm outside, then it is not summer.
hs

Answers

Answer:

If it is warm outside, then it is summer

Step-by-step explanation:

To find the converse, interchange the hypothesis and the conclusion

"If it is summer, then it is warm outside"

If it is warm outside, then it is summer

Answer:

A. If it is warm outside, then it is summer

Step-by-step explanation:

statement "If it is summer, then it is warm outside" : warm=summer

A. If it is warm outside, then it is summer. : warm = summer ✓

B. If it is not warm outside, then it is summer. : not warm = summer x

C. If it is warm outside, then it is not summer. : warm =not  summer x

D. If it is not warm outside, then it is not summer. : not warm = not summer x

The equation of line l is -3y+4x=9 Write the equation of a line that is parallel to line l and passes through the point (-12,6). a) -3y+4x-69=0 b)-3y+4x-69=0 c)-3y+4x-39=0 d) 3x-3y+66=0

Answers

Step-by-step explanation:

Equation of a line is y = mx + c

where

m is the slope

c is the y intercept

- 3y + 4x = 9

3y = 4x - 9

Divide both sides by 3

y = 4/3x - 3

Comparing with the above formula

Slope / m = 4/3

Since the lines are parallel their slope are also the same

So slope of the parallel line l is also 4/3

Equation of the line using point (-12 , 6) is

y - 6 = 4/3(x + 12)

Multiply through by 3

That's

3y - 18 = 4(x + 12)

3y - 18 = 4x + 48

We have the final answer as

4x - 3y + 66 = 0

Hope this helps you

Please help I really need to get it right

Answers

Answer:

Alternate interior angles.

17x + 6 = 18x - 1.

x = 7.

Step-by-step explanation:

According to the diagram below, the angles are alternate interior angles.

Since they are alternate interior angles, they are congruent. So, 17x + 6 = 18x - 1.

17x + 6 = 18x - 1

18x - 1 = 17x + 6

x = 7

Hope this helps!

A box with an open top is to be constructed from a square piece ofcardboard, with sides 6 meters in length, by cutting a square from each of the fourcorners and bending up the sides. Find the dimensions that maximize the volume ofthe box and the maximum volume.

Answers

Answer:

Step-by-step explanation:

Let x be the height of the box . x will be cut at four corners .

each side of the box = 6 - 2x

volume of box V = ( 6 - 2 x )² x

V = ( 36 + 4 x² - 24 x ) x

V = 4x³ - 24 x ² + 36 x

For maximum volume

dV / dx = 12 x² - 48 x + 36 = 0

x² - 4 x + 3 = 0

( x - 3 ) ( x - 1 ) = 0

x = 1 , x = 3 ( not possible )

Possible solution x = 1

Volume  , for x = 1

V = V = ( 6 - 2 x )² x

V = 4² x 1

= 16 m³.

defg is a dilation image of defg which is the correct description of the dilation

Answers

Answer: Center D I think

Step-by-step explanation:

Jack challenged Jill to a race around a curve of a track. Jack took lane 8 with Jill at lane 1. If the radius of lane 1 is half of lane 8, what is the distance in metres Jack has to run if Jill ran a distance of 50m?

Answers

Answer:jac ganko

Step-by-step explanation:

25m if it’s half the length of 8

I NEED HELP PLZ Event A and event B are independent events. Given that P(B)=13 and P(A∩B)=16, what is P(A)?

Answers

Answer:

19

Step-by-step explanation:

The tee for the fifth hole on a golf course is 375 yards from the tee. On that hole, Marsha hooked her ball to the left, as sketched below. Find the distance between Marsha’s ball and the hole to the nearest tenth of a yard.

Answers

Answer:

158.73 yd

Step-by-step explanation:

A picture of the situation is needed, investigating I could find a related one, in the same way the important thing is the solution, the data can be exchanged. I attach the drawing.

Let use the formula of the law of cosine:

c ^ 2 = a ^ 2 + b ^ 2 - 2 * a * b * cos C, to solve the problem

Let the third side be c, we replace:

c ^ 2 = 375 ^ 2 + 240 ^ 2 - 2 * 375 * 240 * cos 16 °

c ^ 2 = 198225 - 173027.10

c ^ 2 = 25197.9

c = 158.73

So the distance is 158.73 yd

Answer: the right answer is 195.4

Step-by-step explanation: this guy does not what's happening

PLEASE HELP: Which is a compound event?

Answers

Answer:

The correct option is;

Heads lands 3 times and tales lands 5 times in 8 coin flips

Step-by-step explanation:

A compound event is one in which the probability of more than one outcome or event to have occurred at the same time is sought. The probability of a compound event is the sum of the probabilities of the individual events less the probabilities already captured in both event probabilities

Answering compound event questions can be done by the use of a tabular or diagram format.

Therefore, the compound event in the list is heads lands 3 times and tales lands 5 times in 8 coin flips.

in how many ways can you select a committee of 3 students out of 10 students ?

Answers

I’m not sure but I think it’s 6 ways

Jenny wants to know the perimeter of the bottom of her tent. It is a rectangle with side lengths of 11 ft. And 7 ft. Which is the perimeter of the bottom of her tent?

Answers

Answer:

36 ft.

Step-by-step explanation:

11+11+7+7=

22+14= 36

Answer:

36 ft

Step-by-step explanation:

The rectangle's sides lengths are 7 ft and 11 ft, wich are the width and the length.

The formula of the perimeter is:

P= 2w+2L with w the width and L the length

P= 2*7+2*11

P= 14+22

P= 36 ft

The perileter is 36 ft

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