answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
TEA [102]
2 years ago
8

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
Mathematics
1 answer:
kari74 [83]2 years ago
8 0

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

You might be interested in
Solve the recurrence relation: hn = 5hn−1 − 6hn−2 − 4hn−3 + 8hn−4 with initial values h0 = 0, h1 = 1, h2 = 1, and h3 = 2 using (
musickatia [10]
(a) Suppose h_n=r^n is a solution for this recurrence, with r\neq0. Then

r^n=5r^{n-1}-6r^{n-2}-4r^{n-3}+8r^{n-4}
\implies1=\dfrac5r-\dfrac6{r^2}-\dfrac4{r^3}+\dfrac8{r^4}
\implies r^4-5r^3+6r^2+4r-8=0
\implies (r-2)^3(r+1)=0\implies r=2,r=-1

So we expect a general solution of the form

h_n=c_1(-1)^n+(c_2+c_3n+c_4n^2)2^n

With h_0=0,h_1=1,h_2=1,h_3=2, we get four equations in four unknowns:

\begin{cases}c_1+c_2=0\\-c_1+2c_2+2c_3+2c_4=1\\c_1+4c_2+8c_3+16c_4=1\\-c_1+8c_2+24c_3+72c_4=2\end{cases}\implies c_1=-\dfrac8{27},c_2=\dfrac8{27},c_3=\dfrac7{72},c_4=-\dfrac1{24}

So the particular solution to the recurrence is

h_n=-\dfrac8{27}(-1)^n+\left(\dfrac8{27}+\dfrac{7n}{72}-\dfrac{n^2}{24}\right)2^n

(b) Let G(x)=\displaystyle\sum_{n\ge0}h_nx^n be the generating function for h_n. Multiply both sides of the recurrence by x^n and sum over all n\ge4.

\displaystyle\sum_{n\ge4}h_nx^n=5\sum_{n\ge4}h_{n-1}x^n-6\sum_{n\ge4}h_{n-2}x^n-4\sum_{n\ge4}h_{n-3}x^n+8\sum_{n\ge4}h_{n-4}x^n
\displaystyle\sum_{n\ge4}h_nx^n=5x\sum_{n\ge3}h_nx^n-6x^2\sum_{n\ge2}h_nx^n-4x^3\sum_{n\ge1}h_nx^n+8x^4\sum_{n\ge0}h_nx^n
G(x)-h_0-h_1x-h_2x^2-h_3x^3=5x(G(x)-h_0-h_1x-h_2x^2)-6x^2(G(x)-h_0-h_1x)-4x^3(G(x)-h_0)+8x^4G(x)
G(x)-x-x^2-2x^3=5x(G(x)-x-x^2)-6x^2(G(x)-x)-4x^3G(x)+8x^4G(x)
(1-5x+6x^2+4x^3-8x^4)G(x)=x-4x^2+3x^3
G(x)=\dfrac{x-4x^2+3x^3}{1-5x+6x^2+4x^3-8x^4}
G(x)=\dfrac{17}{108}\dfrac1{1-2x}+\dfrac29\dfrac1{(1-2x)^2}-\dfrac1{12}\dfrac1{(1-2x)^3}-\dfrac8{27}\dfrac1{1+x}

From here you would write each term as a power series (easy enough, since they're all geometric or derived from a geometric series), combine the series into one, and the solution to the recurrence will be the coefficient of x^n, ideally matching the solution found in part (a).
3 0
2 years ago
Carson owes Nigel $110. If Carson repays this debt at a rate of $15 per week, which graph BEST represents when, in weeks, Carson
AnnyKZ [126]
Im sorry im trying to get some points ): i hope u find ur answer!
8 0
2 years ago
Lance is at the grocery store and has three options for buying boxed mac 3 points
Nataly [62]

Answer:b

Step-by-step explanation:

Because it b

3 0
2 years ago
Adam is using the equation (x)(x + 2) = 255 to find two consecutive odd integers with a product of 255. When Adam solves the pro
kondaur [170]
\bf (x)(x+2)=255\implies x^2+2x=255\implies x^2+2x-255=y
\\\\
\textit{setting y=0}\implies x^2+2x-255=0
\\\\
\textit{now, factoring that}
\\\\
(x+17)(x-15)=0\implies 
\begin{cases}
x=-17\\
x=15
\end{cases}

notice the picture of the graph added here
low and behold, x = -17, y is 0, and x= 15, y is 0
the graph is touching the x-axis, an x-intercept
or so-called, a "solution"

3 0
2 years ago
Read 2 more answers
The cashier at the 76 truck stop has x dollars, all in $5 bills. what expression represents the number of $5 bills the cashier h
MaRussiya [10]

you don't list the choices but you would divide the total dollar amount by 5 to find out the number of bills there are so it should be something like :

 total bills = x/5

4 0
2 years ago
Other questions:
  • Jonah and his friends went to the movie theater. He bought a movie ticket, and he split the cost of a giant popcorn with his fri
    12·2 answers
  • NEED HELP ASAP failing
    10·1 answer
  • 3) Last year Kerry’s take home pay was £15 000 She spent 40% of her take home pay on rent. She used the rest of her take home pa
    10·1 answer
  • Data was collected about the amount of rainfall in inches according to temperature. Describe how to create a scatterplot of the
    9·2 answers
  • A random sample of 1800 NAU students in Flagstaff found 1134 NAU students who love their MAT114 class. Find a 95% confidence int
    11·1 answer
  • The table shows the relationship “Construction workers make 13 dollars per hour.” A 2-column table with 5 rows. Column 2 is labe
    10·1 answer
  • Yash brought apples and bananas to a picnic The number of apples was three more than twice the number of beane Tach brought 11 a
    16·1 answer
  • Martina used 3 4 of a bottle of conditioner in 7 12 of a year. How much conditioner would she use in a full year?
    8·2 answers
  • Steve rides his bike at a rate of 1760 feet per minute. What is his rate in miles per hour?
    5·1 answer
  • A remote ranch has a cylindrical water storage tank. It has a vertical central axis, a diameter of 16 ft, the sides are 5 ft hig
    13·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!