1answer.
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
VMariaS [17]
3 years ago
8

An inchworm ran into a log while on his way to the raspberry patch. The diameter of the log is 32 cm. How far did the inchworm t

ravel while on the log?

Mathematics
2 answers:
notsponge [240]3 years ago
7 0

Maybe I'm overthinking this one, but here's what I think it's talking about.
If I'm wrong, then I ought to at least get a few points for my talent at making
easy things difficult, and inventing obstacles to place in my own path.

-- The worm is 1 inch long.
-- The outside of the log is a cylinder.  Its cross-section is a
perfect circle with a circumference of 32-cm.
-- The axis (length) of the log is perpendicular (across) the path
that leads to raspberry nirvana.  
-- The ground is hard.  The log contacts the ground along a line,
and doesn't sink into it at all.

-- The worm sees the log ahead of him.  He continues crawling, until
he is directly under a point on the log that's 1-inch above him.
He then stands up to his full height, sticks his front legs to the log,
hoists himself up onto the bark, and starts to walk up and over it.

-- When he reaches a point on the other side of the log that's exactly 1-inch
above the ground, he hooks his sticky back feet to it, drops straight down to
the ground, and continues on his quest.

-- The question is:  What's the length of the part of the log's circumference
that he traveled between the two points that are exactly 1-inch off the ground ?

I thought I was going to be able to be able to talk through this, but I can't.
I need a picture.  Please see the attached picture.

Here comes the worm, heading from left to right.
He sees the log in front of him.
He doesn't bother going around it ... he knows he'll be able to get over it.

When he gets under the log, he starts standing straight up, trying to
grab onto the bark.  But he can't reach it.  He's too short, only 1 inch.

Finally, when he gets to point  'F', the bark is only 1" above him,
so he can hook on and haul himself up to point  'A'.

He continues on ... up, around, and over the log.

Eventually it dawns on him that the log won't last forever, and he'll
soon need to get down to the ground.  As he comes down the right
side of the log, he starts looking down.  It's too high.  He can't reach
the ground, and he's afraid to jump. 

Then he reaches point  'B'.  It's exactly 1-inch above the ground, and
he leaves the log and gets down.

What was the length of the path he followed on the log ... the long way,
over the top from  'A'  to  'B' ?

Here's what I did:

Draw radii from the center of the log to  'A'  and  'B' .
Each of them is 16 cm long (1/2 of the diameter).

Draw the radius from the center of the log to the ground (' E ').
It's 16 cm all the way.
Point  'D'  is 1 inch = 2.54 cm above the ground, so the
         vertical leg of each little right triangle is (16 - 2.54) = 13.46 cm.

There are two similar right triangles, back to back, inside the log.
They are  'CAD'  on the left, and  'CBD'  on the right.
I want to know the size of the angles at the top of each triangle.
(One will be enough, since they're equal angles.)

For each of those angles, the side adjacent to it is  13.46 cm.
And the hypotenuse of each right triangle is a radius, so it's 16 cm.
The cosine of those angles is  (adjacent/hypotenuse) = 13.46/16 = 0.84125 .
Each angle is  32.73 degrees.

Both of them put together add up to  65.45 degrees .

The full circumference of the log is  (pi)(D) = 32pi cm.
The short arc between 'A' and 'B' is  (65.45/360) of the full circumference.
The rest of the circumference is the distance that the worm crawled along it. 

     That's    (1 - 65.45/360) times (32 pi)  =  (0.818) x (32 pi) = <em>82.25 cm</em> .

Having already wasted enough time on this one in search of 5 points,
and then gone back through the whole thing to make corrections for
the customary worm crawling over the metric log, I'm not going to bother
looking for a way to check it.

That's my answer, and I'm sticking to it.

Cloud [144]3 years ago
5 0
Is the inchworm going around the log or over the log?

If it goes over the log, it simply travels the diameter, or 32 cm.

If it goes around the log, then it must travel half of the circumference, or 32*pi/2=16pi cm.

Note that this assumes that the inchworm and the raspberry patch are diametrically opposite.
You might be interested in
Hey besties help me
forsale [732]

2x + 6 = 4x/2 + 12/2

To solve this, we need to transpose like terms to the same side.

2x - 4x/2 = 12/2 - 6

2x - 2x = 6 - 6

0 = 0

Since both sides are zero, it means that the equation has infinite number of solutions.

7 0
3 years ago
Read 2 more answers
1. Classify the triangle according to side length and angle measurement.
mezya [45]

Answer:

1. Scalene right

2. Isosceles acute

3. Parallelogram

3 0
3 years ago
Read 2 more answers
What is cos (A)?<br> Pls help!!
Elan Coil [88]
(Sqrt 87)/16
Please mark brainliest
4 0
2 years ago
PLSSS HELP
Dennis_Churaev [7]

The correct standard form of the equation of the parabola is:

(x+3)^{2}= 4(y - 3).

<h3 /><h3>What is a parabola?</h3>

An equation of a curve that has a point on it that is equally spaced from a fixed point and a fixed line is referred to as a parabola. The parabola's fixed line and fixed point are together referred to as the directrix and focus, respectively. It's also crucial to remember that the fixed point is not located on the fixed line. A parabola is a locus of any point that is equally distant from a given point (focus) and a certain line (directrix). An essential curve of the coordinate geometry's conic sections is the parabola.

For the given question,

Vertex of parabola is (-3,3)

Thus, the equation of the parabola is:

(x-h)^{2}=4(y-k)

(x+3)^{2}= 4(y-3)

Learn more about parabolas here:

brainly.com/question/64712

#SPJ1

4 0
2 years ago
Which angle number represents &lt;EHK
kotegsom [21]
Angle #8 represents angle EHK
4 0
3 years ago
Other questions:
  • In 37.2 the ones place and the tenths place are separated by
    15·1 answer
  • Write a function for the situation. Is the graph continuous or discrete. A movie store sells DVD for 11$ each what is the cost.
    8·2 answers
  • The ________ is a basic syst?me international (metric system) unit of mass.
    7·1 answer
  • Reduce −2 + b2 by 7 + b2.
    6·2 answers
  • There are 25 students in the
    8·1 answer
  • Write the decomposition that helps you, and then round to the given place value. Draw number lines to explain your thinking. Cir
    8·1 answer
  • Please help!
    14·2 answers
  • Anyone know this i need help this is for a final
    9·1 answer
  • A plumber charges $25 for a service call plus $50 per hour of service. Write an equation in slope-intercept form for the cost, C
    10·1 answer
  • Find AB using the segment addition postulate. Show all work in setting up and solving your equation.
    14·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!