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Zanzabum
3 years ago
14

Prove that the curve a(t) = (cost, sin 2t, cos 2t) is regular on R and that it self-intersects at (1,0,1). Check the self-inters

ection part by using algebra and also by using Geofte
Mathematics
1 answer:
alexandr402 [8]3 years ago
6 0

Answer:

The function a (t) is a vector function composed of the component functions a_ {1} (t) = cost, a_ {2} (t) = sin2t and a_ {3} (t) = cos2t. How a_ {1} (t), a_ {2} (t), a_ {3} (t) are infinitely derivable functions in R, so they are regular functions in R.

Now, fort = 0, you have to a (0) = (cos (0), sin2 (0), cos2 (0)) = (1, 0, 1). How the functions a_ {1} (t), a_ {2} (t), a_ {3} (t) are periodic functions with period 2 \pi, the vector function a (t) will take the same point (1, 0 , 1) at t = 2n\pi, n = 0, 1, 2, 3, ... then the vector function is auto-intercepted

Step-by-step explanation:

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the answer to that question is 1 mile

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Find k so that the following function is continuous:<br> f(x)={kx8x2if0≤x&lt;5if5≤x.
tankabanditka [31]

Check the one-sided limits:

\displaystyle \lim_{x\to5^-}f(x) = \lim_{x\to5}kx = 5k

\displaystyle \lim_{x\to5^+}f(x) = \lim_{x\to5}8x^2 = 200

If <em>f(x)</em> is to be continuous at <em>x</em> = 5, then these two limits should have the same value, which means

5<em>k</em> = 200

<em>k</em> = 200/5

<em>k</em> = 40

3 0
2 years ago
A company rents out 10 food booths and 25 game booths at the county fair. The fee for a food booth is $100 plus $2 per day. The
svetlana [45]

Answer:

2,250 + 95n

Step-by-step explanation:

Cost of a food booth = 100 + 2n

Cost of 10 food booth = 10(100 + 2n)

= 1,000 + 20n

Cost of a game booth = 50 + 3n

Cost of 25 game booth = 25(50 + 3n)

= 1,250 + 75n

Total amount earned by the company = Cost of 10 food booth + Cost of 25 game booth

= (1,000 + 20n) + (1,250 + 75n)

= 1,000 + 20n + 1,250 + 75n

= 1,000 + 1,250 + 20n + 75n

= 2,250 + 95n

Total amount earned by the company = 2,250 + 95n

4 0
3 years ago
Find f(1/4)<br><br> if f(x)=4x^2-2/3x<br><br>please guys explain it to me I cant understand it ​
Jet001 [13]

Answer:

f(1/4) = 1/12

Step-by-step explanation:

f(x) = 4x^2 - 2/3 x is a function. The name of the function is simply the letter f. It tells you a rule. f(x) is the same as y.

It is the same as having

y = 4x^2 - 2/3 x

For each value of x you are given, you can calculate a corresponding value of y. Instead of calling y, y, we call y "f(x)" which is a way of showing that this relation is a function.

If you were given

y = 4x^2 - 2/3 x and were asked to find the value of y when x = 1/4, what would you do?

You would substitute 1/4 for x in the expression 4x^2 - 2/3 x, and you'd find the value of y.

Being asked to find f(1/4) for function f(x) = 4x^2 - 2/3 x means exactly the same. It means what is the value of the function when x = 1/4? What is the y value corresponding to an x value of 1/4?

Let's calculate it:

f(x) = 4x^2 - 2/3 x

To show we are evaluating the function at an x value of 1/4, we use the notation f(1/4). f(1/4) means find the value of y for function f when x = 1/4. We replace x with 1/4 and do the math.

f(1/4) = 4(1/4)^2 - (2/3)(1/4)

f(1/4) = 4(1/16) - 2/12

f(1/4) = 4/16 - 2/12

f(1/4) = 1/4 - 2/12

f(1/4) = 3/12 - 2/12

f(1/4) = 1/12

6 0
3 years ago
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