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Neko [114]
3 years ago
6

Anybody have a proper answer for this?

Mathematics
1 answer:
skelet666 [1.2K]3 years ago
6 0
John (7%)
Bo (71%)
Mike (75%)

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Consider the parametric curve x = 2t^(3)-3t^(2)+2 and y = t^(3)-12t,-pi leq t leq pi . (a) Find the values of t (if any) where t
bagirrra123 [75]

Answer:

  (a) t = ±2

  (b) t ∈ {0, 1}

  (c) In navigation terms: east by north. The slope is about 0.42 at that point.

Step-by-step explanation:

(a) dy/dx = 0 when dy/dt = 0

  dy/dt = 3t^2 -12 = 0 = 3(t -2)(t +2)

The slope is zero at t = ±2.

__

(b) dy/dx = (dy/dt)/(dx/dt) = <em>undefined</em> when dx/dt = 0

  dx/dt = 6t^2 -6t = 6(t)(t -1) = 0

The slope is undefined for t ∈ {0, 1}.

__

(c) At t=3, dy/dx = (dy/dt)/(dx/dt) = 3(3-2)(3+2)/(6(3)(3-1)) = 15/36 = 5/12

The general direction of movement is away from the origin along a line with a slope of 5/12, about 22.6° CCW from the +x direction.

_____

The first attachment shows the derivative and its zeros and asymptotes. It also shows some of the detail of the parametric curve near the origin.

The second attachment shows the parametric curve over the domain for which it is defined, along with the point where t=3.

5 0
3 years ago
Identify the factors of x2 + 25y2. ...?
Sveta_85 [38]
Is the equation like this? x^2 + 25y^2?
If the equation is like that, the answer would be (x-5y)^2 or (x-5y)(x-5y).
how did I get this? Just divide the factors or the get the square root of 25y^2 and it would be 5y. Then just try if it is positive or negative. In this case, it is negative because there is no factor w/ no exponential form. I hopemy answer helped you.
4 0
3 years ago
Identify the diameter of the disc
Olegator [25]

radius = (4*10^2 + 24^2)/8*10 =

(400 + 576)/80=

976/80 = 12.2

diameter = 12.2 x 2 = 24.4

4 0
3 years ago
Mathematics help please!!!!!!!!!<br><br> what is -0.0833333333333 converted into a fraction?
VladimirAG [237]

Answer:

- 1/12

Step-by-step explanation:

Let -0.0833333 = x  ---  (1)

Multiply both sides by 10.

-0.833333 = 10x   --- (2)

Subtract (2) from (1),

0.75 = -9x

-9x = \frac{75}{100}

= \frac{3}{4}

x=-\frac{3}{36}

x=-\frac{1}{12}


8 0
3 years ago
A father’s age now is three times the age that his son was 4 years ago. In
Mice21 [21]
Let ‘s’ be the son’s age 12 years ago.
Let ‘f’ be the father’s current age.

4 years ago, the son was:

s-4

So, his father is currently:

3(s-4)

=

3s-12

Therefore:

f = 3s-12

In twelve years, the son will be:

s+12

And the father will be:

f+12

This can also be written as:

3s-12+12 as the fathers younger age would be f = 3s+12

=

3s

So, we know that s+12 is half the fathers current age, meaning the father is currently 2(s+12) which is equivalent to 2s+24. Also, we know that the father is currently 3 times the sons age 12 years ago, so 3s (proven by the calculations we made above). Therefore, 2s+24=3s which means 24=s. We can then substitute this, and we will receive 24+12 = 36

Son’s current age: 36

We then substitute the son’s age 12 years ago into 2s+24 to give us the father’s age.

2(24)+24 = 72

Father’s current age: 72










7 0
2 years ago
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