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4 years ago

Assignment 01.12 learning path one activity

Mathematics

1 answer:

hodyreva [135]4 years ago

8 0

Why ask why? ';lkl!!!!!!!!!!

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Find the length of the following two-dimensional curve. r (t ) = (1/2 t^2, 1/3(2t+1)^3/2) for 0 < t < 16

andrezito [222]

Answer:

r = 144 units

Step-by-step explanation:

The given curve corresponds to a parametric function in which the Cartesian coordinates are written in terms of a parameter "t". In that sense, any change in x can also change in y owing to this direct relationship with "t". To find the length of the curve is useful the following expression;

$r(t)=\int\limits^a_b ({r`)^2 \, dt =\int\limits^b_a \sqrt{((\frac{dx}{dt} )^2 +\frac{dy}{dt} )^2)} dt$

In agreement with the given data from the exercise, the length of the curve is found in between two points, namely 0 < t < 16. In that case a=0 and b=16. The concept of the integral involves the sum of different areas at between the interval points, although this technique is powerful, it would be more convenient to use the integral notation written above.

Substituting the terms of the equation and the derivative of r´, as follows,

$r(t)= \int\limits^b_a \sqrt{((\frac{d((1/2)t^2)}{dt} )^2 +\frac{d((1/3)(2t+1)^{3/2})}{dt} )^2)} dt$

Doing the operations inside of the brackets the derivatives are:

1 ) $(\frac{d((1/2)t^2)}{dt} )^2= t^2$

2) $\frac{(d(1/3)(2t+1)^{3/2})}{dt} )^2=2t+1$

Entering these values of the integral is

$r(t)= \int\limits^{16}_{0} \sqrt{t^2 +2t+1} dt$

It is possible to factorize the quadratic function and the integral can reduced as,

$r(t)= \int\limits^{16}_{0} (t+1) dt= \frac{t^2}{2} + t$

Thus, evaluate from 0 to 16

$\frac{16^2}{2} + 16$

The value is $r= 144 units$

5 0

4 years ago

Based on the graphs of f (x) and g(x), what must the domain of (f ⋅ g)(x)be?

dimulka [17.4K]

Answer:

{x ∈ ℝ | x ≠ 2}

Step-by-step explanation:

4 0

3 years ago

How do u round 33 and 89 to estimate their sum

Zolol [24]

33 would round down. (30)

This is because the second 3 is smaller than 5 and when your rounding, if number your rounding is smaller then 5 you will round down

89 would round up. (90)

This is because the 9 is larger than 5 which means you would round up.

Please mark brainlies

6 0

3 years ago

Please help now ASAP!!!!

TiliK225 [7]

Answer:

Step-by-step explanation:

I don't think u can tell from that because u need the length of each movie

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3 years ago

An electrician charges $45 for each home visit plus $19.95 every hour he spends working. Which sentence could be used to find C,

VARVARA [1.3K]

Answer:

C= 45 + 19.95h

Step-by-step explanation:

45 for each home vist means one time payment

19.95 ever hour means you are charged 19.95 every hour

H= hour

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3 years ago