Convert the following fraction to a percentage (round to the nearest tenth if needed). 3/7

Mathematics

1 answer:

lesantik [10]3 years ago

8 0

Answer:

$\huge\boxed{42.9 \%}$

Step-by-step explanation:

=> $\frac{3}{7}$

To make it a percentage, we need to multiply and divide it by 100

=> $\frac{3}{7} * \frac{100}{100}$

=> $\frac{300}{700}$

To make the denominator 100, we'll divide the numerator and denominator by 7

=> $\frac{300/7}{700/7}$

=> $\frac{42.9}{100}$

Percentage means out of hundred, so it becomes

=> 42.9 %

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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,

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