Geometry.

Mathematics

1 answer:

Harman [31]3 years ago

8 0

Check the picture below.

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A graphic designer charges an hourly rate. In July, the only expense is for advertising. The function graphed models the designe

ICE Princess25 [194]

<span>The first one is false, but the other two are true.
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2 years ago

Read 2 more answers

Find four consecutive even integers whose sum is 84. Find the integers.

mina [271]

Suppose the integers are n , n+2 , n+4 and n+6.
84=n+(n+2)+(n+4)+(n+6)=4n+12.
Subtract 12 from both ends to get.
72=4n.
Divide both ends by 4 to get.
n=18.
So the integers are: 18 , 20 , 22 , 24.

4 0

3 years ago

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,

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