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3 years ago

Does the point (9.5, 144) make sense in this context? Explain

Mathematics

2 answers:

Flura [38]3 years ago

7 0

Answer:

No it doesn't

Step-by-step explanation:

You have a table that relates the number of packets of flavoring with the ounces of water needed to make soup.

The rate of ounces of water needed for each packet of flavour is a constant and can be computed as follows:

24/2 = 60/5 = 84/7 = 120/10 = 144/12 = 12

The point (9.5, 144) where 9.5 refers to number of packets of flavoring and 144 to ounces of water,doesn't make sense because doesn't satisfied the previous ratio.

144/9.5 ≈ 15.16

Stolb23 [73]3 years ago

6 0

No, (9.5, 144) does not make sense because there is no point of 9.5 and when you divide the ounces of water by the flavoring packets you end up with 12, and if you were to simplify that it would end up with 1 flavor packet and 12 ounces of water.

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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 $r= 144 units$

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Answer:

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