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3 years ago

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What's a design constraint?

1 answer:

o-na [289]3 years ago

3 0

Constraints refers to demarcations of geometrical charecteristics between two or more entities or solid modeling bodies

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Photosynthesis produces<br> A.<br> energy<br> B. glucose.<br> c. carbon dioxide.<br> D.<br> water.

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Coefficients are used in a chemical formula to show the number of each element. True or False

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The same number of each element present before the reaction takes place must also be present on the product side of the equation. Coefficients are placed in front of a chemical formula to show the number of moles of that substances that are necessary for the reaction to occur.

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Newtons second law of motion states that

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The acceleration of an object as produced by a net force is directly proportional to the magnitude of the net force,

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3 years ago

Definition of contourology

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Science of, or study of contours, or the lines outlining a scene, drawing, etc.

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Salt is poured from a container at 10 cm³ s-¹ and it formed a conical pile whose height at any time is 1/5 the radius of the abo

Romashka-Z-Leto [24]

Answer:

$\displaystyle \frac{dh}{dt} = \frac{1}{10 \pi}$

Explanation:

Volume of a cone:

$\displaystyle V=\frac{1}{3} \pi r^2 h$

We have $\displaystyle \frac{dV}{dt} = \frac{10 \ cm^3}{sec}$ and we want to find $\displaystyle \frac{dh}{dt} \Biggr | _{h\ =\ 6}= \ ?$ when the height is 2 cm.

We can see in our equation for the volume of a cone that we have three variables: V, r, and h.

Since we only have dV/dt and dh/dt, we can rewrite the equation in terms of h only.

We are given that the height of the cone is 1/5 the radius at any given time, 1/5r, so we can write this as r = 5h.

Plug this value for r into the volume formula:

$\displaystyle V =\frac{1}{3} \pi (5h)^2 h$
$\displaystyle V =\frac{1}{3} \pi \ 25h^3$

Differentiate this equation with respect to time t.

$\displaystyle \frac{dV}{dt} =\frac{25}{3} \pi \ 3h^2 \ \frac{dh}{dt}$
$\displaystyle \frac{dV}{dt} =25 \pi h^2 \ \frac{dh}{dt}$

Plug known values into the equation and solve for dh/dt.

$\displaystyle 10 = 25 \pi (2)^2 \ \frac{dh}{dt}$
$\displaystyle 10 = 100 \pi \ \frac{dh}{dt}$

Divide both sides by 100π to solve for dh/dt.

$\displaystyle \frac{10}{100 \pi} = \frac{dh}{dt}$
$\displaystyle \frac{dh}{dt} = \frac{1}{10 \pi}$

The height of the cone is increasing at a rate of 1/10π cm per second.

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3 years ago