Find the length of the third side. If necessary, round to the nearest tenth.<br><br><br>

A company has two packaging machines in a unit, each with a different daily capacity. The capacity of machine 1 is defined by th

ollegr [7]

Total capacity = sum of the individual production capacities.

Here,

Total capacity = sum of f(m) = (m + 4)^2 + 100 and g(m) = (m + 12)^2 − 50.

Then f(m) + g(m) = (m + 4)^2 + 100 + (m + 12)^2 − 50.

We must expand the binomial squares in order to combine like terms:

m^2 + 8 m + 16 + 100

+m^2 + 24m + 144 - 50

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Then f(m) + g(m) = 2m^2 + 32m + 160 + 50

f(m) + g(m) = 2m^2 + 32m + 210, where m is the number of

minutes during which the two machines operate.

6 0

3 years ago

There are 4 cookies for Mrs. Johnson's 5 children to share evenly.

frosja888 [35]

About 80% of a cookie each

6 0

3 years ago

(a) The plane y + z = 13 intersects the cylinder x2 + y2 = 25 in an ellipse. Find parametric equations for the tangent line to t

klemol [59]

Answer:

Step-by-step explanation:

We have a curve (an ellipse) written as the system of equations

$\begin{cases} y+z &= 13\\ x^2+y^2 &= 25\end{cases}$ .

And we want to calculate the tangent at the point (3,4,9).

The idea in this problem is to consider two variables as functions of the third. Usually we consider $y$ and $z$ as functions of $x$ . Recall that a curve in the space can be written in parametric form in terms of only one variable. In this case we are considering the ‘‘natural’’ parametrization $(x, y(x), z(x))$ .

Recall that the parametric equation of a line has the form

$r(t)=\begin{cases} x(t) &= x_0 + v_1t \\ y(t) &= y_0 +v_2t\\ z(t) &= z_0 +v_3t \end{cases}$ ,

where $(x_0,y_0,z_0)$ is a point on the line (in this particular case is (3,4,9)) and $(v_1,v_2,v_3)$ is the direction vector of the line. In this case, the direction vector of the line is the tangent vector of the ellipse at the point (3,4,9).

Now, if we have the parametric equation of a curve $(x, y(x), z(x))$ its tangent line will have direction vector $(1, y'(x), z'(x))$ . So, as we need to calculate the equation of the tangent line at the point $(3,4,9) = (3, y(3), z(3))$ , we must obtain the tangent vector $(1, y'(3), z'(3))$ . This part can be done taking implicit derivatives in the systems that defines the ellipse.