Write a word phrase for 2/3y+4

The height of a ball thrown vertically upward from a rooftop is modelled by h(t)= -4.8t^2 + 19.9t +55.3 where h (t) is the balls

nikitadnepr [17]

By applying the quadratic formula and discriminant of the quadratic formula, we find that the maximum height of the ball is equal to 75.926 meters.

<h3>How to determine the maximum height of the ball</h3>

Herein we have a quadratic equation that models the height of a ball in time and the maximum height represents the vertex of the parabola, hence we must use the quadratic formula for the following expression:

- 4.8 · t² + 19.9 · t + (55.3 - h) = 0

The height of the ball is a maximum when the discriminant is equal to zero:

19.9² - 4 · (- 4.8) · (55.3 - h) = 0

396.01 + 19.2 · (55.3 - h) = 0

19.2 · (55.3 - h) = -396.01

55.3 - h = -20.626

h = 55.3 + 20.626

h = 75.926 m

By applying the quadratic formula and discriminant of the quadratic formula, we find that the maximum height of the ball is equal to 75.926 meters.

To learn more on quadratic equations: brainly.com/question/17177510

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6 0

1 year ago

The _____ states that control is enhanced by concentrating on the exceptions to, or significant deviations from, the expected re

dalvyx [7]

The principle of exception is the managerial principle that states that control is enhanced by concentrating on the exceptions to, or significant deviations from, the expected result or standard.
This also refers to the fact that only what is important in a budget or a plan is shown to the manager, while the rest is excluded.

4 0

3 years ago

Answer the following ratios 55 paise to Rs 1 500ml to 2 liters

AfilCa [17]

55:1

500:2

There ya go!

7 0

3 years ago

Find the point(s) on the surface z^2 = xy 1 which are closest to the point (7, 11, 0)

leonid [27]

Let $P=(x,y,z)$ be an arbitrary point on the surface. The distance between $P$ and the given point $(7,11,0)$ is given by the function

$d(x,y,z)=\sqrt{(x-7)^2+(y-11)^2+z^2}$

Note that $f(x)$ and $f(x)^2$ attain their extrema, if they have any, at the same values of $x$ . This allows us to consider the modified distance function,

$d^*(x,y,z)=(x-7)^2+(y-11)^2+z^2$

So now you're minimizing $d^*(x,y,z)$ subject to the constraint $z^2=xy$ . This is a perfect candidate for applying the method of Lagrange multipliers.

The Lagrangian in this case would be

$\mathcal L(x,y,z,\lambda)=d^*(x,y,z)+\lambda(z^2-xy)$

which has partial derivatives

$\begin{cases}\dfrac{\mathrm d\mathcal L}{\mathrm dx}=2(x-7)-\lambda y\\\\\dfrac{\mathrm d\mathcal L}{\mathrm dy}=2(y-11)-\lambda x\\\\\dfrac{\mathrm d\mathcal L}{\mathrm dz}=2z+2\lambda z\\\\\dfrac{\mathrm d\mathcal L}{\mathrm d\lambda}=z^2-xy\end{cases}$

Setting all four equation equal to 0, you find from the third equation that either $z=0$ or $\lambda=-1$ . In the first case, you arrive at a possible critical point of $(0,0,0)$ . In the second, plugging $\lambda=-1$ into the first two equations gives

$\begin{cases}2(x-7)+y=0\\2(y-11)+x=0\end{cases}\implies\begin{cases}2x+y=14\\x+2y=22\end{cases}\implies x=2,y=10$

and plugging these into the last equation gives

$z^2=20\implies z=\pm\sqrt{20}=\pm2\sqrt5$

So you have three potential points to check: $(0,0,0)$ , $(2,10,2\sqrt5)$ , and $(2,10,-2\sqrt5)$ . Evaluating either distance function (I use $d^*$ ), you find that

$d^*(0,0,0)=170$
$d^*(2,10,2\sqrt5)=46$
$d^*(2,10,-2\sqrt5)=46$

So the two points on the surface $z^2=xy$ closest to the point $(7,11,0)$ are $(2,10,\pm2\sqrt5)$ .

5 0

3 years ago

Can someone please answer. There is one problem. There's a picture. Thank you.

svetoff [14.1K]

You have to find the area of each face and add them all together. You also need to find the unknown side which is indicated in the picture i attached.

Download pdf

5 0

2 years ago

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