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3 years ago

What is the little t in Torricelli’s law

1 answer:

4 0

In its simplest form, Torricelli's law states that water in a tank will escape through a (small) hole in the bottom with the same speed that it would attain falling from the same height to the level of the hole. ... velocity, g is the acceleration due to gravity, and h is the height of the fluid in the container. Hope that helps!

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Use the general slicing method to find the volume of the following solids. The solid whose base is the region bounded by the cur

Y_Kistochka [10]

Answer:

The volume is $V=\frac{64}{15}$

Step-by-step explanation:

The General Slicing Method is given by

Suppose a solid object extends from x = a to x = b and the cross section of the solid perpendicular to the x-axis has an area given by a function A that is integrable on [a, b]. The volume of the solid is

$V=\int\limits^b_a {A(x)} \, dx$

Because a typical cross section perpendicular to the x-axis is a square disk (according with the graph below), the area of a cross section is

The key observation is that the width is the distance between the upper bounding curve $y = 2 - x^2$ and the lower bounding curve $y = x^2$

The width of each square is given by

$w=(2-x^2)-x^2=2-2x^2$

This means that the area of the square cross section at the point x is

$A(x)=(2-2x^2)^2$

The intersection points of the two bounding curves satisfy $2 - x^2=x^2$ , which has solutions x = ±1.

$2-x^2=x^2\\-2x^2=-2\\\frac{-2x^2}{-2}=\frac{-2}{-2}\\x^2=1\\\\x=\sqrt{1},\:x=-\sqrt{1}$

Therefore, the cross sections lie between x = -1 and x = 1. Integrating the cross-sectional areas, the volume of the solid is

$V=\int\limits^{1}_{-1} {(2-2x^2)^2} \, dx\\\\V=\int _{-1}^14-8x^2+4x^4dx\\\\V=\int _{-1}^14dx-\int _{-1}^18x^2dx+\int _{-1}^14x^4dx\\\\V=\left[4x\right]^1_{-1}-8\left[\frac{x^3}{3}\right]^1_{-1}+4\left[\frac{x^5}{5}\right]^1_{-1}\\\\V=8-\frac{16}{3}+\frac{8}{5}\\\\V=\frac{64}{15}$

5 0

3 years ago

⚠️ Urgent PLS HELP links will be reported Find the value of x .

OLga [1]

Answer: x=18

Step-by-step explanation: ...

6 0

3 years ago

Evaluate the given algebraic expression for x = 2 and y= 3. -Зху -6 -12 -18 -24

mrs_skeptik [129]

Answer:

-18

Step-by-step explanation:

-3xy,X=2 ,y=3

-3(2)(3)

-3(6)

=-18

4 0

3 years ago

What is the value of x with clear working out please?

nirvana33 [79]

Answer:

Answer:  x is 46° 

Step-by-step explanation:

• Let's first find Angle ACB

${ \rm{ \angle ACB + 23 \degree + 90 \degree = 180 \degree}} \\ \\ { \rm{ \angle ACB = (180 - 90 - 23) \degree}} \\ \\ { \underline{ \rm{ \: \angle ACB = 67 \degree}}}$

• From alternative angles, x = Angle BAC.

• Since AB = AC, then Angle ABC = Angle ACB

${ \rm{x + \angle ABC + \angle ACB = 180 \degree}} \\ \\ { \rm{x + 67 \degree + 67 \degree = 180 \degree}} \\ \\ { \rm{x + 134 \degree = 180 \degree}} \\ \\ { \boxed{ \rm{x = 46 \degree}}}$

5 0

3 years ago

Read 2 more answers

The first 5 terms of a quadratic sequence are

Mashcka [7]

Step-by-step explanation:

an = 2n^2 - 3 · Anonymous. -1, 5, 15, 29, 47, ... an = 2 n^2 - 3.

8 0

3 years ago