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3 years ago

15

The local fair is creating a dunk tank the shape of an oblique cylinder so that the dunked candidate is

1 answer:

alexgriva [62]3 years ago

6 0

Answer:

a. the same amount of water

Step-by-step explanation:

You might be interested in

How do you determine the area under a curve in calculus using integrals or the limit definition of integrals?

RSB [31]

Answer:

Please check the explanation.

Step-by-step explanation:

Let us consider

$y = f(x)$

To find the area under the curve $y = f(x)$ between $x = a$ and $x = b$ , all we need is to integrate $y = f(x)$ between the limits of $a$ and $b$ .

For example, the area between the curve y = x² - 4 and the x-axis on an interval [2, -2] can be calculated as:

$A=\int _a^b|f\left(x\right)|dx$

= $\int _{-2}^2\left|x^2-4\right|dx$

$\mathrm{Apply\:the\:Sum\:Rule}:\quad \int f\left(x\right)\pm g\left(x\right)dx=\int f\left(x\right)dx\pm \int g\left(x\right)dx$

$=\int _{-2}^2x^2dx-\int _{-2}^24dx$

solving

$\int _{-2}^2x^2dx$

$\mathrm{Apply\:the\:Power\:Rule}:\quad \int x^adx=\frac{x^{a+1}}{a+1},\:\quad \:a\ne -1$

$=\left[\frac{x^{2+1}}{2+1}\right]^2_{-2}$

$=\left[\frac{x^3}{3}\right]^2_{-2}$

computing the boundaries

$=\frac{16}{3}$

Thus,

$\int _{-2}^2x^2dx=\frac{16}{3}$

similarly solving

$\int _{-2}^24dx$

$\mathrm{Integral\:of\:a\:constant}:\quad \int adx=ax$

$=\left[4x\right]^2_{-2}$

computing the boundaries

$=16$

Thus,

$\int _{-2}^24dx=16$

Therefore, the expression becomes

$A=\int _a^b|f\left(x\right)|dx=\int _{-2}^2x^2dx-\int _{-2}^24dx$

$=\frac{16}{3}-16$

$=-\frac{32}{3}$

$=-10.67$ square units

Thus, the area under a curve is -10.67 square units

The area is negative because it is below the x-axis. Please check the attached figure.

6 0

3 years ago

A closed container has 5.04 ⋅ 1023 atoms of a gas. Each atom of the gas weighs 1.67 ⋅ 10–24 grams.

never [62]

Answer:

Step-by-step explanation:

Each atom of the gas weighs 1.67 ⋅ 10−24 grams. 6.71 grams, because (5.04 + 1.67) ⋅ (1023⋅ 10−24 ) = 6.71. ... 0.67 grams, because (5.04 + 1.67) ⋅ (1023⋅ 10−24 ) = 6.71 ⋅ 10−1.

3 0

3 years ago

2(8x +9) -8(7-5x)<br><br> Please can someone help

Paha777 [63]

Answer:

56x-38

Step-by-step explanation:

2(8x+9)-8(7-5x)

16x+18

-8(7-5x)

-56+40x

16x+18-56+40x

Add all like terms

56x-38

8 0

3 years ago

Read 2 more answers

Find the product of 8.12 and 2.4<br> Plz someone help .

vesna_86 [32]

Answer:

19.488

Step-by-step explanation:

8.12 x 2.4 = 19.488

8 0

3 years ago

I don't understand how to solve this pls help

Charra [1.4K]

the sine function is a many-to-one function and therefore has no inverse function.

However if the domain is restricted to -90° ≤ x ≤ 90°

Then the function is one-to-one for this domain

Thus, $sin^{-1}$ x is defined as the angle such that - π/2 ≤ x ≤ π/2

5π/6 is therefore outwith the domain

7 0

4 years ago