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3 years ago

Write the steps you would use to find a formula for the volume of the figure at right. Then write the formula.

Mathematics

1 answer:

Stels [109]3 years ago

8 0

So there are two shapes: a hemisphere and a cylinder

(1) Volume of a sphere = (4/3)*πr^3, therefor the volume of a hemisphere would be (2/3)*πr^3

(2) Volume of cylinder = πr^2h
Here the height is r therefor volume = πr^2*r = πr^3

So total volume = (2/3)*πr^3 + πr^3
= (5/3)*πr^3

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Calculate the double integral. $$\iint_{R}{\color{red}4} xye^{x^{2}y}\hspace*{3pt}dA, \quad R = [0, 1] \times [0, {\color{red}7}

Lady_Fox [76]

Answer:

$\mathbf{\int \int _R \ 4xy e^{x^2 \ y} \ dA = 2 (e^7 -8)}$

Step-by-step explanation:

Given that:

$\int \int _R 4xye^{x^2 \ y} \ dA, R = [0,1]\times [0,7]$

The rectangle R = [0,1] × [0,7]

R = { (x,y): x ∈ [0,1] and y ∈ [0,7] }

R = { (x,y): 0 ≤ x ≤ 1 and 0 ≤ x ≤ 7 }

$\int \int _R \ 4xy e^{x^2 \ y} \ dA = \int^{7}_{0}\int^{1}_{0} 4xye^{x^2 \ y} \ dx dy$

$\int \int _R \ 4xy e^{x^2 \ y} \ dA = \int^{7}_{0} \begin {bmatrix} ye^{yx^2} \dfrac{4}{2y} \end {bmatrix}^1 _ 0 \ dy$

$\int \int _R \ 4xy e^{x^2 \ y} \ dA = \int^{7}_{0} \begin {bmatrix} ye^{y1^2} \dfrac{4}{2y} - ye^{y0^2} \dfrac{4}{2y} \end {bmatrix}\ dy$

$\int \int _R \ 4xy e^{x^2 \ y} \ dA = \int^{7}_{0} \dfrac{4}{2}(e^y -1) \ dy$

$\int \int _R \ 4xy e^{x^2 \ y} \ dA = \dfrac{4}{2}[e^y -1]^7_0 \ dy$

$\int \int _R \ 4xy e^{x^2 \ y} \ dA = 2 [(e^7 -7)-(e^0 -0)]$

$\int \int _R \ 4xy e^{x^2 \ y} \ dA = 2 [(e^7 -7)-1]$

$\mathbf{\int \int _R \ 4xy e^{x^2 \ y} \ dA = 2 (e^7 -8)}$

3 0

4 years ago

A coin is tossed 40 times and shows heads 23 times. Calculate the experimental probability of the coin showing heads.

Over [174]

Answer:

0.575

Step-by-step explanation:

There are two types of probabilities:

1. Theoretical Probability

2. Experimental Probability

The probability based on mathematical theories is called theoretical probability. It is not always true. i.e. the probability of getting a head in a toss of coin is 1/2 or 0.5 or 50%

Experimental probability is based on experiments. Experimental probability is always going to change whenever the experiment is performed.

The theoretical probability of getting a head while tossing a coin will always be 50% while experimental probability might be different the next time, experiment is performed.

In this case, the experimental probability will be 23/40 or 0.575 ..

8 0

3 years ago

If f(x)= -6x+6 then f^-1(x)=

drek231 [11]

Recall that, to get the inverse relation of any expression, we start off by doing a quick switcharoo on the variables, then we solve for "y".

$\bf \stackrel{f(x)}{y}=-6x+6\qquad inverse\implies \boxed{x}=-6\boxed{y}+6
\\\\\\
x-6=-6y\implies \cfrac{x-6}{-6}=y\implies -\cfrac{x}{6}+1=\stackrel{f^{-1}(x)}{y}$

3 0

3 years ago

Helppppppppppppppppppppp

melamori03 [73]

Answer:

58 ft squared.

Step-by-step explanation:

The formula for area of a trapezoid is (h/2)(b1 + b2). Let's plug in the values:

(4/2) * (12+17) = 2 * 29 = 58ft^2.

3 0

3 years ago

Read 2 more answers

Need help with these two

Brilliant_brown [7]

Before we start to answer, let's get our formulas put in.
4 qt = 1 gal.
1 c = 0.5pt (or 2 cups to 1 pt)

Now that we've gotten the formulas out of the way, let's plug in our numbers.

We have 5 qt.
Since we have 4 qt per gal, let's subtract 4 from 5.
5 - 4 = 1. We have 1 gal (due to having a whole 4) and 1 qt left over.
5 qt = 1 gal 1 qt.

We have 7 c.
Since we have 2 cups per pint, let's divide 7 by 2.
7 / 2 = 3.5

We have 3.5 Pt.

7c = 3.5pt

Your answers are:
1 gal 1 qt
3.5pt

I hope this helps!

4 0

4 years ago