Answer:
176 miles
Step-by-step explanation:
88x2=176
A spherical tank is 3 m tall and therefore has a capacity of about 14000 L (NOTE that 3m is its diameter, and one cubic meter is 1000 L). You have been asked to put level lines on the tank showing the depths where the tank contains 1000, 5000, and 10000 L of liquid. (a) Use calculus to determine the height of each line (to the nearest cm). (b) Plot the circular cross-section of the tank and the level lines (NOTE the lines do not have to stay within the circle).
Answer:
(a) 1) When V = 1000 L, the height of the liquid in the tank is approximately 62 cm
2) When V = 5,000 L, the height of the liquid in the tank is approximately 106 cm
3) When V = 10,000 L, the height of the liquid in the tank is approximately 202 cm
b) The drawing of the spherical tank showing the height of the liquid level for each volume created with Microsoft Excel is attached
Step-by-step explanation:
(a) The height of the spherical tank = 3 m
The diameter of the spherical tank, d = 3 m
The capacity of the spherical tank = 14,000 L
The volume of a sphere, V = (4/3) × π × r³ =
Where, r = d/2
∴ r = 3 m/2 = 1.5 m
V = (4/3) × π × (1.5)³ ≈ 14.1371669412 m³
Using calculus, we have;
[tex]V = 2 \times \pi \times \int\limits^r_{0} {(r^2 - y^2)} \, dx = 2 \times \pi \times \left[r^2 \cdot y - \dfrac{y^3}{3} \right]^y_0[/tex]
For the two halves, we have;
[tex]V = \pi \times \left[r^2 \cdot y - \dfrac{y^3}{3} \right]^{\dfrac{y}{2}} _0 + \pi \times \left[r^2 \cdot y - \dfrac{y^3}{3} \right]^y_{\dfrac{y}{2}}[/tex]
[tex]V = 2 \times \pi \times \left[y^3- \dfrac{y^3}{3} \right]^y_0 = \dfrac{4 \cdot \pi \cdot y^3}{3}[/tex]
1) For V = 1000 L, we have;
[tex]1000 \ L = \dfrac{4 \cdot \pi \cdot y^3}{3}[/tex]
1000 L =
When V = 1000 L, we have;
[tex]y = \sqrt[3]{\dfrac{3 \times 1 \, m^3}{4 \times \pi } } \approx 0.62 \ m[/tex]
The liquid level, y ≈ 0.62 m = 62 cm
2) When V = 5,000 L, we have;
[tex]y = \sqrt[3]{\dfrac{3 \times 5 \, m^3}{4 \times \pi } } \approx 1.06 \ m[/tex]
The liquid level, y ≈ 1.06 m = 106 cm
3) When V = 10,000 L, we use the height of the unfilled volume at the top which is the volume of the sphere less the 10,000 L as follows;
For the volume of the sphere of 14,000 L, we have;
Volume at the top = 14,000 L - 10,000 L = 4,000 L = 4 m³
Therefore
[tex]y_{top} = \sqrt[3]{\dfrac{3 \times 4 \, m^3}{4 \times \pi } } \approx 0.985 \ m[/tex]
The height of the liquid in the tank, y = d - [tex]y_{top}[/tex]
∴ y = 3 m - 0.985 m = 2.015 m
The liquid level, y ≈ 2.015 m = 201.5 cm ≈ 202 cm
b) Please find attached the drawing of the spherical tank created with Microsoft Excel
a) (i) The level line for 1000 liters is set at a height of 0.486 meters.
(ii) The level line for 5000 liters is set at a height of 1.203 meters.
(iii) The level line for 10000 liters is set at a height of 1.926 meters.
b) The sphere is represented by the equation [tex]x^2+(y-1.5)^{2} = 2.25[/tex] and the level lines are represented by the linear functions [tex]y = 0.486[/tex], [tex]y = 1.203[/tex] and [tex]y = 1.926[/tex]. Please see the second image attached.
How to determine and plot the heights of a spherical tanka) First, we derive an expression for the volume of a spherical section ([tex]V[/tex]), in cubic meters, in terms of tank radius ([tex]R[/tex]), in meters, and liquid height ([tex]h[/tex]), in meters. The volume can be found by using the slicing method integral equation:
[tex]V = \int\limits^{H}_{0} {A(h)} \, dh[/tex] (1)
Where:
[tex]A(h)[/tex] - Area of the infinitesimal circular cross section, in square meters. [tex]H[/tex] - Required height of the liquid, in meters.If we know that [tex]A = \pi\cdot [R^{2}-(R-h)^{2}][/tex], then the volume formula is:
[tex]V = \pi\int\limits^H_0 {h\cdot (2\cdot R-h)} \, dh[/tex]
[tex]V = 2\pi\cdot R\int\limits^{H}_{0} {h} \, dh - \pi \int\limits^{H}_{0} {h^{2}} \, dh[/tex]
[tex]V = \pi\cdot R\cdot H^{2}-\frac{\pi\cdot H^{3}}{3}[/tex]
Then we obtain the following third order polynomial:
[tex]\frac{\pi\cdot H^{3}}{3}-\pi\cdot R\cdot H^{2}+V = 0[/tex] (2)
Now we proceed to solve numerically for each case:
Case 1 - [tex]R = 1.5\,m[/tex], [tex]V = 1\,m^{3}[/tex][tex]H = 0.486\,m[/tex]
The level line for 1000 liters is set at a height of 0.486 meters. [tex]\blacksquare[/tex]
Case 2 - [tex]R = 1.5\,m[/tex], [tex]V = 5\,m^{3}[/tex][tex]H = 1.203\,m[/tex]
The level line for 5000 liters is set at a height of 1.203 meters. [tex]\blacksquare[/tex]
Case 3 - [tex]R = 1.5\,m[/tex], [tex]V = 10\,m^{3}[/tex][tex]H = 1.926\,m[/tex]
The level line for 10000 liters is set at a height of 1.926 meters. [tex]\blacksquare[/tex]
b) The sphere is represented by the equation [tex]x^2+(y-1.5)^{2} = 2.25[/tex]level lines are represented by the linear functions [tex]y = 0.486[/tex], [tex]y = 1.203[/tex] and [tex]y = 1.926[/tex]. By a graphing tool we have the following result. [tex]\blacksquare[/tex]
To learn more on volumes, we kindly invite to check this verified question: https://brainly.com/question/1578538
what is the LCM of 3and 6
Answer:
L.c.m of 3 and 6 is 6
Answer:
Lcm of 3&6 is:
3*2 & 6*1 (DONE LIKE THIS BECAUSE THAT LCM OF 3 & 6 IS FOUND TO BE 6 AS BOTH 3 & 6 HAS THE SMALLEST COMMON MULTIPLE AS 6)
6 & 6
There fore LCM is 6
del puerto de cabo San Lucas México salen dos barcos el barco México 1,navega con una trayectoria de x+y=88;el barco México 2 navega con una trayectoria de 2x + 2y= -176 en que punto se encontrarán los dos barcos?
Find the slope of the line through the points (-2, -3) and (2, 1).
Answer:
1
Step-by-step explanation:
i did it
18 lollipop at the same number of lollipops on the nine tables how many levels did she pop on each table
Answer:
2
Step-by-step explanation:
.....................
map of field: 12 in × 15 in
scale of map: 1 in = 3 ft
What are the dimensions
of the actual field?
mark invested a certain amount at 5 % simple interest per year after 10 year he received an interest of 50000 how much did he invest
Answer:
100,000
Step-by-step explanation:
Presented below are the financial statements for the Amphlett Corporation, as of year-end 2012 and 2013.
AMPHLETT CORPORATION
Consolidated Balance Sheets
As of Year-End ($ thousands) 2013 2012
Assets
Current
Cash $18,000 $108,000
Marketable securities 240,000 -
Accounts receivable (net) 708,000 528,000
Inventory 720,000 738,000
Total current assets 1,686,000 1,374,000
Noncurrent
Long-term investments 372,000 468,000
Property & equipment 2,160,000 1,320,000
Less: Accumulated depreciation (600,000) (600,000)
Property & equipment (net) 1,560,000 720,000
Intangibles (net) 114,000 126,000
Total noncurrent assets 2,046,000 1,314,000
Total assets $3,732,000 $2,688,000
Liabilities & Shareholders' Equity
Accounts payable $1,080,000 $1,020,000
Short-term bank debt 228,000 -
Total liabilities 1,308,000 1,020,000
Shareholders' equity
Common stock, $10 par value 930,000 810,000
Additional paid-in-capital 456,000 360,000
Retained earnings 1,038,000 498,000
Total shareholders' equity 2,424,000 1,668,000
Total liabilities & shareholders' equity $3,732,000 $2,688,000
AMPHLETT CORPORATION
Consolidated Income Statement
For Year Ended ($ thousands)
2013
2012
Revenues
$1,716,000
$1,440,000
Less: Cost of goods sold
600,000
504,000
Gross margin
1,116,000
936,000
Less: Selling, general & administrative expenses
180,000
144,000
Operating income
936,000
792,000
Gain on sale of investments
84,000
-
Net income before taxes
1,020,000
792,000
Less: Income taxes
60,000
13,200
Net income after taxes
$960,000
$778,800
The footnotes to the Amphlett Corporation's financial statements revealed the following additional information:
Property and equipment costing $540 million was sold for its book value of $240 million.
Long-term investments were sold for $180 million, which included a gain of $84 million.
Required
Using the above financial data for the Amphlett Corporation, prepare the firm's statement of cash flow for 2013 using the indirect method.
Use a negative sign with answers to indicate a decrease in cash.
Amphlett Corporation
Statement of Cash Flows
For Year Ended 2013
(in thousands)
Cash flow From Operations BLANK
Net Income $Answer
Add:
Depression Expense Answer
Amortization expense Answer
Less:
Gain on Sale of Investments Answer
Accounts receivable (net) Answer
Inventory Answer
Accountable Payable Answer
Cash Flow From Operations Answer
Cash Flow for Investing BLANK
Marketable securities Answer
Long-term investments Answer
Purchase of property and equipment Answer
Sale of Property and Equipment Answer
Cash Flow for Investing Answer
Cash From Financing BLANK
Short-term bank debt Answer
Common stock + additional paid in capital Answer
Dividends Paid Answer
Cash From Financing Answer
Decrease in Cash Answer
Cash, beginning of year Answer
Cash, end of year $Answer
Answer:
For Year Ended 2013
(in thousands)
Cash flow From Operations BLANK
Net Income 792,000
Add:
Depression Expense 300,000
Amortization expense 12,000
Less:
Gain on Sale of Investments
Accounts receivable (net) -180,000
Inventory 18,000
Accountable Payable Answer 60,000
Cash Flow From Operations 1,002,000
Cash Flow for Investing
Marketable securities -240,000
Long-term investments 96,000
Purchase of property and equipment -1,380,000
Sale of Property and Equipment 280,000
Cash Flow for Investing -1,244,000
Cash From Financing
Short-term bank debt 228,000
Common stock + additional paid in capital 96,000
Dividends Paid 8,000
Cash From Financing 332,000
Decrease in Cash 90,000
Cash, beginning of year 18,000
Cash, end of year 108,000
108,000
0
Step-by-step explanation:
Assets
Current
Cash $18,000 $108,000
Marketable securities 240,000
Accounts receivable (net) 708,000 528,000
Inventory 720,000 738,000
Total current assets 1,686,000 1,374,000
Noncurrent
Long-term investments 372,000 468,000
Property & equipment 2,160,000 1,320,000
Less: Accumulated depreciation -600,000 -600,000
Property & equipment (net) 1,560,000 720,000
Intangibles (net) 114,000 126,000
Total noncurrent assets 2,046,000 1,314,000
Total assets $3,732,000 $2,688,000
Liabilities & Shareholders' Equity
Accounts payable $1,080,000 $1,020,000
Short-term bank debt 228,000
Total liabilities 1,308,000 1,020,000
Shareholders' equity
Common stock, $10 par value 930,000 810,000
Additional paid-in-capital 456,000 360,000
Retained earnings 1,038,000 498,000
Total shareholders' equity 2,424,000 1,668,000
Total liabilities & shareholders' equity $3,732,000 $2,688,000
AMPHLETT CORPORATION
Consolidated Income Statement
For Year Ended ($ thousands) 2013 2012
Revenues $1,716,000 $1,440,000
Less: Cost of goods sold 600,000 504,000
Gross margin 1,116,000 936,000
Less: Selling, general & administrative expenses 180,000 144,000
Operating income 936,000 792,000
Gain on sale of investments 84,000
Net income before taxes 852,000 792,000
Less: Income taxes 60,000 13,200
Net income after taxes $792,000 $778,800
For Year Ended 2013
(in thousands)
Cash flow From Operations BLANK
Net Income 792,000
Add:
Depression Expense 300,000
Amortization expense 12,000
Less:
Gain on Sale of Investments
Accounts receivable (net) -180,000
Inventory 18,000
Accountable Payable Answer 60,000
Cash Flow From Operations 1,002,000
Cash Flow for Investing
Marketable securities -240,000
Long-term investments 96,000
Purchase of property and equipment -1,380,000
Sale of Property and Equipment 280,000
Cash Flow for Investing -1,244,000
Cash From Financing
Short-term bank debt 228,000
Common stock + additional paid in capital 96,000
Dividends Paid 8,000
Cash From Financing 332,000
Decrease in Cash 90,000
Cash, beginning of year 18,000
Cash, end of year 108,000
108,000
0
please help me please i really need help please
Answer:
x = -22/3 and y = -1
Step-by-step explanation:
First, simplify the equation 12x + 20y = -108 by dividing both sides by 4:
3x + 5y = -27
now, you can subtract the two equations:
3x + 5y = -27
- (3x - 12y = -10)
17y = -17
y = -1
plug y = -1 into the equation 3x - 12y = -10
3x - 12 *(-1) = -10
3x + 12 = -10
3x = -22
x = -22/3
Answer:
-(22/3,-1)
Step-by-step explanation:
[tex]-(x+9)2=64[/tex]
A family has four children. If the genders of these children are listed in the order they are born, there are sixteen possible outcomes: BBBB, BBBG, BBGB, BGBB, GBBB, BGBG, GBGB, BGGB, GBBG, BBGG, GGBB, BGGG, GBGG, GGBG, GGGB, and GGGG. Assume these outcomes are equally likely. Let represent the number of children that are girls. Find the probability distribution of . Part: 0 / 20 of 2 Parts Complete Part 1 of 2 Your Answer is incorrect (a) Find the number of possible values for the random variable . There are possible values for the random variable .
Answer:
X : ___ 0 ____ 1 _____ 2 _____ 3 _____ 4
P(x): _ 1/16 __ 1/4 ____ 3/8 ____ 1/4 ____ 1/16
Step-by-step explanation:
Given the listed possible occurrence of boys and girls :
B = boys ; G = girls
BBBB, BBBG, BBGB, BGBB, GBBB, BGBG, GBGB, BGGB, GBBG, BBGG, GGBB, BGGG, GBGG, GGBG, GGGB, and GGGG
Let x = distribution of girls
P = required outcome / Total possible outcomes
For :
x = 0 ;(BBBB) = 1
P(x) = 1/16
x = 1 ; (BBBG, BBGB, BGBB, GBBB) = 4
P(x) = 4 / 16 = 1/4
P(x = 2) ; (BGBG, GBGB, BGGB, GBBG, BBGG, GGBB) = 6
P(x) = 6 / 16 = 3/8
P(x = 3) ; (BGGG, GBGG, GGBG, GGGB) = 4
P(x) = 4 / 16 = 1/4
P(x = 4) ; (GGGG) = 1
P(x) = 1 / 16
X : ___ 0 ____ 1 _____ 2 _____ 3 _____ 4
P(x): _ 1/16 __ 1/4 ____ 3/8 ____ 1/4 ____ 1/16
Let C represent the cost in dollars and R represent the revenue in dollars. What is the break-even point? Use a table to help if necessary. C=15x+150 And R=45x
Answer:
[tex]x = 5[/tex]
[tex]R = C = 225[/tex]
Step-by-step explanation:
Given
[tex]C = 15x + 150[/tex]
[tex]R = 45x[/tex]
Required
The break even point
To do this, we make use of:
[tex]R =C[/tex]
[tex]45x=15x + 150[/tex]
Collect Like Terms
[tex]45x-15x = 150[/tex]
[tex]30x = 150[/tex]
[tex]x = 5[/tex]
Substitute 5 for x in [tex]R = 45x[/tex]
[tex]R = 45 * 5[/tex]
[tex]R = 225[/tex]
Hence, the break even point is:
[tex]x = 5[/tex]
[tex]R = C = 225[/tex]
The fraction 4/5 is equivalent to which of the following percentages
Answer:
80 percent but could you please take a picture of the question...
Step-by-step explanation:
1. You have three standard decks of cards in front of you. What is the probability of drawing a heart card from all three decks?
2.12%
9.38%
1.56%
17.31%
Answer:
1.56%
Step-by-step explanation:
A standard deck of cards has 52 cards, and 13 of these are hearts, as there are 4 suits, and 52/4=13. This means the probability of choosing a heart card from a deck of cards is 1/4, or 25%. Now to find the probability of doing this from 3 decks in a row, we simply cube 1/4 to get 1/64, and in percentage this is ~1.56%.
Answer: 1.56%
Step-by-step explanation: there's really nothing to explain here.
Quiz From Buzz (Acceleration Education)
Hope it helps you!
Decrease 1428g by 38.5%
Answer:
1428 (1-0.385) = 878.22
Step-by-step explanation:
what is 70000000000000000 divided by 100000 plus 797970605 plus 023475748392
Answer:
7.000002427×10¹⁶
Answer:
723555545997
Step-by-step explanation:
I hope this helps, i had to use a calculator because that was a long math equation question, I mean, who else can't do that?
And plz rate it 5 starts, give brainilest, and thank me
Jack knows that one-third of his total trip is 640 miles. How far is Jack's total trip?
At the grocery store, almonds ore on soe for
$3.8 per pound What is the price of 4.5pounds??
Answer:
$17.10
Step-by-step explanation:
Almonds being on sale
$3.8 per pound
4.5 pounds
___________________
We know that for every pound, the cost is three dollars and eighty cents, we are looking for 4.5 pounds in total.
Multiply the amount per pound to the amount of pounds being asked :
3.8 * 4.5
$17.10
I need help ASAP pls
5) Un pedazo de pizza cuesta $30, un jugo cuesta $15. ¿Cuánto de deben sobrar de
$500 al comprar 5 pedazos de pizza y 5 jugos?
Answer:
I think it is 275 if you are subtracting
i need help with
−5 × −8 =
Answer:
40
Step-by-step explanation:
-5 * (-8) = 40
Answer:
40
Step-by-step explanation:
Because multiplication of subtract will be added
Show your work and explain how you can determine which is a better deal:
10 ounces of orange juice for $2.40 or 8 ounces for $2.08?
divide 10 by 2.40 it gives you a decimal 4.16 and go on. Round it and its 4.20.
What value of x and y will make the polygon a parallelogram
105°
V
15x
Answer
60
Step-by-step explanation:
105+15= 120
180-120=60
I think this is the correct answer but I dont know
What is the slope of the line shown in the graph?
Answer:
y = -3/2x - 2.5
Step-by-step explanation:
First, identify the slope by using y-y1/x-x1
2- -1 = 3, -3 - -1 = -2 the slope is -3/2
Then, you have y = -3/2x + b
To find b, you have to plug in a value of x and y
I will use the point (-3,2) for this example.
2 = -3(-3/2) + b
2 = 9/2 + b
2 = 4.5 + b
b = -2.5
Once you assemble your equation, you should get y = -3/2x - 2.5
can someone help me?
9514 1404 393
Answer:
8.39
Step-by-step explanation:
In the right triangle, the hypotenuse and side opposite the angle are shown. The applicable trig relation is ...
Sin = Opposite/Hypotenuse
Opposite = Hypotenuse × Sin
x cm = (15 cm)×sin(34°)
x ≈ 8.39
HELP IM BEING TIMED ON THIS
Answer:
im pretty sure its 1
Step-by-step explanation:
Answer:
the answer is (3 4)
Step-by-step explanation:
Y varies directly with x. If y = 150 when x = 3, what is x when y = 600
Answer:
Step-by-step explanation:
Y varies directly with x:
y=kx
for some non-zero constant k
substitute y=150 and x=3:
150=3k
k=50
When y=600:
600=(50)x
x=12
To make meatloaf. mix 2 pounds of beef and 0.5 of a cup of breadcrumbs. How many pounds of beef
would you mix with 4.5 cups of breadcrumbs
Answer:
18 pounds of beef.
Step-by-step explanation:
For every 0.5 cups of breadcrumbs there's 2 pounds of beef.
0.5 x 9 = 4.5
9 x 2 = 18 or 2 x 9 = 18
multiples of two: 2 4 6 8 10 12 14 16 18
This shows that when we multiply 2 nine times we get 18!
The sum of two consecutive even integers is 98 find the larger number
Answer:
50
Step-by-step explanation:
Let's say the smaller number is x then
x + x + 2 = 98
2x+2 = 98
2x = 96
x = 48
==> 48, 50
The sum of two consecutive even integers is 98 has 50 as larger number.
Given that the sum of two consecutive even integers is 98, we need to find the larger number,
Let's denote the two consecutive even integers as x and x + 2. According to the given information, their sum is 98.
So we can write the equation:
x + (x + 2) = 98
Simplifying the equation:
2x + 2 = 98
Subtracting 2 from both sides:
2x = 96
Dividing both sides by 2:
x = 48
Therefore, the larger number (x + 2) is:
48 + 2 = 50
So, the larger number is 50.
Learn more about Consecutive Numbers click;
https://brainly.com/question/29775116
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Estimate 307‾‾‾‾√ between two consecutive whole numbers. Enter the numbers in the boxes below.
Answer:
17, 18
Step-by-step explanation:
closest perfect square that is lower than 307 is 289
closest perfect square that is greater than 307 is 324
[tex]\sqrt{289} < \sqrt{307} < \sqrt{324}[/tex]
[tex]17<\sqrt{307} <18[/tex]
