A flag in the shape of a right triangle is hung over the side of a building as shown below. The total weight of the flag is 250 pounds and it has uniform density. a = 15 and b = 39.
Answers
Answer:
(a) The density of flag is [tex]\dfrac{25}{27}[/tex] Pounds per square foot
(b) The weight of strip is [tex]\dfrac{20}{9}(15-h)\Delta h[/tex] Pounds
(c) The work is [tex]\dfrac{20}{9}(15-h)h\Delta h[/tex] foot-pounds
(d) The exact work by roof is 1250 foot-pounds
Step-by-step explanation:
(a) We are given a flag in the shape of a right triangle.
The total weight of flag is 250 pounds and Uniform density.
Base of the flag [tex]=\sqrt{b^2-a^2}[/tex]
[tex]=\sqrt{39^2-15^2}=36[/tex]
Area of the flag [tex]=\dfrac{1}{2}\times 36\times 15 = 270[/tex]
Weight of flag = 250 pounds
[tex]Density =\dfrac{Weight}{Area}=\dfrac{250}{270}=\dfrac{25}{27}[/tex]
Hence, The density of flag is [tex]\dfrac{25}{27}[/tex]
(b) Weight of strip which is h feet below the roof.
Length of strip [tex]=\dfrac{36}{15}(15-h)[/tex]
Width of strip [tex]\Delta h[/tex]
Weight = Density x area
[tex]=\dfrac{25}{27}\times \dfrac{36}{15}(15-h)[/tex]
[tex]=\dfrac{20}{9}(15-h)\Delta h[/tex]
Hence, The weight of strip is [tex]\dfrac{20}{9}(15-h)\Delta h[/tex]
(c) Work slice to move h feet above to the roof
work[tex]=Weight\times displacement[/tex]
[tex]=\dfrac{20}{9}(15-h)\Delta h\times h[/tex]
[tex]=\dfrac{20}{9}(15-h)h\Delta h[/tex]
Hence, The work is [tex]\dfrac{20}{9}(15-h)h\Delta h[/tex] foot-pounds
(d) Exact work on the roof by hanging flag
[tex]W=\int_0^{15}\dfrac{20}{9}(15-h)hd h[/tex]
[tex]W=\dfrac{20}{9}(\dfrac{15h^2}{2}-\dfrac{h^3}{3})|_0^{15}[/tex]
[tex]W=1250-0[/tex]
[tex]W=1250[/tex]
Hence, The exact work by roof is 1250 foot-pounds
Final answer:
The weight of the flag is distributed uniformly across its area, with the entire 250 pounds concentrated at the centroid point.
Explanation:
To find the centroid of a right triangle, we can use the following formulas:
[tex]\[ x_c = \frac{b}{3} \][/tex]
[tex]\[ y_c = \frac{a}{3} \][/tex]
Where:
[tex]- \( x_c \)[/tex] is the x-coordinate of the centroid.
[tex]- \( y_c \)[/tex] is the y-coordinate of the centroid.
[tex]- \( a \)[/tex] is the length of the side perpendicular to the base (height).
[tex]- \( b \)[/tex] is the length of the base.
Given \( a = 15 \) and \( b = 39 \), we can calculate the centroid as follows:
[tex]\[ x_c = \frac{39}{3} = 13 \][/tex]
[tex]\[ y_c = \frac{15}{3} = 5 \][/tex]
So, the centroid of the triangle is located at the point (13, 5).
Now, regarding the weight distribution, if the flag has uniform density, the center of mass (or centroid) would be the point where the total weight is concentrated. Since the total weight of the flag is 250 pounds, and the centroid is the point of concentration of mass, the entire weight of the flag, 250 pounds, can be considered to act at the centroid.
Therefore, the weight of the flag is distributed uniformly across its area, with the entire 250 pounds concentrated at the centroid point.
Related Questions
you work for a dress maker and your boss sends you to the fabric store to buy blue fabric she tells you to buy the best deal what's is the best deal
20 yards for $30.00
40 yards for $45.00
50 yards for $70.00
65 yards for $85.00
Answers
Given 40 yards for $45.00, unit rate = $45 / 40 yards = $1.13 per yard
Given 50 yards for $70.00, unit rate = $70 / 50 yards = $1.4 per yard
Given 65 yards for $85.00, unit rate = $85 / 65 yards = $1.31 per yard
The best deal is the cheapest rate which is 40 yard for $45.00
draw or write to explain why 1 hundred 4 tens and 14 tens name the same amount
Answers
4 tens=40
14 tens= 140
When we add them all we get 280 ones or 2.8 hundreds or 28 tens.
find factors of 5x^3+10x^2+35x
Answers
First, let’s take a look at our terms.
5x^3 + 10x^2 + 35x
All of our terms have an x, so we can factor out this expression/trinomial with our variable. Now, let’s find the GCF (Greatest Common Factor) for our coefficients (or our numbers).
5x^3 + 10x^2 + 35x
Each of these have a factor of 5, so divide each term by 5x (since all our terms have an ‘x’). While we do this, write our GCF outside of a parenthesis and divide our terms by the GCF. The quotient will be inside of our parenthesis.
5x^3 + 10x^2 + 35x
5x(x^2 + 2x + 7)
The terms inside of the parenthesis are our simplified factors; x^2 + 2x + 7.
I hope this helps!
The outside diameter of a pipe is 5 and 7/32 inches. The walls of the pipe are 5/32 inches thick whats the inside diameter
Answers
Mr. Yu applies 1/2 ounce of fertilizer to every 5/8 square meter of his lawn. How many ounces of fertilizer does Mr. Yu use per square meter for his lawn? Enter your answer in the box as a fraction in simplest form.
Answers
(1/2)/(5/8)
1/2*8/5
8/10
4/5
Answer:
[tex]\frac{4}{5} [/tex] ounce
Step-by-step explanation:
We can use rule of three to answer this problem.
The data we have is the following:
fertilizer (ounces) area(m^2)
1/2 ⇒ 5/8
x ⇒ 1
the x represents the unknown quantity of fertilizer that is used in one square meter.
Now we multiply the cross quantities and divide by the remaining value.
[tex]x=\frac{1}{2}*1[/tex] ÷ [tex]\frac{5}{8}[/tex]
[tex]x=\frac{1*8}{2*5} =\frac{8}{10} =\frac{4}{5}[/tex]
He will use 4/5 ounces of fertilizer per square meter.
We can solve for x using a technique called successive approximations. step 1: if we assume that x is very small compared to 0.100 (such that 0.100 x ≈ 0.100) then our first approximation of x (let\'s call it x1) can be calculated as
Answers
Supposed that we are given the equation:
7.20 x 10^-5 = x(0.100+x)^2
So assuming that x is very small so that:
0.100 + x ~ 0.100
and calling it x1, so:
7.20 x 10^-5 = x1 (0.100)^2
Then we simply solve for x1:
x1 = 7.20 x 10^-5 / (0.100)^2
x1 = 7.20 x 10^-3
Final answer:
Successive approximations involve iterative guesses to find a solution, Newton's Method refines initial guesses using derivatives, and the Intermediate Value Theorem guarantees a solution in a given interval.
Explanation:
Successive Approximations: When solving for x using successive approximations, we make iterative guesses, refining our estimation with each step. The method involves making an initial guess, then refining it until a sufficiently accurate solution is obtained.
Newton's Method: Newton's method is a numerical technique used to find roots of a function. It involves making an initial guess and then iteratively improving upon it by using the function's derivative.
Intermediate Value Theorem: The intermediate value theorem states that a continuous function that takes on values of opposite signs at two points must have at least one root within that interval.
A box contains marbles of five different colors: red, green, blue, yellow, and purple. there is an equal number of each color. assign probabilities to each color in the sample space. (give your answers as fractions.)
Answers
P(green) = 1/5
P(blue) = 1/5
P(yellow) = 1/5
P(purple) = 1/5
The reason the fractions are all the same is that there are equal numbers of each color. For example, if there were 7 marbles of each color, there would be a total of 35 marbles.
P(red) = 7/35 = 1/5
Similar for the other colors.
To assign probabilities to each color in the sample space of marbles in a box, you need to determine the total number of marbles and the number of marbles of each color. Assuming there is an equal number of each color, the probability of drawing each color is 1/5.
Explanation:To assign probabilities to each color in the sample space, we need to determine the total number of marbles and the number of marbles of each color. Since there is an equal number of each color, let's assume there are n marbles of each color.
The total number of marbles is 5n. The probability of drawing a red marble is n/5n = 1/5. Similarly, the probability of drawing a green marble is n/5n = 1/5, the probability of drawing a blue marble is n/5n = 1/5, the probability of drawing a yellow marble is n/5n = 1/5, and the probability of drawing a purple marble is n/5n = 1/5.
James has 875 feet of rope. There are 13 teams of hikers. If James gives an equal amount of rope to each team how much rope will each team receive
Answers
Answer:
67.307 feet of rope per team
Step-by-step explanation:
Taylor bought 200 shares of stock for $18.12 per share last year. He paid his broker a fl at fee of $30. He sold the stock this morning for $21 per share, and paid his broker 0.5% commission. a. What were Taylor's net proceeds?
Answers
Final answer:
Taylor's net proceeds from the stock transaction are $525, after accounting for the initial purchase cost and broker's commissions on both the buying and selling of the stock.
Explanation:
Taylor bought 200 shares of stock at $18.12 per share and paid a flat brokerage fee of $30. To find the initial cost, we multiply the number of shares by the purchase price and then add the fee:
200 shares × $18.12/share + $30 = $3,654
When Taylor sold his shares at $21 per share, his gross proceeds were:
200 shares × $21/share = $4,200
The broker commission of 0.5% on the selling price is calculated as:
$4,200 × 0.005 = $21
To find Taylor's net proceeds, we subtract both the initial cost and the selling commission from the gross proceeds:
$4,200 - $3,654 - $21 = $525
Therefore, Taylor's net proceeds from the stock transaction are $525.
mrs. ellis wants to tile a rectangular room that is 16 feet long and 12 feet wide with square tiles. each square floor is 2 feet. the tiles cost $0.84 per tile. what is the cost to tile the room not including labor?
Answers
192:2=96 tiles need Mrs Ellis
96*0,84 $=80,64 $ is the cost
Mrs. Ellis would need 48 tiles to cover the area of her room. The cost of a single tile is $0.84, so the total cost to tile the room not including labor would be $40.32.
Explanation:To determine the cost to tile the room, we first need to figure out how many tiles Mrs.Ellis needs. We know that each tile covers an area of 2ft * 2ft, which is 4 square feet. Now, we must find out the area of the room by multiplying the length by the width (16ft * 12ft), resulting in 192 square feet. To find out how many tiles are needed, we can divide the total area of the room by the area of one tile (192ft² / 4ft² = 48). Therefore, Mrs. Ellis needs 48 tiles to cover the entire room. Since each tile costs $0.84, the total cost would be 48 * $0.84 = $40.32. Thus, the cost to tile the room excluding labor charges is $40.32.
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Let n be a natural number such that the remainder of the division of 4294 by n is 10, and the remainder of the division of 3521 by n is 11. what is n?
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What is the simplified form of the expression k^3(K^7/5)^-5
Answers
a light bulb consumes 3600 Watts hours per day. how long does it take to consume 12600 Watts hours?
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because 12600 divided by 3600 is 3.5
it would take 84 hours,or 3.5 days,hope this helps
forty more than twice malia's age is 64
Answers
A major stadium has 45,000 seats. If baseball fans have bought 5/8 of the seats for the next game, how many seats are available?
Answers
if 5/8 were bought then 3/8 are still available ( 5/8 +3/8 = 1)
45000 * 3/8 = 135000/8 = 16,875 seats are still available
What percentage is 1022.40 of 1420 and how do i solve
Answers
So here's the question
"Melissa knitted a scarf with 9 1/5
yards of red yarn. She used another 3 11/25 yards of blue yarn to finish knitting. How much more red than blue yarn did Melissa use?"
I need help solving it, and it is subtraction, right?
Answers
first off, let's convert the mixed fractions, to "improper", and then subtract.
[tex]\bf \stackrel{red~yarn}{9\frac{1}{5}}-\stackrel{blue~yarn}{3\frac{11}{25}}[/tex]
[tex]\bf -------------------------------\\\\ \stackrel{mixed}{9\frac{1}{5}}\implies \cfrac{9\cdot 5+1}{5}\implies \stackrel{improper}{\cfrac{46}{5}} \\\\\\ \stackrel{mixed}{3\frac{11}{25}}\implies \cfrac{3\cdot 25+11}{25}\implies \stackrel{improper}{\cfrac{86}{25}}\\\\ -------------------------------\\\\ \cfrac{46}{5}-\cfrac{86}{25}\impliedby \textit{our LCD is 25}\implies \cfrac{(5\cdot 46)~~-~~(1\cdot 86)}{25} \\\\\\ \cfrac{230~-~86}{25}\implies \cfrac{144}{25}\implies 5\frac{19}{25}[/tex]
Does the function satisfy the hypotheses of the mean value theorem on the given interval? f(x) = x3 + x − 9, [0, 2]
Answers
which supports the mean value theorem, you want even better news
if the function is a polynomial it will always follow the mean value theorem
60 bricklayers began a 16-day project to build a castle. After five days, five of the bricklayers quit the job. If they work the same amount each day, how many extra day(s) (beyond the original estimate of 16) will the remaining bricklayers need?
Answers
(60)(16) = (5)(60) + (11 + x)(60 - 5)
where x is the number of extra days that the bricklayers will still have to work to complete the job. The value of x from the equation is 1
Answer: 1
A car travels down a highway at 45 m/s. An observer stands 200 m from the highway.
How fast is the distance from the observer to the car increasing when the car passes in front of the observer?
How fast is the distance increasing 40 s later?
Answers
so, the left-side is when the car is right in front of the observer, at that point, notice the y-distance, is pancaked, so is 0, but increasing, we know dy/dt is 45 m/s, and notice the "r" distance, is the same as the "x" distance, keeping in mind that whilst "r" is increasing or moving about, "x" is static, is a constant.
[tex]\bf \stackrel{\textit{pythagorean theorem}}{r^2=x^2+y^2}\implies 2r\cfrac{dr}{dt}=\stackrel{constant}{0}+2y\cfrac{dy}{dt} \\\\\\ 2r\cfrac{dr}{dt}=0+2(0)(45)\implies \cfrac{dr}{dt}=0[/tex]
now, 40 seconds later, since the car is going at 45 m/s, in 40 seconds it has covered 40 * 45 meters, or 1800, so y = 1800, x = 200, what is "r"?
[tex]\bf r^2=x^2+y^2\implies r=\sqrt{200^2+1800^2}\implies r=\sqrt{3280000} \\\\\\ r=\sqrt{200^2\cdot 82}\implies r=200\sqrt{82}\\\\ -------------------------------\\\\ 2r\cfrac{dr}{dt}=0+2y\cfrac{dy}{dt}\implies \cfrac{dr}{dt}=\cfrac{y\frac{dy}{dt}}{r}\quad \begin{cases} r=200\sqrt{82}\\ y=1800\\ \frac{dy}{dt}=45 \end{cases} \\\\\\ \cfrac{dr}{dt}=\cfrac{1800\cdot 45}{200\sqrt{82}}\implies \cfrac{dr}{dt}=\cfrac{405}{\sqrt{82}}\implies \cfrac{dr}{dt}=\cfrac{405\sqrt{82}}{82}[/tex]
you have a standard deck of 52 cards. you pick one card from the deck and then , without putting the first card back , pick a second card . what is the probability that both cards will be 9s??
Answers
there are 4 9's in a deck
so first pick = 4/52 reduces to 1/13
second pick there would be 3 9's left and 51 cards so it would be 3/51 reduces to 1/17
probability of both happening = 1/13 * 1/17 = 1/221 (fraction form)
if you need it in decimal it = 1/221 = 0.00452, rounded to 0.005
Which rows represent when (p ∧ q) ∨ (p ∧ r) is true?\
Answers
or p ∧ (q ∨ r).
Answer:
The answer is B. A, B, and C
Step-by-step explanation:
Just took the test on edg
Baruka has gallon of milk left in the 1/2 fridge. How many 5/64 gallon (10-ounce) servings of milk does she have left? Show your work
Answers
Baruka has [tex]\( \frac{32}{64} \)[/tex] gallons left. [tex]\( \frac{32}{5} \) servings of \( \frac{5}{64} \)[/tex] gallons; she has 6 servings.
To find out how many [tex]\( \frac{5}{64} \)[/tex] gallon servings of milk Baruka has left, we need to first convert the amount of milk she has in gallons to the same unit as [tex]\( \frac{5}{64} \)[/tex] gallons.
Since [tex]\( 1 \)[/tex] gallon is equivalent to [tex]\( \frac{64}{64} \)[/tex] gallons, and she has [tex]\( \frac{1}{2} \)[/tex] gallon left, she has [tex]\( \frac{1}{2} \times \frac{64}{64} = \frac{32}{64} \)[/tex] gallons left.
Now, we can find out how many [tex]\( \frac{5}{64} \)[/tex] gallon servings are in [tex]\( \frac{32}{64} \)[/tex] gallons:
[tex]\[ \frac{\frac{32}{64}}{\frac{5}{64}} = \frac{32}{5} \][/tex]
Now, we divide [tex]\( 32 \) by \( 5 \)[/tex] to find the number of servings:
[tex]\[ \frac{32}{5} = 6.4 \][/tex]
So, Baruka has [tex]\( 6.4 \)[/tex] servings of [tex]\( \frac{5}{64} \)[/tex] gallon servings of milk left. However, since she can't have a fraction of a serving, she has [tex]\( 6 \)[/tex] servings left.
The three incoming currents at a node in an electrical circuit measure 0.7 amps, 0.68 amps, and 0.47 amps two of the three outgoing current measure 0.8 amps and 0.55 amps find the measure of the third outgoing current
Answers
The measure of the third outgoing current will be 0.5 amperes.
What is Algebra?The analysis of mathematical representations is algebra, and the handling of those symbols is logic.
The three incoming currents at a node in an electrical circuit measure 0.7 amps, 0.68 amps, and 0.47 amps two of the three outgoing currents measure 0.8 amps and 0.55 amps.
Then the measure of the third outgoing current will be
We know that the sum of the incoming current will be equal to the sum of the outgoing current at a junction.
Let the incoming current be I₁, I₂, and I₃. And the outgoing current is I₄, I₅, and I₆. Then we have
I₁ + I₂ + I₃ = I₄ + I₅ + I₆
0.7 + 0.68 + 0.47 = 0.8 + 0.55 + I₆
1.85 = 1.35 + I₆
I₆ = 0.5
Thus, the measure of the third outgoing current will be 0.5 amperes.
More about the Algebra link is given below.
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please help im really dumb lol
Answers
Samantha puts an initial $500 into a savings account. The account has a 4% annual compound interest rate. What is the function that best represents Samantha's account and how much does she have in savings after 5 years? Round your answer to the nearest dollar. Hint: Use the formula, f(x) = P(1 + r)x. (5 points)
Answers
a. The function that would best represent Samantha's account is f(5) = 500(1 + 0.04)^5. This is because $500 is the principal, the interest rate is 4%, and we're looking for the amount in the savings account 5 years later.
b. Okay. 1 = 0.04 is 1.04. 1.04^5 is 1.216652902. It's a long decimal, but don't delete it. Multiply that decimal by 500 and you get 608.32645 and other numbers behind it or 608 when rounded to the nearest dollar. Samantha will have about $608 in her savings account in 5 years.
Note: The formula goes like this: f(x) = P(1 + r)^x. This means, you add 1 and the simple interest rate in decimal form together and raise that up by the exponent. There is no shortcuts for this, so you'll have to use the calculator. There will be a very long decimal, but don't clear it. Instead, multiply it by the principal to get the answer. It seems very complicating, but if you do this right, it gets easier overtime and you'll make less errors. There are more complex problems out there, so this formula is very important, but it was kept simple for this question.
Answer: The answer is y = 500(1.04) x
Step-by-step explanation: The formula is y = P (1 + r) x
So, given that P which is the initial value 500(1+0.4) x
f(x)=500(1.04) x
If p(a) = 0.62, p(b) = 0.47, and p(a or
b.= 0.88, then p(a and
b.= _____
Answers
P(A or B)=P(A)+P(B)-P(A and B)
Substitute given values,
0.88=0.62+0.47-P(A and B)
=>
P(A and B)=0.62+0.47-0.88=0.21
Probabilities are used to determine the chances of an event
The value of P(a and b) is 0.21
The given parameters are:
P(a) = 0.62
P(b) = 0.47
P(a or b) = 0.88
P(a and b) is calculated using the following formula
P(a and b) = P(a) + P(b) - P(a or b)
So, we have:
P(a and b) = 0.62 + 0.47 - 0.88
P(a and b) = 0.21
Hence, the value of P(a and b) is 0.21
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simplify the fraction 48 over 75
Answers
Reduce by 3
16/25
48/75
both numbers are divisible by 3
so it simplifies to 16/25
Jan has a 12 ounce milkshake four ounces in the milkshake are vanilla and the rest is chocolate what are two equivalent fraction of the milkshake is vanilla
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Answer:
In this item, we are given that out of 12 ounces of ingredients comprising the milkshake, there are 4 ounces vanilla. Expressing this into fraction will give us an answer of 4/12. This fraction can be one of the answers. Since we are asked for two fractions, we can simplify 4/12 such that we get an equivalent fraction that is equal to 2/6. Hence, the answers to this question are 4/12 and 2/6...
hope it helps
Tony buys a CD that is priced at $13.59. He has a coupon for $1.85 off. He pays with a $20 bill. Which is the best whole number estimate of how much change he gets? $8