A vertical plate is submerged in water and has the indicated shape.
A triangle is submerged in water pointed up. The top most vertex of the triangle touches the surface of the water. The base of the triangle is 6 m and is parallel to the surface of the water. The height of the triangle is 15 m.
Express the hydrostatic force (in N) against one side of the plate as an integral (let the positive direction be upwards) and evaluate it. (Use 9.8 m/s2 for the acceleration due to gravity. Recall that the weight density of water is 1,000 kg/m3.)
Answers
The hydrostatic force is given by the integral of the force acting on
small horizontal strips from the base to the top of the triangle.
Response:
The hydrostatic force one one side of the plate is 4.41 MNHow can the hydrostatic force acting on the plate be calculated?The given parameters are;
Base of the triangle = 6 m
Height of the triangle = 15 m
Acceleration due to gravity, g ≈ 9.8 m/s²
Weight density of water, ρ ≈ 1,000 kg/m³
Required:
Hydrostatic force on one side of the plate
Solution:
Considering a thickness, dx, having area, dA = y·dx
The pressure on the strip = ρ·g·x
Force on the strip, dF = ρ·g·x·y·dx
Using similar triangles, we have;
[tex]\dfrac{x}{15} = \dfrac{y}{6}[/tex]
Which gives;
[tex]y = \dfrac{x}{15} \times 6 = \mathbf{ \dfrac{2}{5} \cdot x}[/tex]
Therefore;
[tex]dF = \rho \cdot g \cdot x \cdot \dfrac{2}{5} \cdot x \cdot dx = \mathbf{\rho \cdot g \cdot x^2 \cdot \dfrac{2}{5} \cdot dx}[/tex]
Which gives;
[tex]F =\displaystyle \int\limits^{15}_0 { \rho \cdot g \cdot x^2 \cdot \dfrac{2}{5} } \, dx = \mathbf{\left[\rho \cdot g \cdot x^3 \cdot \dfrac{2}{3\times 5} \right]^{15}_0}[/tex]
Therefore;
[tex]F = \rho \cdot g \cdot \left[x^3 \cdot \dfrac{2}{3\times 5} \right]^{15}_0 = \mathbf{ \rho \cdot g \times 15^3 \cdot \dfrac{2}{3\times 5}} = 450 \cdot \rho \cdot g[/tex]
Which gives;
F = 450 m³ × 1,000 kg/m³ × 9.8 m/s² = 4,410,000 N = 4.41 MN
The hydrostatic force one one side of the plate, F = 4.41 MNLearn more about hydrostatic force here:
https://brainly.com/question/14201809
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Find the range of possible values for x.
Answers
Answer:
x is between 5 and 33 ⇒ 5 < x < 33Step-by-step explanation:
The two triangles have two equal side measures:
4 units and the sides marked as equal,The third side is different and the given angles are opposite them.
It means the angle measure 4x - 20 is smaller than 112:
4x - 20 < 1124x < 132x < 132/4x < 33On the other hand, the angle measure is positive:
4x - 20 > 04x > 20x > 5So the possible range of x is:
5 < x < 33First it must be positive
4x-20>04(x-5)>0x-5>0x>5And
4x-20<1124x<132x<33So solution range
(5,33)assuming all variables are positive,. use the properties of logarithms to write an expression as a sum or difference log2(x^3y^8/5)
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Answer:
hola es 553586;(8)5-?+&5%€3-+(?))%-!++533++&€3€-((+%6544-++86
=
The scale on a map reads 0.5 inches = 75 miles. The distance between two
cities on the map is 3.25 inches, find the actual distance between the
cities.
Answers
Answer:
0.5inches=75miles
[tex]3.5 = 75 \times 7 = 525[/tex]
so it means the distance between the two towns is 525miles
Find the measure of each bolded arc. Round to the nearest hundredth. Any help I will give 5 stars and a thanks!
Answers
Answer:
Step-by-step explanation:
Solve for c.
4(3+ c) +c=c+4
Answers
4c=-8
C=-2
Please brainiest and like
Step-by-step explanation:
[tex]4(3 + c) + c = c + 4 \\ 12 + 4c + c = c + 4 \\ 12 + 5c = c + 4 \\ 12 + 4c = 4 \\ 4c = 4 - 12 \\ 4c = - 8 \\ c = - 2[/tex]
5.4×18 =
pls explain properly
Answers
Answer:
[tex]5.4x18 = 97.2[/tex]
Step-by-step explanation:
5.4
×
18
=97.2
Answer:
4x18=72 that's the correct answer I use calculator
can someone please help
Answers
Multiply the inside and out and this will simplify
Please like and brainliest
Answer:
-24xy
Step-by-step explanation:
First:
6x-4= -24
Second Add the variable:
-24xy
Third: Solution
-24xy
Six students are running for the positions of president and vice-president, and five students are running for secretary and treasurer. If the two highest vote getters in each of the two contests are elected, how many winning combinations can there be?
Answers
Using the permutation formula, it is found that there can be 600 winning combinations.
There are roles involved(president, vice-president, secretary and treasures), hence the order is important and the permutation formula is used.
What is the permutation formula?The number of possible permutations of x elements from a set of n elements is given by:
[tex]P_{(n,x)} = \frac{n!}{(n-x)!}[/tex]
In this problem:
For president and vice-president, 2 students are chosen from a set of 6.For secretary and treasurer, 2 students are chosen from a set of 5.Hence:
[tex]T = P_{6,2}P_{5,2} = \frac{6!}{4!} \times \frac{5!}{3!} = 30 \times 20 = 600[/tex]
There can be 600 winning combinations.
More can be learned about the permutation formula at https://brainly.com/question/25925367
Please help!! this is due in 2 hours!!
Answers
Step-by-step explanation:
AB/BD=AC/CE
12/8=15/CE
12CE/12=120/12
CE=10
It takes 3 hours of 10 pumps to pump 40000 liters of water into a farm dam.How long will it take nine similar pumps to pump 60000 liters of water into the dam
Answers
It will take 5 hours to pump 60000L of water using 9 pumps
Data;
10 pumps = 40000L in 3 hours9 pumps = 60000L in x hoursRate of the PumpRate = Time * number of pumps
[tex]\frac{a}{3*10} = \frac{60000}{40000}\\ \frac{a}{30} = \frac{6}{4} \\a = 45[/tex]
But since we've established the equation above, let's substitute the values and solve for the time required to pump 60000L into the dam using 9 pumps as compared to 10 pumps. We can easily do this by calculating the rate of the pump.
Rate = time * number of pumps
[tex]45=x*9\\x = \frac{45}{9} \\x = 5 hours[/tex]
It will take 5 hours to pump 60000L of water using 9 pumps
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I need help please help!
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Answer:
50.5 m^3
Step-by-step explanation:
Volume of pyramid = 1/3 × base area × height.
Height: 11Base Dimensions: 4.3 and 3.2Area of Base:
[tex]4.3 * 3.2[/tex] [tex]13.76[/tex]Next, we multiply 13.76 by 11.
13.76 × 11151.36Lastly, divide by 3 and round to nearest tenth.
151.36 ÷ 3 50.453333..≈ 50.5Therefore, the answer is 50.5 m^3
The multiple choices are 29,58,111,116,444 please explain to me I'm confuse
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Which of the following points are
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Answer:
(2;-5) and (0;-4).
Step-by-step explanation:
if the given graph is the same as in the attached picture (y=-0.5x-4), then two points only belong to it.
Use the figure for Exercises 17-23. Write true or false. If a statement is false,
rewrite it so it is true.
Answers
Answer:
17. False: ∠QUR is a right angle.
18. True
19. False: change supplementary into complementary.
20. True.
21. False: change 40 into 55.
22. False: change the second 150 into 30.
23. False: change 180 into 90.
Which of the following segments is a diameter of o
O?
Answers
Answer: A
Step-by-step explanation:
The segment passes through the center of the circle, O, and its endpoints lie on the circumference of the circle.
The segment ZX is the diameter of the circle O. Then the correct option is A.
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The diameter of the circle is the longest chord that is passing through the center of the circle.
The segment ZX is the diameter of the circle O.
Then the correct option is A.
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Evaluate the expression z2 - 6 if z = 4 The solution is:
Answers
Answer:
4 x 2 - 6
= 8 - 6
=2
Step-by-step explanation:
Evaluate each expression 4x0x9.17 and 1.8x1x2
Answers
Answer:
0 and 3.6
Step-by-step explanation:
4x0x9.17= 0
1.8x1x2= 3.6
Answer:
0
3.6
Step-by-step explanation:
4x0x9.17=0
1.8x1x2=3.6
What is the solution for the linear system 4x + 2y = 8 and
2x+2y=2
Answers
Answer:
(3,-2)
Step-by-step explanation:
See image
a herd of 27 horses and 4 white and some black horses. what is the ratio of white to black
Answers
Answer:
4:23
Step-by-step explanation:
4 to 23 is the ratio because if some is representing the rest of the horses then there is 23 black and 4 white so 4 to 23 is the ratio of white to black horses.
Hope it helps have a great day :)
Please help me with this math problem!! Will give brainliest if correct! NO links please!
Answers
Answer:
equation: sin 20 = 15/x
x=43.86
Step-by-step explanation:
sin = opposite over hypotenuse = 15/x from the corner with angle 20
Which number is an irrational number?
Answers
Answer:
(b) -√3
Step-by-step explanation:
Any fraction or terminating decimal is rational. (a) and (c)
Any repeating decimal is rational.
Any square root of a perfect square is rational. (d)
Any square root of an integer that is not a perfect square is irrational. (c)
The sign of the number is irrelevant.
__
Of these numbers, the irrational one is -√3.
A line passes through the points (4,22) and (8,26) Write a linear function rule in terms of x and y for this line.
Answers
Answer:
y = x + 18
Slope = 1
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Step-by-step explanation:
I feel like this graph would be better at describing it than words. Basically, for every time that it goes up once, it also goes over once, and it starts at the height of 18.
300 people attended a concert.
5% of the people came from Scotland.
30% of the people came from Wales.
How many more people came from Wales than from Scotland?
Answers
Answer:
75
Step-by-step explanation:
0.3*300=90
0.05*300=15
90-15=75
Answer:
ok so we want to find out 30% of 300 is
so first lets turn it into its decmil form by multiplying by 0.01 so
30*0.01=0.3
then lets multiply that by 300 so
300*0.3=90
90 people were from whales
15 people from scotland
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Hope This Helps!!!
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Answer:
M=5+sr of 15/10, 5-sr of 15/10
Make X the subject in the following relation. y=2x+3
Answers
Answer:
[tex]x = \frac{y - 3}{2} \\ [/tex]
Step-by-step explanation:
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There are 110 sixth-grade students in a Florida
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Answers
Answer:
44 students play video games
Step-by-step explanation:
110*0.40 = 44
i hope this helps! have a wonderful rest of ur day :)
Answer:
40/100
Step-by-step explanation:
40% of 110 is 44 so we make this a fraction 44/110 and then simplify to get 2/5 and after that we know that 2/5 is also 40/100, meaning 40 out of 100 students like video games.
What is the solution to this equation -8x - 40 = 8
Answers
The answer is -6 :)
1. Add 40 to both sides of the equation.
-8x-40=8
-8x-40+40=8+40
2. Add the numbers.
-8x=48
3. Divide both sides of the equation by the same term.
-8x=48
[tex]\frac{-8x}{-8}[/tex]=[tex]\frac{48}{-8}[/tex]
4. Cancel terms that are in both the numerator and denominator and divide the numbers.
x=-6
hope this helped! :)
I need help 20 points!
Answers
Answer:
192 cm3
Step-by-step explanation:
The volume of any pyramid is 1/3 × b × h, where b = area of base of the pyramid and h = height of the pyramid.
In this case, the dimensions for the base are 6 and 8.The height is 24Area of Base:
[tex]\frac{6*8}{2}[/tex] [tex]48/2[/tex] [tex]24[/tex]Now, we multiply 24 by 24.
[tex]24*24[/tex] [tex]576[/tex]Lastly, we divide by 3.
[tex]576/3[/tex] [tex]192[/tex]Therefore, the answer is 192 cm^3.
What is the slope of the line that passes through (-4,2) and (6,-8)
Answers
Answer:
y = x + -2
Step-by-step explanation:
I know you're probably asleep but here's the answer. And I'm 14 years old, so I might be young and undereducated.
(-4,2) and (6,-8)
-8-2 = -10
6 -(-4) = 10 (-10/10 = -1)
-8 = 6(-1) + b
-8 = -6 + b
-2 = b
can someone help me pls
Answers
Answer:
20
Step-by-step explanation:
The grid lines are 1 unit apart, so you can determine the dimensions of the trapezoid by counting grid squares. The parallel bases have lengths 6 and 2. They are 5 units apart.
The area is given by ...
A = 1/2(b1 +b2)h
A = 1/2(6 +2)(5) = 20
The area of the trapezoid is 20 square units.