The equation of the line through (0, 1) and (c, 0) is
y - 0 = (0 - 1)/(c - 0) (x - c) ==> y = 1 - x/c
Let L denote the given lamina,
L = {(x, y) : 0 ≤ x ≤ c and 0 ≤ y ≤ 1 - x/c}
Then the center of mass of L is the point [tex](\bar x,\bar y)[/tex] with coordinates given by
[tex]\bar x = \dfrac{M_x}m \text{ and } \bar y = \dfrac{M_y}m[/tex]
where [tex]M_x[/tex] is the first moment of L about the x-axis, [tex]M_y[/tex] is the first moment about the y-axis, and m is the mass of L. We only care about the y-coordinate, of course.
Let ρ be the mass density of L. Then L has a mass of
[tex]\displaystyle m = \iint_L \rho \,\mathrm dA = \rho\int_0^c\int_0^{1-\frac xc}\mathrm dy\,\mathrm dx = \frac{\rho c}2[/tex]
Now we compute the first moment about the y-axis:
[tex]\displaystyle M_y = \iint_L x\rho\,\mathrm dA = \rho \int_0^c\int_0^{1-\frac xc}x\,\mathrm dy\,\mathrm dx = \frac{\rho c^2}6[/tex]
Then
[tex]\bar y = \dfrac{M_y}m = \dfrac{\dfrac{\rho c^2}6}{\dfrac{\rho c}2} = \dfrac c3[/tex]
but this clearly isn't independent of c ...
Maybe the x-coordinate was intended? Because we would have had
[tex]\displaystyle M_x = \iint_L y\rho\,\mathrm dA = \rho \int_0^c\int_0^{1-\frac xc}y\,\mathrm dy\,\mathrm dx = \frac{\rho c}6[/tex]
and we get
[tex]\bar x = \dfrac{M_x}m = \dfrac{\dfrac{\rho c}6}{\dfrac{\rho c}2} = \dfrac13[/tex]
The center of mass for a uniform triangular shape is on its centroid. The y-coordinate of the center of mass of the lamina is 1/3 (independent of c).
What is the center of mass for a triangular shape?If the surface is plane triangle approximately and mass is uniformally distributed, then its center of mass will lie on the centroid of that triangle.
What is centroid of a triangle and its coordinates?The point of intersection of a triangle's medians is its centroid (the lines joining each vertex with the midpoint of the opposite side).
If the triangle has its vertices as [tex](x_1, y_1), (x_2, y_2) , \: (x_3, y_3)[/tex], then the coordinates of the centroid of that triangle is given by:
[tex](x,y) = \left( \dfrac{x_1 + x_2 + x_3}{3} + \dfrac{y_1 + y_2 + y_3}{3} \right)[/tex]
For this case, the triangular lamina has vertices (0, 0), (0, 1) and (c, 0)
Assuming its mass is spread regularly, the coordinates of its center of mass would be:
[tex](x,y) = \left( \dfrac{x_1 + x_2 + x_3}{3} + \dfrac{y_1 + y_2 + y_3}{3} \right)\\\\(x,y) = \left( \dfrac{0+0+c}{3} + \dfrac{0+1+0}{3} \right) = (c/3, 1/3)[/tex]
Thus, the y-coordinate of the center of mass of the lamina is 1/3 (independent of c).
Learn more about centroid here:
https://brainly.com/question/7358842
Can someone please help me? Please C: And thanks!
How much would you need to deposit in an account each month in order to have $50,000 in the account in 8 years? Assume the account earns 4% annual interest compounded monthly.
Answer:
$540.98
Step-by-step explanation:
future value= $ 50,000
number of deposits (n)= 8*12 = 96
rate (r) = 4% per month
= 4÷12 per annum
= 0.33% p.a
i = 0.33÷100
= 0.0033
We know,
Future value of annuity = P÷i [ (1 + i)^n - 1 ]
$50,000 = P÷ 0.0033 [ ( 1+0.0033)^96 - 1]
$50,000 * 0.0033=P [ (1.0033)^96 - 1 ]
$165 = P*0.305
P = $165÷0.305
P = $ 540.98
Rough::
let x= 1.0033)^96
log x = 96 * log (1.0033)
log x = 0.1156
x = Antilog (0.1156)
= 1.305
1.305 - 1 = 0.305
Find theta to the nearest tenth of a degree, if theta is between 0 degrees and 360 degrees for sin theta = 0.4649 with theta in quadrant 2
9514 1404 393
Answer:
152.3°
Step-by-step explanation:
The arcsine function only gives angles in quadrants I and IV. Since this is a quadrant II angle, its value will be ...
θ = 180° -arcsin(0.4649) = 180° -27.7°
θ = 152.3°
if sin150=1/2 then find sin75
Sin75° = Sin(30° + 45°)
= Sin30°.Cos45° + Sin45°.Cos30°
= 1/2 . √2/2 + √2/2.√3/2
= √2/2 ( 1/2 + √3/2 )
= √2/2 ((1+√3 ) /2 )
= (√2 + √6 )/ 4
Julio is paid 1.1 times his normal hourly rate for each hour he works over 28 hours in a
week. Last week he worked 43 hours and earned $631.90.
Enter and solve an equation to find Julio's normal hourly rate, r. Complete the explanation
how you know that your answer is reasonable.
The earnings equation is $631.90 =
Julio's hourly l'ate is $
per hour.
This is reasonable because working 43 hours at a rate of $14 per hour is
43 · 14 = 43(10 + 4) = 430 + 172 =
and $
is close to $631.90.
Answer:
43-28= 15 extra hours
normal hourly rate = a
extra hourly rate = 1.1a
28a + 15(1.1a) = 631.90
28a + 16.5a = 631.90
11. Find the equation of the straight line that passes through (-4,2), (3,2) and (7,2).
Step-by-step explanation:
[tex](2 - 1 \frac{3 {3}^{2} }{?} [/tex]
Answer:
[tex]y=2[/tex]
Step-by-step explanation:
To solve this question, we can use the point-slope formula as we are given points on the line. This is the format:
[tex]y-y_{1} =m(x-x_{1} )[/tex]
The first step is to find the slope by substituting in two of the points. Let's try using (7,2) and (3,2):
[tex]2-2=m(7-3)\\0=4m\\m=0[/tex]
So now we have found that our slope is 0 meaning it is a flat line (shown by the unchanging y values through all three points).
The form for line equations is:
[tex]y=mx+c[/tex]
However, since our m=0, it is simplified to this:
[tex]y=c[/tex]
The y-value for all the points is 2, meaning c=2 (as it is also the y-intercept)
Therefore our final equation is:
[tex]y=2[/tex]
Hope this helped!
solve 8x=5x+3 pls pls pls
Answer:
x = 1
Step-by-step explanation:
8x = 5x + 3
Subtract 5x from both sides
8x - 5x = 5x - 5x + 3
Simplify
3x = 3
Divide both sides by 3
3x/3 = 3/3
Simplify
x = 1
Help with any of the questions what be appreciated
Answer:
The answer is s = d/t
Step-by-step explanation:
For question 12, I think this is called a literal equation, I might be wrong but I believe so it is a literal equation. They are asking you to get s on one side. And they are asking you what s is in terms of d and t. So what you do is, d = s x t. You multiply the t with the s and get d = st. Then you will divide t from both sides so, d/t = s/t, this will eliminate t from the s, and add it on to the d (distance). Which will leave you s on one side and d and t on the other. The answer is s = d/t.
Section 3
12) a) Here, as we need that s or speed is the subject so speed should be in place of distance. So, we get
s = d/t
Here, s is speed, d is distance and t is the time
12) b) We know that :
Average Speed = Total Distance/Total Time
Here, total distance is given 748 km
total time 11.5 hrs
Avg. Speed = 748/11.5
Avg. Speed = 65.04 km/h
Hence, the answer is 65.04 km/h
13) a) We know that volume of a rabbit hutch is
Volume of rabbit hutch = ½ × b × h × l
Here,
b is the breadth, h is the height and l is the length
Volume= ½ × 50 cm × 50 cm × 2.5 m
Now, here Length is in metre so we need to convert to cm
1 m = 100 cm
2.5 m = 2.5 × 100 = 250 cm
So, now
Volume= ½ × 50 cm × 50 cm × 250 cm
Volume = 50 cm × 50 cm × 125 cm
Volume = 312,500 cm³
Hence, the volume of this hutch is 312,500 cm³
13) b) Let us assume that the orange be a sphere
So, volume of orange = 4/3πr³
Here, r is the radius and π is pi
radius is 4 cm
Volume = 4/3π(4)³
Volume = 4/3 × 64π
Volume = 85.33π cm³
Volume of the orange is 85.33π cm³
Find m2 ABD.
A
D
40°
B
C
Find the distance of the point (4,4,−4) from the line r(t)=⟨−1+2t,1+2t,3−3t⟩.
Translate the given point and line together so that you get a new point and a new line that passes through the origin. This turns the problem into finding the distance between the new point,
p = (4, 4, -4) - (-1, 1, 3) = (5, 3, -7)
and the new line,
r*(t) = r(t) - ⟨-1, 1, 3⟩ = ⟨2t, 2t, -3t⟩
Let p = ⟨5, 3, -7⟩, the vector starting at the origin and pointing to p. Then the quantity ||p - r*(t)|| is the distance from the point p to the line r*(t).
Let u be such that ||p - r*(t)|| is minimized. At the value t = u, the vector p - r*(t) is orthogonal to the line r*(t), so that
(p - r*(u) ) • r*(u) = 0
I've attached a sketch with all these elements in case this description is confusing. (The red dashed line is meant to be perpendicular to r*(t).)
Solve this equation for u :
p • r*(u) - r*(u) • r*(u) = 0
p • r*(u) = r*(u) • r*(u)
and x • x = ||x||² for any vector x, so
p • r*(u) = ||r*(u)||²
⟨5, 3, -7⟩ • ⟨2u, 2u, -3u⟩ = (2u)² + (2u)² + (-3u)²
10u + 6u + 21u = 4u ² + 4u ² + 9u ²
17u ² - 37u = 0
u (17u - 37) = 0
==> u = 0 or u = 37/17
We ignore u = 0, since the dot product of any vector with the zero vector is 0.
Then the minimum distance distance between the given point and line is
||p - r*(u)|| = ||⟨5, 3, -7⟩ - 37/17 ⟨2, 2, -3⟩|| = √(42/17)
Question 1 of 10
What is the measure of ZXYZ shown in the diagram below?
Y
S
(369
7
Х
1140
Plz help
Answer:
B
Step-by-step explanation:
Secant-secant with vertex outside the circle
1/2(larger-smaller arc)
1/2(114-36)
1/2(78)
39
find the alternateof AHG
Answer:
angle HGD
Step-by-step explanation:
alternate angles are in Z position
What should be added to p to get p+q?
Answer:
Step-by-step explanation:
The correct answer is q
Because we have been given the equation p + q already so if we observe the equation carefully we see that if we add the variable q to the variable p we get the answer p + q
name all sets of numbers to which each real number belongs
Answer:
1. Natural Number
2. Integer
3. Rational Number
4. Rational Number
5. Irrational Number
6. Rational Number
7. Rational Number
8. Natural Number
9. Irrational Number
10. Integer
11. Irrational Number
12. Natural Number
If f(x) = 4x + 5 and fog(x) = 8x + 13 then find g(x).
Answer:
given
f(x).4x+5
fog(x).8x+13
now
fog(x):8x+13
4x+5(g(x)):: 8x+13
g(x):: 8x+13/4x+5
Answer:
g(x) = 2x + 2
Step-by-step explanation:
One is given the following information:
f(x) = 4x + 5f o g (x) = 8x + 13One is asked to find the following:
g(x)Remember, (f o g (x)) is another way of representing a composite function. A more visual way of representing this composite function is the following (f(g(x)). In essence, one substitutes the function (g(x)) into the function (f(x)) in places of the varaible (x). Thus, represent this in the form of an equation:
f(g(x)) = 8x + 13
Substitute the given infromation into the equation:
4(g(x)) + 5 = 8x + 13
Solve for (g(x)) in terms of (x). Remember to treat (g(x)) as a single parameter:
4(g(x)) + 5 = 8x + 13
Inverse operations,
4(g(x)) + 5 = 8x + 13
4(g(x)) = 8x + 8
g(x) = (8x + 8) ÷ 4
g(x) = 2x + 2
Sandra has $75 to spend on a new outfit. She finds a
sweater that costs twice as much the skirt. What is the most
the skirt can cost?
Let s represent the cost of the skirt.
Inequality: _____________________
The most the skirt can cost is _____________________.
The skirt = s
The sweater is twice as much so 2s
The total sum has to equal or be less than $75
Inequality = s + 2s <=75
Simplify to 3s <= 75
Most the skirt can cost: solve for s:
3s <= 75
Divide both sides by 3
S <= 25
The most the skirt can cost is $25
Answer:
Inequality: s ≤ 25
Max skirt cost: $25
Step-by-step explanation:
s = skirt cost
x = sweater cost
Since the sweater costs twice as much as the skirt, an equation will look like this:
x = 2s
Since her budget is $75, that means she can spend $75 or less but not more, so another equation will look like this:
x + s ≤ 75
Plug 2s into the bottom equation
2s + s ≤ 75
Add up the terms
3s ≤ 75
Divide both sides by 3, the coefficient, to isolate s, the variable.
3s/3 ≤ 75/3
s ≤ 25
That means she can spend $25 or less on a skirt.
Given h(x) = 3x² - 6x +4, find h( - 6).
....
h( - 6) =
Answer:
h(-6) = 3(-6)² - 6(-6) + 4
= 3(36) + 36 + 4
= 148
You basically just substitute x with -6 that's all
f (x) = x - 5. Find f'(x) and its domain.
Answer:
C
Step-by-step explanation:
f(x) = √x - 5
domain: [0. ∞)
range: [-5, ∞)
Let y = √x - 5
√x = y+5
x = (y+5)²
Switch x and y:
y = (x+5)²
f⁻¹(x) = (x+5)²
domain of f⁻¹(x) is the range of f(x): [-5,∞)
Adding and subtracting intergers. FREE BRAINLIST AND POINTS!. WRONG OR SCAM ASNWERS WILL BE REPORTED AND DEALED WITH. RIGHT ANSWERS ONLY!
1. 19 -(-2)=
2. (-4) + (-18)=
3. (-12) -7=
4. 3 + (-20) =
5. (-15) - (-10)
6. (-6) - (-17)
7. (-13) + 20=
8. 5 - 14 =
9. 10 + (-16)
10. (-8) - 12=
11. (-19) + 18 =
12. 11 - (-9)
13. (-7) + (-14)=
Answer:
1. 21
2. -22
3. -19
4. -17
5. -5
6. 11
7. 7
8. -9
9. -6
10. -20
11. -1
12. 20
13. -21
Step-by-step explanation:
You are trying to get an important customer order out the door, but your boss keeps coming over to ask you about the status of this order and several other orders. He's just nervous and wants to be
Solve for d.
d - 5
———- = -1
-3
Answer:
d = 8
Step-by-step explanation:
(d-5)/ -3 = -1
Multiply each side by -3
(d-5)/ -3 *-3 = -1*-3
d-5 = 3
Add 5 to each side
d-5+5 = 3+5
d = 8
Please Help!! Whoever helps and gets it correct gets Brainliest and 5 star rating!!
Answer:
the reasoning states that "all the numbers begin with a 7 or an 8"
however this is not accurate as they can be in different placements
which can make a big difference in the total estimate.
for example:
the number could've been an 8, or an 80
they both begin with an 8
however have totally different values and could have messed up the total estimated number.
hope this helps :D
what is the answer of
445+584-85
Answer:
944 is the correct answer
Answer:
the answer it's 944
445+558=1,029
1,029-85=. [944]✓
A sports stadium has a capacity of 42,000. On a
particular night, 35,000 spectators attend an event. At
the end of the event, spectators leave the stadium at a rate
of 320 spectators every minute. If m represents the
number of minutes after spectators begin to leave the
stadium, which of the following inequalities describes
the times when there are still spectators in the stadium?
A) 42,000 - 35,000m < 320
B) 35,000 - 320m > 0
C) 35,000 + 320m < 42,000
D) 320m < 87,000
Answer:
B
Step-by-step explanation:
The inequality will be 35000-320m>0
9. Find the volume of x and y if, (3x,10)=(9,5y).
Answer:
x=3 and y=2
Step-by-step explanation:
Comparing the oder pair, we have 3x=9 and 10=5y. x=3 and y=2
If a ants can dig b tunnels in c hours, how many tunnels can b ants dig in a hours?
9514 1404 393
Answer:
b²/c tunnels
Step-by-step explanation:
The number of tunnels per ant-hour is ...
b/(ac)
Multiplying that by the new number of ant-hours, we have ...
(b/(ac))(ab) = b²/c . . . . tunnels
Which is an estimate of V75 to the
nearest whole number?
Answer:
9
Step-by-step explanation:
if that v is root symbol
I don’t understand this
Answer:
cccccccccccccccçccccccccc
Answer:
if the dot is filled (black) it is ≤ or ≥
if it is not filled it is < or >
you graph goes from 6 to 10
the unfilled one is 6 the filled one is 10
thus 6 < x ≤ 10
which says x is greater than 6 and also less than or equal to 10
Step-by-step explanation:
what is 2x2x2x3x3 please give me answer
Answer:
The answer is 72.
I am right .
Big sleds must hold 3 children and small sleds must hold 2 children. If 17 children want to go sledding at the same time, how many of each type of sled is needed?
Answer:
5 big sleds and 1 small sled
In a closed box there are 7 blue balls and 5 red balls. Randomly pick one from the box one at a time until the ball is green, then stop. Find the probability that the person stops after the 4th time
Answer:
1/7 is the probabiltiy
Step-by-step explanation:
