Answers
9514 1404 393
Answer:
AC = 2.0 mm = 41.3 kgStep-by-step explanation:
The sum of torques about the pivot point is zero when the system is in equilibrium. That means the total of clockwise torques is equal to the total of counterclockwise torques. For this purpose, torque can be modeled by the product of mass and its distance from the pivot. The uniform beam can be modeled as a point mass at its center.
__
a) Let E represent the location of the center of mass of the beam. So, AE = 1.5 m. Then the distance from C to E is AC-AE = AC -1.5 and the CCW torque due to the beam's mass is (16 kg)(AC -1.5 m).
The distance from B to C is 3 m - AC, so the CW torque due to the particle at B is (7 kg)(3 -AC m)
These are equal, so we have ...
16(AC -1.5) = 7(3 -AC)
16AC -24 = 21 -7AC . . . . . eliminate parentheses
23AC = 45 . . . . . . . . . . . add 7AC+24
AC = 45/23 ≈ 1.957 . . divide by the coefficient of AC
AC ≈ 2.0 meters . . . . rounded to 1 dp
__
b) The torques in this scenario are ...
M(0.7) = 16(0.8) +7(2.3) . . . . . . AD = 0.7 m, DE = 0.8 m, DB = 2.3 m
M = 28.9/0.7 ≈ 41.286 . . . . simplify, divide by the coefficient of M
M = 41.3 kg . . . . rounded to 1 dp
_____
Additional comment
Torque is actually the product of force and distance from the pivot. Here, the forces are all downward, and due to the acceleration of gravity. The gravitational constant multiplies each mass, so there is no harm in dividing the equation by that constant, leaving the sum of products of mass and distance.
Related Questions
4 football is kicked with a speed of 18.0 m/s at an angle of 36.9to the horizontal. 8. How long is the football in the air? Neglect air resistance. A ) 1.1 s B C ) 2.2 D) 3.3 E) 4.0
Answers
9514 1404 393
Answer:
C) 2.2 seconds
Step-by-step explanation:
The initial vertical speed of the football is ...
v = (18.0 m/s)sin(36.9°) ≈ 10.807 m/s
Since the ball starts and ends at ground level, its speed when it hits the ground is the same as its launch speed. That is, the acceleration due to gravity causes the velocity to change from +v to -v. The time required to do that is ...
t = 2v/g = 2(10.807 m/s)/(9.8 m/s^2) = 21.614/9.8 s ≈ 2.206 s
The football is in the air about 2.2 seconds.
If a and b are positive numbers, find the maximum value of f(x) = x^a(2 − x)^b on the interval 0 ≤ x ≤ 2.
Answers
Answer:
The maximum value of f(x) occurs at:
[tex]\displaystyle x = \frac{2a}{a+b}[/tex]
And is given by:
[tex]\displaystyle f_{\text{max}}(x) = \left(\frac{2a}{a+b}\right)^a\left(\frac{2b}{a+b}\right)^b[/tex]
Step-by-step explanation:
Answer:
Step-by-step explanation:
We are given the function:
[tex]\displaystyle f(x) = x^a (2-x)^b \text{ where } a, b >0[/tex]
And we want to find the maximum value of f(x) on the interval [0, 2].
First, let's evaluate the endpoints of the interval:
[tex]\displaystyle f(0) = (0)^a(2-(0))^b = 0[/tex]
And:
[tex]\displaystyle f(2) = (2)^a(2-(2))^b = 0[/tex]
Recall that extrema occurs at a function's critical points. The critical points of a function at the points where its derivative is either zero or undefined. Thus, find the derivative of the function:
[tex]\displaystyle f'(x) = \frac{d}{dx} \left[ x^a\left(2-x\right)^b\right][/tex]
By the Product Rule:
[tex]\displaystyle \begin{aligned} f'(x) &= \frac{d}{dx}\left[x^a\right] (2-x)^b + x^a\frac{d}{dx}\left[(2-x)^b\right]\\ \\ &=\left(ax^{a-1}\right)\left(2-x\right)^b + x^a\left(b(2-x)^{b-1}\cdot -1\right) \\ \\ &= x^a\left(2-x\right)^b \left[\frac{a}{x} - \frac{b}{2-x}\right] \end{aligned}[/tex]
Set the derivative equal to zero and solve for x:
[tex]\displaystyle 0= x^a\left(2-x\right)^b \left[\frac{a}{x} - \frac{b}{2-x}\right][/tex]
By the Zero Product Property:
[tex]\displaystyle x^a (2-x)^b = 0\text{ or } \frac{a}{x} - \frac{b}{2-x} = 0[/tex]
The solutions to the first equation are x = 0 and x = 2.
First, for the second equation, note that it is undefined when x = 0 and x = 2.
To solve for x, we can multiply both sides by the denominators.
[tex]\displaystyle\left( \frac{a}{x} - \frac{b}{2-x} \right)\left((x(2-x)\right) = 0(x(2-x))[/tex]
Simplify:
[tex]\displaystyle a(2-x) - b(x) = 0[/tex]
And solve for x:
[tex]\displaystyle \begin{aligned} 2a-ax-bx &= 0 \\ 2a &= ax+bx \\ 2a&= x(a+b) \\ \frac{2a}{a+b} &= x \end{aligned}[/tex]
So, our critical points are:
[tex]\displaystyle x = 0 , 2 , \text{ and } \frac{2a}{a+b}[/tex]
We already know that f(0) = f(2) = 0.
For the third point, we can see that:
[tex]\displaystyle f\left(\frac{2a}{a+b}\right) = \left(\frac{2a}{a+b}\right)^a\left(2- \frac{2a}{a+b}\right)^b[/tex]
This can be simplified to:
[tex]\displaystyle f\left(\frac{2a}{a+b}\right) = \left(\frac{2a}{a+b}\right)^a\left(\frac{2b}{a+b}\right)^b[/tex]
Since a and b > 0, both factors must be positive. Thus, f(2a / (a + b)) > 0. So, this must be the maximum value.
To confirm that this is indeed a maximum, we can select values to test. Let a = 2 and b = 3. Then:
[tex]\displaystyle f'(x) = x^2(2-x)^3\left(\frac{2}{x} - \frac{3}{2-x}\right)[/tex]
The critical point will be at:
[tex]\displaystyle x= \frac{2(2)}{(2)+(3)} = \frac{4}{5}=0.8[/tex]
Testing x = 0.5 and x = 1 yields that:
[tex]\displaystyle f'(0.5) >0\text{ and } f'(1) <0[/tex]
Since the derivative is positive and then negative, we can conclude that the point is indeed a maximum.
Therefore, the maximum value of f(x) occurs at:
[tex]\displaystyle x = \frac{2a}{a+b}[/tex]
And is given by:
[tex]\displaystyle f_{\text{max}}(x) = \left(\frac{2a}{a+b}\right)^a\left(\frac{2b}{a+b}\right)^b[/tex]
Find y when x = 22, if y varies directly as x,
and y = 42 when x = 5.
Answers
Answer:
184.8
Step-by-step explanation:
y =kx
k=y/x
k=42/5=8.4
y=8.4*22
One number is 6 less than a second number.
Twice the second number is 9 less than 5 times
the first. Find the two numbers.
Answers
Answer:
-7
Step-by-step explanation:
x = y - 6
2x = 5y - 9
Use the internet for full steps
x = -7
y = -1
Again need help with these ones I don’t understand and they have to show work
Answers
[tex]x^2 - 18x + 81= 65 + 81[/tex]
[tex](x - 9)^2 = 146[/tex]
Taking the square root of both sides, we get
[tex]x - 9 = \pm\sqrt{146}[/tex]
or
[tex]x = 9 \pm \sqrt{146} = 9 \pm 12.1 = 21.1\:\text{and}\:-3.1[/tex]
Maria, Kevin, and Dan have a total of 96$ in their wallets. Dan has 6$ less than Maria. Kevin has 3 times what Dan has. How much do they have in their wallets?
Answers
Answer:
Hi Keke,
Let Amy have x dollars. Then Jose has x - 8 dollars and Milan has 4(x - 8) dollars.
x + (x-8) + 4(x-8) = 152
6x - 40 = 152
6x = 192
x = 32
Amy has $32
Jose has 32 - 8 = $24
Milan has 4*24 = $96
Pls if anyone knows the answer that will be greatly appreciated :)
Answers
Answer:
For octagon =1080.......
Explanation:
180(8-2)
180×6
1080°
"What mathematical ideas are you curious to know more about as a result of takingthis class? Give one example of a question about the material that you'd like to explorefurther, and describe why this is an interesting question to you."
Answers
One mathematical idea I've always been curious about is "integration and derivation".
Integration is about assimilating different variables. Derivation is a mathematical process whereby a result is gotten from some initial assumptions.
Integration is used everyday in different aspects of our lives. For example, if a person is travelling from let's say point A to point B, the speed used by the person might vary but through integration, one can easily get the accurate speed.
Through the division of equations into smaller bits, once can use integration to get the answer that one seeks. Architect can use integration in building the right structures at the exact places where the structures fits.
Likewise derivatives can be used by businesses in assessing whether a profit or loss will be made for a particular transaction or sale of product.
You can read more on:
https://brainly.com/question/14295614
In a class of 40 statistics majors, each one constructs a 90% confidence interval for the unknown probability p of a weighted coin landing heads. About how many of the 40 intervals will capture the value of the unknown parameter p? About how many will miss it?
Answers
Answer:
36 intervals will capture the value of the unknown parameter p, and 4 will miss it.
Step-by-step explanation:
x% confidence interval:
A confidence interval is built from a sample, has bounds a and b, and has a confidence level of x%. It means that we are x% confident that the population mean is between a and b. x% of confidence intervals capture the unknown parameter.
About how many of the 40 intervals will capture the value of the unknown parameter p?
90% of them will capture, so:
0.9*40 = 36
0.1*40 = 4
36 intervals will capture the value of the unknown parameter p, and 4 will miss it.
The price of a item has reduced by 85% the original price was $60
Answers
Answer:
The price now would be 9 dollars
Step-by-step explanation:
60 x 85% is 51 and you subtract that from 60
Find the missing side length in the image below
Answers
Answer:
87.5
Step-by-step explanation:
Let the missing side be x.
28 / 35 = x / 50
4 / 7 = x / 50
4 ( x ) = 7 ( 50 )
4x = 350
x = 350 / 4
x = 87.5
Jake has corn growing on 66 2/3% of his 330 acres. How many acres are being used for corn?
Answers
on 220 acres
66 ⅔% is just ⅔ of 100%
330 * 2 / 3 = 220
6 + 7* log base 2 of x = 21
Answers
6 + 7* log base 2 of x = 21
Answer:
Step-by-step explanation:
Hi. I need help with part b thank you so much if you can do so
Answers
9514 1404 393
Answer:
Yes, that distance is the hypotenuse of a right triangle whose sides are known
Step-by-step explanation:
The diagram seems to show the path of the ball as being two segments that are at right angles to each other. Then the direct-line distance to the hole from the tee is the hypotenuse (part A) of the triangle.
Since the leg lengths are known, the Pythagorean theorem can be used (part B) to find the length of the hypotenuse. (The answer to Part B is also the answer to Part C.)
The expression y + y + 2y is equivalent to ??
because ??
Answers
Answer:
4y
They would have the same value if a number was substituted for y
Step-by-step explanation:
y+y+2y =
Combine like terms
4y
These are all like terms
They would have the same value if a number was substituted for y
Let y = 5
5+5+2(5) = 5+5+10 = 20
4(5) =20
What are the domain and range of f(x) = |x + 6|?
Answers
9514 1404 393
Answer:
domain: all real numbersrange: y ≥ 0Step-by-step explanation:
The function is defined for all values of x, so its domain is all real numbers.
The function can produce values of f(x) that are 0 or greater, so its range is ...
y ≥ 0
If a point in quadrant IV is reflected in the y-axis, its image will lie in quadrant:
A. IV
B. II
C. I
D. III
Answers
Answer:
Option D is correct.
Step-by-step explanation:
A plane mirror shows that the image formed by it is of same size as that of object, same distance as that of object and same orientation and laterally inverted.
So, when a point is in IV quadrant and reflection is from Y axis, the image is in III quadrant.
please give me correct answer
Answers
Answer:
150 e udi,auwdbkhg
disha
eiwiwisj8293
ajesjhf
8ઈઘુઘ
Subtract.
7x2-5x+3
-(2x2 + 7X - 4)
Answers
Answer:
5x^2-12x+7
Step-by-step explanation:
7x^2-5x+3-(2x^2 + 7X - 4)
Distribute the minus sign
7x^2-5x+3 - 2x^2 - 7X + 4
Combine like terms
5x^2-12x+7
Answer:
-12x + 17
Step-by-step explanation:
hope this helps!
Five students sit at a circular table. Their chairs are number in order 1 through 5. Abby sits next to both Ben and Colin. Dalia sits next to both Ben and Sarah. The numbers on Abbys and Colins chairs add up to 6. Who is in chair number 3?
Answers
Question 7
In circle P below, angle OPM equals 124 degrees and line segments ON and MN are tangents to the circle
What is the measure of Angle ONM?
A 56
B 62
С 74
D 90
Answers
Answer:
B) 62 is the answer. I'm sure
Which is equal to (3x + 2)(x – 3)?
Please answer asappp
Answers
(3x +2)(x -3)
FOIL method
3x^2 -9x + 2x -6
3x^2 -7x -6
Your answer: 3x^2 -7x -6
2+4? I am omisha please give me answer
Answers
Answer:
6
Step-by-step explanation:
2+4 = 6
..............
Answer:
Here is your answer omisha
2+4=6
If the area A of a triangle is 60 m- (square meters) and the base b is 20 m, what is the altitude h?
Answers
Answer:
not sure
Step-by-step explanation:
a+B+C+=d
help
What is 5 added to 3 4?
6. 12
Answers
Answer:
8.4
Step-by-step explanation:
jjdijendjndoendidnie
Amanufacturer of potato chips would like to know whether its bag filling machine works correctly at the 433 gram setting. It is believed that the machine is underfilling the bags. A 26 bag sample had a mean of 427 grams with a variance of 324. A level of significance of 0.05 will be used. Assume the population distribution is approximately normal. Is there sufficient evidence to support the claim that the bags are underfilled?
Answers
Answer:
There is not enough evidence to support the claim that the bags are under filled.
Step-by-step explanation:
Given :
Population mean, μ = 433
Sample size, n = 26
xbar = 427
Variance, s² = 324 ; Standard deviation, s = √324 = 18
The hypothesis :
H0 : μ = 433
H0 : μ < 433
The test statistic :
(xbar - μ) ÷ (s/√(n))
(427 - 433) / (18 / √26)
-6 / 3.5300904
T = -1.70
The Pvalue :
df = 26-1 = 25 ; α = 0.05
Pvalue = 0.0508
Since Pvalue > α ; WE fail to reject the Null and conclude that there is not enough evidence to support the claim that the bags are underfilled
Regression and Correlation are two of the most often used and abused tools in research.
a. True
b. False
Answers
A.True
Answer:
it is true
Step-by-step explanation:
Madison represented the sentence "The product of 3 and the difference of and the quotient of a number and is at most 5" by using the inequality . Which best describes Madison’s error?a) The difference of –4 and the quotient of a number and –2" should be written as . b) The product of 3 and the difference of –4 and the quotient of a number and –2" should be written as . c) The less than symbol should be replaced with the less than or equal to symbol. d) The less than symbol should be replaced with the greater than symbol.
Answers
Answer:
c) The less than symbol should be replaced with the less than or equal to symbol.
Step-by-step explanation:
3(-4 - n/-2) < 5
The equation written above could be interpreted as :
The product of 3 and the difference of -4 and the quotient of a number, n and -2 is less than 5
This means that the only error in Maddison's representation is the inequality sign, the inequality sign used by Maddison is wrong.
The equation should be used with a ≤ sign and expressed thus :
3(-4 - n/-2) ≤ 5
This means the left hand side (L. H. S) is less than or equal to 5 ; this means the L. H. S is at most 5
Answer:
C
Step-by-step explanation:
How do I solve this?
Answers
The question is somewhat poorly posed because the equation doesn't involve θ at all. I assume the author meant to use x.
sec(x) = csc(x)
By definition of secant and cosecant,
1/cos(x) = 1/sin(x)
Multiply both sides by sin(x) :
sin(x)/cos(x) = sin(x)/sin(x)
As long as sin(x) ≠ 0, this reduces to
sin(x)/cos(x) = 1
By definition of tangent,
tan(x) = 1
Solve for x :
x = arctan(1) + nπ
x = π/4 + nπ
(where n is any integer)
In the interval 0 ≤ x ≤ 2π, you get 2 solutions when n = 0 and n = 1 of
x = π/4 or x = 5π/4
Select the statement that best justifies the conclusion based on the given information.
l is in plane M,
x is on line l
Conclusion: x is in plane M.
a. A plane contains at least three points not all on the same line.
b. If two points lie in a plane, then the line containing them lies in that plane.
c. If a plane contains a line, it contains the points on the line.
d. Exactly one plane contains a given line and a point not on the line.
Answers
9514 1404 393
Answer:
c. If a plane contains a line, it contains the points on the line.
Step-by-step explanation:
The only statement relating a point on a line to the plane containing the line is the one shown above.
_____
Additional comment
Identifying true statements is a reasonable strategy for many multiple-choice questions. Another strategy that can be employed is finding the one true statement that is relevant to the question being asked.
