determine the required thickness of member bc to the nearest 1/16 in
Answers
The required thickness of member BC to the nearest 1/16 in. and the diameter of the pins at A and B is dA= [tex]1\frac{1}{8}[/tex] in
To solve thsi It is necessary to determine the thickness of BC. The allowed normal stress is σ[tex]_{allow[/tex]=29 ksi and the permissible shear stress is τ[tex]_{allow[/tex]=10 ksi.
In the first we will determine the reactions of the system.
We apply the conditions of equilibrium:
→+∑Fₓ=0
+↑∑F[tex]_y[/tex]=0
+↺∑M=0
From picture b
∑M[tex]_B[/tex]=0
⇒−2⋅8⋅4+Ay⋅8=0
⇒Ay=8 kip
∑Fy=0
⇒−2⋅8+Ay+By=0
⇒−2⋅8+8+By=0
⇒By=8 kip
From picture c)
∑M[tex]_C[/tex]=0
⇒+By⋅cos60∘−Bx⋅sin60∘=0
⇒+8⋅cos60∘−Bx⋅sin60∘=0
⇒Bx=4.6188 kip
In the next step we will determine the dimensions of the BC rod:
[tex]\sigma BC= \frac {F_{BC}}{A_{BC}}\leq \sigma _{allow}[/tex] =29 ksi
The cross-sectional area has a value:
[tex]A_{BC}=1.5.t[/tex]
The force acting in the BC stick is calculated as follows:
[tex]F_{BC}=\sqrt{4.6188^2+8^2}=9.258 \ kip \\\\=\frac{9.258}{1.5.t}=29 \\\\=t=0.2128 \ in=1/4in[/tex]
Now we can switch to determining the diameter of the pins.
Pin B:
τB=VB/AB⩽τallow=10 ksi
The cross-sectional area has a value:
AB=π/4⋅d²B
The force acting in the BB pin is calculated as follows:
VB=[tex]\sqrt{4.618^2+82^2[/tex]=4.629 kip
[tex]\frac{4.629}{\pi/4 . d^2_B} =10[/tex]
⇒dB=0.767in=13/16in
Now we can switch to determining the diameter of the pins.
Pin A
τA=VA/AA⩽τallow=10 ksi
The cross-sectional area has a value:
[tex]A_A=\pi/4 . d^2B[/tex]
The force acting in the AA pin is calculated as follows:
[tex]V_A=4.618^2+8^2[/tex]=9.258 ki
9.258 ÷ π/4⋅d²A=10
⇒dA=1.0859in=[tex]1\frac{1}{8}[/tex]in
The solution is:
{σs=208 MPa}
{dB=13/16in}
{dA=[tex]1\frac{1}{8}[/tex]in}
Complete Question:
Determine the required thickness of member BC to the nearest 1/16in. and the diameter of the pins at A and B if the allowable normal stress for member BC is σ allow =29 ksi and the allowable shear stress for the pins is τ allow =10τ allow =10 ksi.
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Related Questions
In hopes of encouraging healthier snacks at school, Camille brought in a tray of carrot sticks and apple slices to share. She brought 16 carrot sticks and 48 apple slices. What percentage of the snacks were carrot sticks?
Answers
Answer:
The number of carrot sticks and apple slices is 16 + 48 = 64.
The percentage of carrot sticks is (16 / 64) * 100 = 25%.
Determine the vertical change of a line with an x-Intercept at (-2, 0) and a y-Intercept at (0, 2). Type a numerical
answer in the space provided. If necessary, use the / key as a fraction bar. Do not type spaces in your answer.
Answers
The vertical change of the line is 1 unit and the horizontal change is 1 unit, thus the slope of the line is 1.
What is the equation of the line?The general equation of a line is given below as follows:
y = ax + b
where;
a is the slopeb is the y-interceptThe slope of the line is determined as follows:
Slope = y₂ - y₁/ x₂- x₁
y₂ = 2
y₁ = 0
x₂ = 0
x₁ = -2
Slope = (2 - 0) / (0 -{-2})
Slope = 2/2
Slope = 1
The equation of the line will be:
y = x + 2
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Two ladders are leaning against the wall as shown below. What is the length of the longer ladder?
Answers
The length of the longer ladder is 50 ft. Therefore, the answer is D.
How to find the length of the longer ladder?Two ladders are leaning against the wall as shown below. The length of the longer ladder can be found as follows:
The triangles formed are right angle triangle. The triangles are similar to each other.
Similar triangles are the triangles that have corresponding sides in ratio to each other and corresponding angles congruent to each other.
Therefore, using proportion,
15 / x = 3 / 10
cross multiply
150 = 3x
divide both sides by 3
x = 150 / 3
x = 50
Therefore,
length of the ladder = 50 ft
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for what values of k does the quadractoc eqiation (k 4)x^2 -3kx -4(k-2)=0 have two roots differing by 1
Answers
As per the quadratic equation, the value of k is 48 ± 8√26.
The term called quadratic equation is known as the polynomial equation whose highest degree is two
Here we know that the value of the quadratic equation is written as,
=> (k - 4)x² - 3kx - 4(k -2) = 0.
Here we have identified that the given equation is in the form of ax² + bx + c = 0.
Then the value of a = k - 4, b = -3k and c = 4(k-2)
Now, we have to use the quadratic formula to identify the value of k, then it can be written as.
=> (-3k)² - (4 x (k - 4) x 4(k-2))
=> 9k² - ((4k - 16) x (4k - 8))
=> 9k² - (16k² - 32k - 64k + 128)
=> 9k² - 16k² +96k -128 = 0
=> -5k² + 96k - 128 = 0
When we factorize the expression then we get the value of k as,
=> k = 48 ± 8√26.
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The domain is all real numbers, and the range is all real numbers. The domain is all integers, and the range is all integers that are multiples of 3. The domain is all real numbers, and the range is all integers that are multiples of 3. The domain is all integers, and the range is all real numbers.
Answers
The domain is all integers, and the range is all integers that are multiples of 3.
What is a function?A relation is a function if it has only One y-value for each x-value.
The given function is f(x)=-3x
We need to find the domain and range.
The domain of a function is the set of values that we are allowed to plug into our function. This set is the x values in a function such as f(x).
The range of a function is the set of values that the function assumes. This set is the values that the function shoots out after we plug an x value in
Domain is (-∞, -∞) and range is (-∞, -∞)
Hence, the domain is all integers, and the range is all integers that are multiples of 3.
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vikas ranks 9th in the class. how many students are there in the class? statements : 1) his friend got the 35th rank which is the last rank. ii) his rank from the last is 27th
Answers
There are total 35 students in the class.
Given that,
Vikas ranks 9th in the class,
Assume that there are 'n' number of students in the class
Therefore,
There are 8 students who have scored better than him.
So, The total number of students with a rank better or equal to Vikas,
= 8 + 1 (Vikas himself)
= 9.
Now, his friend got the 35th rank which is the last rank
This means that there are a total of 35 students in the class.
Also, also given that,
Vikas's rank from the last is 27th,
This means that there are 26 students who have scored lower than Vikas.
So, the total number of students with a rank worse or equal to Vikas,
= 26 + 1 (Vikas himself)
= 27.
Therefore, The total number of students in the class = 35.
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X=7-3y ; 4x-7y=-10
I need help with this question
Answers
Therefore , the solution of the given problem of equation comes out to be x value is 79/19 and y = 18/19.
Equation : What is it?The equal symbol (=) is used in mathematical equations to denote equality between two propositions. Mathematical equations, which seem to be expressions of reality, are used to demonstrate how different numerical elements can be compared. For instance, the equal sign splits the integer 12 or the equation y + 6 = 12 into 2 different halves. One can compute how many characters each edge of a symbol has. Contradictory meanings are common in symbols.
Here,
Given :
=> x = 7 -3y
and
=> 4x -7y = 10
=> 4(7-3y) - 7y = 10
=> 28 -12y - 7y = 10
=> 28 - 19y = 10
=> 18 = 19y
=> y = 18/19
=> x = 7 - 3(18/19)
=> x = 133 - 54 / 19
=> x = 79 /19
Therefore , the solution of the given problem of equation comes out to be x value is 79/19 and y = 18/19.
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find value of each variable
Answers
To solve for x, bring the variable to one side, and bring all the remaining values to the other side by applying arithmetic operations on both sides of the equation. Simplify the values to find the result.
Find value of each variable ?
The value of the variable, which is the value the variable name represents, might be categorized as follows: A constant, which is a number that is expressed as: An integer (12) A decimal (12.5) A floating point number (1.25E2).Age, sex, business income and expenses, country of birth, capital expenditure, class grades, eye colour and vehicle type are examples of variables. It is called a variable because the value may vary between data units in a population, and may change in value over time.The value refers to the worth of each digit depending on where it lies in the number. We calculate it by multiplying the place value and face value of the digit.To learn more about variable refers to:
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For the given figure, the value of different angles, x = 122° and w = 90°.
An angle is a shape in planar geometry made up of two rays or lines that have a common termination. The Latin word "angulus," which meaning "corner," is where the English term "angle" originates. The shared termini of two rays are the vertex and the two rays, which are referred to as the sides of an angle, respectively. When two rays meet at a point, they create an angle. The "angle," which is the term used to describe the "opening" between these two rays, is represented by the symbol. Angles are typically expressed as 60°, 90°, etc. and are measured in degrees.
For the given figure,
The value of angle w is 90°.
The value of angle x = 180 - 58 = 122°
The value of 2w - 25 will be = 2 × 90 - 25 = 155°
The value of x + 6 will be = 122 + 6 = 128
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At Pharoah’s Palace, a hypothetical Las Vegas casino, management has tampered with the dice. Management modified a standard six-sided die so that the probability of each side is now proportional to the number of spots on the side. [That is, the probability of a 2 is twice the probability of a 1; the probability of a 3 is three times the probability of a 1; etc.]
What is the uncertainty distribution for the number of spots on the up side when the die is thrown? Write down all of the possible outcomes and their probabilities. [Hint: The probabilities must add up to 1.]
Calculate the mean of the uncertainty distribution.
Calculate the standard deviation of the uncertainty distribution.
Suppose that you know all about the casino’s tampering with the dice. Now the casino offers to pay you $1,000 for each spot showing on the up side of a single throw of the die. But the casino will charge you $4,000 for the right to play the game. Would you accept the casino’s offer to play? Why or why not?
Answers
The mean of the uncertainty distribution is 3.7
The probability distribution of a random event describes the likelihood of each possible outcome of that event.
In the case of the modified die at Pharaoh's Palace, the management has changed the standard probability distribution so that the probability of each side is proportional to the number of spots on the side.
The possible outcomes are 1, 2, 3, 4, 5, and 6, and their probabilities can be calculated by summing up the probabilities of each side and ensuring that they add up to 1.
The mean of the uncertainty distribution is calculated by taking the sum of each possible outcome multiplied by its probability and dividing by the number of possible outcomes.
In this case, the mean is approximately 3.7.
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Help
Which of the following graphs has a slope of negative two thirds and a y-intercept of 2?
graph of a line passing through the points 0 comma 2 and 3 comma 0
graph of a line passing through the points 0 comma 2 and 2 comma negative 1
graph of a line passing through the points 0 comma 3 and 2 comma 0
graph of a line passing through the points 0 comma 3 and 3 comma 1
Answers
The required graph A has a slope of negative two-thirds and a y-intercept of 2. Option A is correct.
What is the slope of the line?The slope of the line is a tangent angle made by line with horizontal. i.e. m = tax where x in degrees.
m = (y₂ - y₁) / (x₂ - x₁)
The graph of lines A has the slope of -2/3 and 2 as,
m = (y₂ - y₁) / (x₂ - x₁)
Put points (0, 2) and (3, 0) in the above expression
m = 0-2/3-0
m = -2/3
And at x = 0 there y = 2
Thus, the required graph A has a slope of negative two-thirds and a y-intercept of 2. Option A is correct.
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use synthetic division
f(x)= 2×^3+X^2-8X+5 BY X+3
Answers
markdown
Copy code
_________
|2 1 -8 5|
|3 3 0 0|
|0 -3 -8 2|
|0 0 -24 6|
_________
The final row represents the polynomial 2x^2 - 3x - 24, which is the remainder. The quotient is 2x^2 + 3x + 3.
So, f(x) divided by x + 3 is equal to (2x^2 + 3x + 3) + (2x^2 - 3x - 24)/(x + 3).
Answer:
f '(x) =6x² +2x-8+5by
Step-by-step explanation:
I SERIOUSLY NEED HELP! My homework is due Monday and I have no idea how to solve this: m<2=4x-26, m<3=3x+4
Answers
The solution to the given system of inequalities is x belongs to (-1/3, 7).
The system of two inequalities represents two lines in a 2D plane and the solution is the common area between the two lines that satisfies both inequalities. Here's one way to solve this system:
Solve each inequality for x to get the equation of a line:
m<2: 4x - 26 < 2 -> 4x < 28 -> x < 7
m<3: 3x + 4 < 3 -> 3x < -1 -> x < -1/3
Plot both lines on a coordinate plane and shade the region where both inequalities are satisfied.
The solution is the set of all points that satisfy both inequalities and lies in the shaded region, which is x < 7 and x < -1/3. The solution is therefore x < min(7, -1/3) = -1/3 < x < 7.
So, the solution to the system of inequalities is x belongs to (-1/3, 7).
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Donna is running around a track. It takes her 3 1/2 minutes to run 1/4 of a lap. If she keeps running at the same speed:
1. How long will it take her to run 5 laps?
2. Rate needed?
3. Unit rate?
4 Interpretation of unit rate?
Answers
If Donna is running around a track. It takes her 3 1/2 minutes to run 1/4 of a lap. If she keeps running at the same speed. The time it take her to run 5 laps is: 70 minutes .
How to find the time?1. It takes Donna 3 1/2 minutes to run 1/4 of a lap. So,
it takes her 3 1/2 * 4 = 14 minutes to run 1 full lap.
Thus, it will take her 14 * 5 = 70 minutes to run 5 laps.
2. To find the rate needed, we need to know the time and distance. Since Donna runs 1/4 of a lap in 3 1/2 minutes.
The rate can be expressed as 1/4 lap / 3 1/2 minutes.
3. To find the unit rate, we need to convert the time to a common unit, such as seconds.
So,
3 1/2 minutes = 3.5 * 60
= 210 seconds.
The unit rate will then be 1/4 lap / 210 seconds.
3. The interpretation of the unit rate is the speed at which Donna is running.
Therefore the time it take her to run 5 laps is: 70 minutes .
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PLEASE HELP ASAP! PLEASE ITS DUE TODAY. Thanks have a great day! :)
Part A: Solve the inequality, showing all necessary steps. (3 points)
Part B: Describe the graph of the solution. (3 points)
*WILL MARK BRANLIST*
Answers
The solution to the inequality is x = 0
The graph of x = 0 is a line that separates the plane into two half-planes
How to determine the inequalityFrom the question, we have the following parameters that can be used in our computation:
|1/5x + 2| + 4 >= 6
This gives
|1/5x + 2| >= 2
Remove the absolute bracket
2 <= 1/5x + 2 <= 2
So, we have
0 <= 1/5x <= 0
Evaluate
0 <= x <= 0
This means that
x = 0
Describe the graph of the solutionThe graph of x = 0 is a vertical line in the coordinate plane that passes through the origin (0,0) and extends infinitely in both positive and negative directions along the y-axis.
It represents all points that have an x-coordinate of 0.
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please help I have 20 points to spare and I will mark you as brainliest
Answers
Answer: you have to put -1 1/2 in the first line second one you have to put 1 4/6 in the fourth line of one
Step-by-step explanation if you have 1 4/6 where you see one that goes to 2 you have to count 4 lines and that will be your answer for -1 1/2 first because if you see 1/2 it means that you have to put it on the first one because 1/2 and there are only two numbers and 1/2 so just put it on the first line
refer to the market for good x. p0=$15, pa=$21, p*=$31, pb=$44, p1=$57, q0=10, q*=30, q1=50, and q2=70. how many units are exchanged when the price is $44?
Answers
At a price of $44, 30 units of good x are exchanged. This can be calculated by subtracting the quantity supplied at price $15 (q0=10) and the quantity supplied at price $31 (q*=30) from the quantity demanded at price $44 (q1=50).
At a price of $44, the quantity of good x that is exchanged can be calculated by subtracting the quantity supplied at price $15 (q0=10) and the quantity supplied at price $31 (q*=30) from the quantity demanded at price $44 (q1=50). The quantity supplied at price $15 is 10 units, the quantity supplied at price $31 is 30 units, and the quantity demanded at price $44 is 50 units. Therefore, the quantity exchanged at price $44 is 50 units minus 10 units (q0) minus 30 units (q*) which equals 10 units. Thus, the quantity of good x exchanged at price $44 is 10 units.
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Do taller people tend to jump higher? Student researchers investigated this question by measuring the height in inches and standing vertical leap of 74 different students. Here is a scatterplot of the data, along with the regression line equation, ŷ = -31.20+0.70x, where y= vertical jump in inches and x= height in inches. Predict the vertical leap of a student who is 68 inches tall.
Answers
Answer:
Yes they do. The vertical leap is -31.27 degrees to the power of the square root of 3.
Step-by-step explanation:
I am also 68 inches so...yeah.
Shanice goes on vacation. She has $1,750 saved in her checking account for vacation. Each day, she withdraws $125 to pay for meals & entertainment expenses.
Brianna has $550 in her account when Shanice goes on vacation. Then, Brianna deposits $75 from her
On which day will the amount in Brianna's saving account be equal to the amount in Shanice's checking account?
Please enter your answer then show the steps.
Answers
By solving linear equations, we will see that Shanice and Brianna will have the same amount after 6 days.
On which day will the amounts be equal?We know that Shanice has $1,750 saved in her checking account for vacation. Each day, she withdraws $125 to pay for meals & entertainment expenses. Then the amount in her account after x days is modeled by the linear equation:
S = 1,750 - 125*x
And Brianna has $550 and adds $75 each day, so she as:
B = 550 + 75*x
Both of them will have the same amount when:
1,750 - 125*x = 550 + 75*x
1,750 - 550 = 75*x + 125*x
1200 = 200*x
1200/200 = x
6 = x
They will have the same amount after 6 days.
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What type of triangle is this triangle?
•
acute scalene
•
acute isosceles
right scalene
right isosceles
Answers
Answer:
Right isosceles
Step-by-step explanation:
AB = BC
∠ABC = 90°
An isosceles triangle with a right angle is known as an isosceles right triangle
A jar of quarters and dimes has  a total value of $20.70. The jar has 10 more quarters than dimes. To find the number of quarters and dimes in the jar, Addison wrote the following system of equations. Explain Addison’s error.
0.25x+0.10y=20.75
Y=x+10
Answers
Addison's error is that the second equation should be 0.25x + 0.10y = 20.70, not 20.75.
What is equation?An equation is a mathematical statement consisting of an expression and an equal sign. It is used to express a relationship between two or more variables, and is often used to solve mathematical problems. An equation can be written in a variety of forms, such as a single line, two lines, or a system of equations. An equation typically contains two elements: an expression and an equality sign. An expression is a combination of terms, such as numbers, variables, and operations.
Addison's error is that the second equation should be 0.25x + 0.10y = 20.70, not 20.75. This is because the total value of the quarters and dimes is $20.70, not $20.75. The second equation should also state that y is equal to x plus 10, not just x.
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What is the percentage increase from 520 to 800
Answers
f:x-2x+3 is a mapping defined on the set R of real numbers. Determine the pre-images of (a) 1 (b) -1 (c) 7 (d) -5
Answers
F[g(x-1)] has a value of 2x2-4x+9. Applying the multiplication operation to functions and replacing the functions led to the discovery of the answer.
What are Operations on functions?The functions can be added, subtracted, multiplied, or divided in the same manner that we add, subtract, multiply, and divide the terms in a function.
Consider f(x) and g, two functions (x). These are the notations:
To add, use the formula (f+g)(x) = f(x) + g(x)
for subtraction (f-g)(x) = f(x) - g(x)
To multiply, use the formula (fg)(x) = f(x)* g(x)
The division formula is (f/g)(x) = (f(x))/(g(x)).
A function that considers one function to be a component of another function is created when we replace one function for another.
So now, f(g) = 2g-3.
When provided, g = x^2+5
So, g(x-1) = (x-1)^2+5
By changing g's value (x-1)
F[g(x-1)] has a value of 2x²-4x+9. Applying the multiplication operation to functions and replacing the functions led to the discovery of the answer.
F[g(x-1)] has a value of 2x²-4x+9. Applying the multiplication operation to functions and replacing the functions led to the discovery of the answer
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Quadrilateral ABCD is a rhombus. If mzCDB = 6y° and mZACB = (2y + 10)°, find the value of y.
Answers
Answer: [tex]y=10[/tex]
Step-by-step explanation:
Note that [tex]\angle ACB \cong \angle ACD[/tex] because diagonals of a rhombus bisect the angles from which they are drawn.
Now, because [tex]m\angle DEC=90^{\circ}[/tex] since diagonals of a rhombus are perpendicular, it follows that [tex]m\angle CDB+m\angle ABC=90^{\circ}[/tex].
[tex]6y+2y+10=90\\\\8y+10=90\\\\8y=80\\\\y=10[/tex]
I am so confused with this can someone please help me?
Answers
The required coordinate of point H is given as (d+c, b), as per the given condition.
Coordinate, is represented as the values on the x-axis and y-axis of the graph. while the coordinate x is called abscissa and the coordinate of the y is called ordinate.
Here,
As point H is collinear with point G so the y coordinate of the Point H is equal to y coordinate point G,
So
Y coordinate of point H = b
Now,
x coordinate of point H is given as,
Line GH is parallel with LINE FE
So, x-coordinate = FE = d-(-c) = d+ c
Thus, the required coordinate of point H is given as (d+c, b), as per the given condition.
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The sum of two integers with different signs is 6. Select all the pairs of integers that fit this description.
Answers
Answer:
12 and -6
-4 and 10
Step-by-step explanation:
an amount of $31,000 is borrowed for 11 years at 3% interest, compounded annually. If the loans is paid in full at the end of that period, how much must be paid back?
Answers
The total amount to be paid back would be $35,731.73.
What is the amount ?The amount is 100 words. Plagiarism is not allowed, so the answer must be original and unique.The amount is unspecified and cannot be determined without further information.
This can be calculated using the formula for compound interest:
A = P(1 + r/n)^nt,
where A is the total amount to be paid back, P is the principal amount (31,000), r is the annual interest rate (3%), n is the number of times the interest is compounded per year (annually in this case), and t is the number of years (11).
Plugging this into the formula, we get:
A = 31000 (1 + 0.03/1)^11
A = 31000 (1.03^11)
A = 31000 (1.357364)
A = $35,731.73
Therefore, the total amount to be paid back would be $35,731.73.
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Andrew invested a total of 23,000 into two types of bonds. one pays 7.5% simple interest while the other pays 13% .last year the annual interest earned on the two investments was 2,880. how much was invested at each rate.
Answers
Andrew invested $3520 at 7.5% and $19,480 at 13%.
How to calculate the investmentLet's call the amount invested in the 7.5% bond "A" and the amount invested in the 13% bond "B".
We know that:
A + B = 23,000
0.075A + 0.13B = 2,880
We can use the second equation to solve for one of the variables, then substitute that value back into the first equation to solve for the other. For example:
0.075A + 0.13B = 2,880
0.13B = 2,880 - 0.075A
B = (2880 - 0.075A) / 0.13
Substituting this expression for B back into the first equation:
A + (2880 - 0.075A) / 0.13 = 23,000
0.875A + 2880 / 0.13 = 23,000 * 0.13
0.875A = 23,000 * 0.13 - 2880 / 0.13
0.875A = 3080
A = 3520
So Andrew invested $3520 at 7.5% and $23,000 - $3520 = $19,480 at 13%.
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Challenge A bicycle wheel makes five rotations. The bicycle travels 45.79 ft. Find the diameter of the wheel in inches. Use 3.14 for T. The diameter of the wheel is about in. (Round to the nearest whole number as needed.)
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The width of the wheel's face, measured from bead seat to bead seat, is known as the wheel diameter or rim diameter.The wheel's circumference is 81.64 inches as a result.
What is the diameter of a wheel?The width of the wheel's face, measured from bead seat to bead seat, is known as the wheel diameter or rim diameter.Considering that's where the tire and wheel meet, it's measured in this manner.
The diameter is 16 inches in our case.The equation for diameter can be solved by dividing both sides by since we already know that C (circumference) = x D (diameter). We discover that D = C/ after doing so.
The wheel's circumference is 81.64 inches.
A circle's circumference is determined by:
C is a circle's circumference.
A circle's diameter is given by d.
As stated in the sentence:
Bike wheels measure 26 inches in diameter.d equals 26 inches.
The wheel's circumference must be determined.
value used = 3.14
The wheel's circumference is 3.14 x 26 or 81.64 inches.
The wheel's circumference is 81.64 inches as a result.
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26.5 %change to fraction in lowest terms
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Answer:
Step-by-step explanation: Step 1: Write down the percent divided by 100 like this: 26.5% = 26.5 / 100
Step 2: Multiply both top and bottom by 10 for every number after the decimal point: ...
Step 3: Simplify (or reduce) the above fraction by dividing both numerator and denominator by the GCD (Greatest Common Divisor) between them.
find the change in the density rho of a substance, when the temperature changes by δt . assume βδt≪1 .
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The change in the density rho of a substance when the temperature changes by δt is dρ = -β × δt × ρ.
The change in density, dρ, of a substance when the temperature changes by delta_t (δt) can be calculated using the coefficient of thermal expansion, beta (β):
dρ = -β × δt × ρ
Where rho is the original density of the substance. If beta * delta_t is much less than 1 (beta * delta_t << 1), then the change in density can be considered to be small, and the original density can be used in the calculation.
Therefore, the change in density rho is -β × δt × ρ.
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