It depends on the purpose of dividing 30. There is no specific answer for dividing 30 into a certain number of parts. It can be divided into any number of parts, as long as it is a whole number.
Answer:
it depends upon ur requirement that hw many parts is needed by u
Step-by-step explanation:
like if u need 2 parts it can happen by having 15 on one side and 15 on the other similarly it,s the way to divide it to many parts required by u
a polynomial finction with real coefficients has no real zeros. what can you say sbout the degree of the polynomial?explain
A polynomial function is a function in an equation, such as the quadratic equation, cubic equation, etc.
What is polynomial function?A polynomial function is a function in an equation, such as the quadratic equation, cubic equation, etc., that only uses non-negative integer powers or only positive integer exponents of a variable. A polynomial with an exponent of 1 is, for instance, 2x+5. A polynomial is a function that has the formula f(x) = anxn + anxn + anxn+1 +... + a2x2 + a1x + a0. The highest power of x in the formulation of a polynomial is its degree. Constant (non-zero) polynomials, linear polynomials, quadratics, cubics, and quartics, respectively, are polynomials of degree 0, 1, 2, 3, and 4.A polynomial is an expression in mathematics that solely uses the operations of addition, subtraction, multiplication, and powers of positive-integer variables. It consists of indeterminates and coefficients.
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a concrete block has a volume of 34 cubic meters and the dimensions shown. find the value of X
The value of x is obtained as follows:
x = 2.83.
How to obtain the volume of the rectangular prism?The volume of a rectangular prism, with dimensions length, width and height, is given by the multiplication of these dimensions, as follows:
Volume = length x width x height.
Considering the dimensions in this problem, and the volume of 34 cubic meters, the equation is given as follows:
x(2x - 3)(3x - 4) = 34.
x(6x² - 17x + 12) = 34
6x³ - 17x² + 12x - 34 = 0.
Which is a cubic equation with coefficients given as follows:
a = 6, b = -17, c = 12, d = -34.
Using a calculator, the real solution are given as follows:
x = 2.83.
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Venus has an angular diameter of about 0.018° when it is a distance of about 38.5 million km from Earth.
What is its true diameter (physical size)? Round to the nearest hundred km.
The true diameter of the Venus given the angular diameter of 0.018 is about 39.7 million km.
What is angular diameter?An angular distance used to describe how big a sphere or circle seems from a certain point of view is known as the angular diameter, angular size, apparent diameter, or apparent size. It is known as the visual angle in the vision sciences and as the angular aperture in optics (of a lens). The angular diameter may also be thought of as the angle that a camera or eye must spin around in order to view from one side of an apparent circle to the other.
Given that the angular diameter of Venus is 0.018 degrees.
The true diameter of the planet is calculate using the following formula:
diameter = distance (angular diameter / 57.3)
Substitute the value of distance = 38.5 million and angular diameter = 0.018 degrees.
diameter = 38.5 * 10^6 (0.018 / 57. 3)
diameter = 39. 7 million
Hence, the true diameter of the Venus given the angular diameter of 0.018 is about 39.7 million km.
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Luis has a piece of wood of 102.45 cm if he needs to cut them into 5 equal parts, how much to measure each part?
Answer: Each part of 20.49 cm.
Step by step explanation:
Data :
I have = 102.45 cmI need = 5 equal partsIn this problem we have to divide the piece of wood that is 102.45 cm, with 5 equal parts:
[tex]\bf \: \cfrac{ 102.45 }{5} = \boxed{ \bf20.49 \: cm}[/tex]
Rpt: Each part of 20.49 cm.
Answer: 20.49
Step-by-step explanation:
102.45/5=20.49
A linear equation is graphed
Answer:
(t,v) =(5,61)
Step-by-step explanation:
re-write expression
v=61
t=5
a posible solution
then check the solution
then the ordered pair is the solution
Simplify the following union [-1,8]∪(8,14)
Suppose that a study of elementary school students reports that the mean age at which children begin reading is 5.9
years with a standard deviation of 0.8
years.
Step 2 of 2 : If a sampling distribution is created using samples of the ages at which 68
children begin reading, what would be the standard deviation of the sampling distribution of sample means? Round to two decimal places, if necessary.
The standard deviation of the sampling distribution of sample means will be 0.097.
What is a normal distribution?The Gaussian Distribution is another name for it. The most significant continuous probability distribution is this one. Because the curve resembles a bell, it is also known as a bell curve.
Assume that an investigation of primary school understudies reports that the mean age at which youngsters start perusing is 5.9 years with a standard deviation of 0.8 years.
The standard deviation of the sampling distribution of sample means is given as,
⇒ 0.8 / √68
⇒ 0.8 / 8.246
⇒ 0.097
The standard deviation of the sampling distribution of sample means will be 0.097.
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in the diagrams below parallel lines I and m are crossed by transversal n at an 108 degree angle as shown. which set of angles are supplementary to the 108° angle?
Our assumption that m II is intersected by a transversal n is wrong, thus none of the set of angles are supplementary to 108°.
What is transversal?A transversal in geometry is a line that intersects two other lines in the same plane at two different locations. It is possible to determine whether two or more other lines in the Euclidean plane are parallel by using transversals.
A line that crosses two lines in the same plane at two different geometric locations is referred to as a transversal. The angles that result from a transversal crossing of two lines in pairs can be successive internal angles, matching angles, or alternate angles.
The transversal angles. There are numerous angles created when a transversal splits two parallel lines. They are referred to as transversal angles.
Given, ∠1 = 70°
∠7 = 80°
Vertically opposite angles are equal.
∠1 = ∠3
⇒ ∠1 = ∠3 = 70°
As per the diagram, line 1 is intersected by line n.
Vertically opposite angles are equal.
∠5 = ∠7
=> ∠5 = ∠7 = 80°
Let m II l is intersected by a transversals n.
Then the pair of corresponding angles should be equal. i.e.,
∠1 = ∠5
= ∠3 = ∠7
but ∠1 = 70
and ∠5 = 80°
Therefore, our assumption that m II is intersected by a transversal is wrong.
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Using technology, find the measures of central tendency for the following raw quantitative data set. Round the answers to two decimal places. 59.8 61.4 69 71.2 78.7 83.5 89.6 94.1 84 75.2 79.7 83.6 74.8 74 83.3 73.8 90 68.3 71.7 74.2 69.3 68.5 71.3 78.5 73.2 91.4 78.7 56.4 73 65.6 69.9 73.8 80.1 78.7 75.8 66.7 79.7 66 73 85.3 72.1 78.5 79.9 75.6 71.3 69.6 58.6 64.3 63.2 79.9 70.1 80.4 88.2 79.4 74.6 65.2 70.6 77 73.2 81.5 83.3 77 82 78.5 75.4 78.5 73.6 86.8 74.4 65.2 mean - 85.16 Enter an integer or decimal number (more.. median - 35.5 I
The median of the data set is 75.80, rounded to two decimal places.
The mean of the data set can be calculated by adding up all the values and dividing by the number of values.
The formula is:
mean = (sum of all values) / (number of values)
For the given data set, mean = (59.8 + 61.4 + 69 + 71.2 + 78.7 + 83.5 + 89.6 + 94.1 + 84 + 75.2 + 79.7 + 83.6 + 74.8 + 74 + 83.3 + 73.8 + 90 + 68.3 + 71.7 + 74.2 + 69.3 + 68.5 + 71.3 + 78.5 + 73.2 + 91.4 + 78.7 + 56.4 + 73 + 65.6 + 69.9 + 73.8 + 80.1 + 78.7 + 75.8 + 66.7 + 79.7 + 66 + 73 + 85.3 + 72.1 + 78.5 + 79.9 + 75.6 + 71.3 + 69.6 + 58.6 + 64.3 + 63.2 + 79.9 + 70.1 + 80.4 + 88.2 + 79.4 + 74.6 + 65.2 + 70.6 + 77 + 73.2 + 81.5 + 83.3 + 77 + 82 + 78.5 + 75.4 + 78.5 + 73.6 + 86.8 + 74.4 + 65.2) / 60 = 6288.6 / 60 = 104.81
So, the mean of the data set is 104.81, rounded to two decimal places.
The median of the data set can be calculated by arranging the values in ascending order and finding the middle value. If there are an odd number of values, the median is the middle value. If there are an even number of values, the median is the average of the two middle values.
For the given data set, the median can be found as follows:
56.4 58.6 63.2 64.3 65.2 65.6 66 66.7 68.3 68.5 69 69.3 69.6 69.9 70.1 70.6 71 71.3 71.7 73 73 73.2 73.6 73.8 74 74 74.2 74.4 74.6 75.2 75.4 75.6 75.8 76.7 77 78 78.5 78.5 78.5 78.7 79 79.4 79.7 79.7 79.9 80.1 80.4 81.5 82 83 83.3 83.3 83.5 83.6 84 85.3 86.8 89.6 90 91.4 94.1
The median is 75.8.
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A bottle contains 36 tablets. If a client took 1/3 of the tablets. How many tablets are left?
Answer:
24
Step-by-step explanation:
36 * 1/3 = 12
36 - 12 = 24
Answer:
24
Step-by-step explanation:
36/3 = 12
2/3 of 36 = 24
Lee has made a nonrefundable deposit of the first month’s rent (equal to $900) on a
apartment lease to 6 months. The same day later Lee finds a different apartment that
he likes just as well, but its monthly rent is cheaper and negotiable. Assume a nominal
rate interest rate of 8% convertible monthly. The rent will be paid monthly and at the
beginning of each month. [8]
(i) Write down the cash flow and compute the present value (to 2 decimal numbers)
of 6 months if Lee rents the first apartment ($900).
(ii) Find the range of the rent (to 2 decimal numbers) of the cheaper apartment such
that Lee would switch to rent the new apartment.
It would be wiser for the couple to stay in the old apartment and save $1400.
What is multiplication?In mathematics, multiplication is a method of finding the product of two or more numbers. It is one of the basic arithmetic operations, that we use in everyday life.
here, we have,
Explanation:
If they stay until the end of the lease, total money that will be paid out is $1000 x 6 = $6000,
If they leave, they'll have to forgo $1000.
If they move to their new apartment, they'll pay $900 x 6 = $5400
total expenditure if they move to the new place at the end of the six months period will be, the $1000 that will not be refunded back to them on the old apartment, plus this new $5600 for six month's rent in this new apartment, and that will be a total of $6400.
It would be wiser for the couple to stay in the old apartment and save $1400.
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What is the tangent of the angle shown on the figure?
The tangent of the given angle shown above would be = 1.43. That is option C.
How to calculate the tangent of an angle?The formula that is used to calculate the tangent of the given angle ;
Tan θ = opposite/adjacent
Where the opposite = 60ft
the adjacent = 42ft
Tan θ = 60/42
= 1.43°
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A baker will supply 22 jumbo cinnamon rolls to a cafe at a price of $3.46 each. If she is offered $3.16, then she will supply 2 fewer rolls to the cafe. The cafe's demand for jumbo cinnamon rolls is given by p = D(x) = -0.25x + 6.56. What is the equilibrium point?
If a baker will supply 22 jumbo cinnamon rolls to a cafe at a price of $3.46 each. the equilibrium point is: 20 rolls and the price is $4.86.
How to find the price?The equilibrium point is where the supply and demand curves intersect, representing the price and quantity where the market is in balance.
Let's call the number of rolls the baker supplies x.
At the original price of $3.46 each, she supplies 22 rolls.
When offered $3.16, she will supply 2 fewer rolls, so she supplies x = 22 - 2 = 20 rolls.
We can use the demand equation to find the corresponding quantity demanded for each price:
p = D(x) = -0.25x + 6.56
D(22) = -0.25 * 22 + 6.56 = 4.56
D(20) = -0.25 * 20 + 6.56 = 4.86
The intersection of the two points (22, 4.56) and (20, 4.86) gives us the market equilibrium quantity and price.
So the equilibrium point is:
x = 20 rolls
p = $4.86 each.
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PLEASE HELP 20 POINTS!
A new cruise ship line has just launched 3 new ships: the Pacific Paradise, the Caribbean Paradise, and the Mediterranean ParadiseThe Caribbean Paradise has 16 more deluxe staterooms than the Pacific Paradise. The Mediterranean Paradise has 28 fewer deluxe staterooms than four times the number of deluxe staterooms on the Pacific Paradise Find the number of deluxe staterooms for each of the ships if the total number of deluxe staterooms for the three ships is 1176
ANSWERS MUST ADD UP TO 1176
Answer:
Pacific Paradise = 198 deluxe stateroomsCaribbean Paradise = 214 deluxe stateroomsMediterranean Paradise = 764 deluxe stateroomsCheck: 198+214+764 = 1176 total rooms
==========================================================
Explanation
I'll define these variables:
p = number of deluxe staterooms on Pacific Paradisec = number of deluxe staterooms on Caribbean Paradisem = number of staterooms on Mediterranean ParadiseWe have these given facts:
The Caribbean Paradise has 16 more deluxe staterooms than the Pacific Paradise. The Mediterranean Paradise has 28 fewer deluxe staterooms than four times the number of deluxe staterooms on the Pacific Paradise The total number of deluxe staterooms for the three ships is 1176Fact 1 allows us to form the equation c = p+16
Fact 2 allows us to form the equation m = 4p-28
Fact 3 leads to the equation p+c+m = 1176
Let me know if you have any questions about how I formed the equations.
---------------------
The system of equations is:
[tex]\begin{cases}c = p+16\\m = 4p-28\\p+c+m = 1176\\\end{cases}[/tex]
Notice how the first two equations have the variable p on the right hand side, and no other variable. We'll use this to apply substitution and solve for p.
p+c+m = 1176
p+(p+16)+m = 1176 ... replace c with p+16
p+(p+16)+(4p-28) = 1176 ... replace m with 4p-28
6p-12 = 1176
6p = 1176+12
6p = 1188
p = 1188/6
p = 198
Use this value of p to find the other variables.
c = p+16 = 198+16 = 214
m = 4p-28 = 4*198-28 = 764
---------------------
Summary:
We found that p = 198, c = 214, and m = 764.
Pacific Paradise = 198 deluxe stateroomsCaribbean Paradise = 214 deluxe stateroomsMediterranean Paradise = 764 deluxe stateroomsAs a check,
198+214+764 = 1176 total rooms
The answer is confirmed.
A ramp is designed with the profile of a right triangle.
The measure of one acute angle is 2 times the measure
of the other acute angle. Find the measure of each
acute angle.
The measure of each acute angle [tex]30^{0}[/tex]
What is the acute angle?Angles that are less than 90° are considered acute, and a protractor can be used to measure these angles. Acute, Obtuse, Right, Straight, Reflex, and Full Rotation are the names of the basic angles. Two rays are joined at their ends to create the geometric shape known as an angle. Typically, angles are expressed in terms of degrees. A triangle that has each angle less than 90 degrees is said to be acute.Triangles are not sharp even when one of their angles is 90 degrees. The fact that all angles (60°) in an equilateral triangle are less than 90° ensures that it is always sharp.If you need to see the algebra, the acute angles in a right triangle are complementary, adding to 90 degrees:
x + 2x = 90
3x = 90
x = 30
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Write the other side of this equation so it's true for all values of x:
1/2(6x - 10) - x =
write the other side of this equation so it's true for no values of x:
1/2(6x - 10) - x =
The other side of this equation so it's true for all values of x: 1/2(6x - 10) - x = 2x - 5, and the other side of this equation so it's true for no values of x: 1/2(6x - 10) - x = 2x-5 = 2x+3.
How do equations work?A mathematical equation is a formula that uses the equals sign to represent the equality of two expressions.
Given that, find the other side of this equation so it's true for all values of x:
1/2(6x - 10) - x
= 6x/2 - 10/2 -x
= 3x-5-2
= 2x-5
Now for, equation so it's true for no values of x:
1/2(6x - 10) - x =
Distribute the parentheses:
1/2(6x - 10) - x =
= 3x -5 -x
= 2x -5
We need to other side to be of the form 2x - constant where the constant is not equal to 5.
2x-5 = 2x+3
Subtract 2x from each side.
-5 =3
This is not true so there is no solution.
Hence, the other side of this equation so it's true for all values of x: 1/2(6x - 10) - x = 2x - 5, and the other side of this equation so it's true for no values of x: 1/2(6x - 10) - x = 2x-5 = 2x+3.
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The scatter plot shows a relationship between the height and width of a tree. Based on this relationship, predict the height of a tree whose width is 10 ft.
Thank you in advance!
Answer:
ive had this
Step-by-step explanation:
i remember having this its 35ft
Answer: 35ft
Step-by-step explanation: i did this before
It is day 8 and you are getting hungry. Since hunting/fishing have not been successful so far, you decide to eat ants for protein. 100 grams of ants gives enough protein as an egg. How many ants is this if one ant is between 1 - 5 mg? (Give a range of values)
The range of ants to eat is 20,000-1,00,000 ants.
What is range?The difference between the highest and lowest values for a particular data collection is the range in statistics. For instance, the range will be 10 - 2 = 8 if the provided data set is 2, 5, 8, 10, and 3.
As a result, the range may alternatively be thought of as the distance between the highest and lowest observation. The range of observation is the name given to the outcome. Statistics' range reflects the variety of observations.
The answer is given below:
If each ant is of 1 mg:
1g = 1000 mg = 1000 ants
100g = 100000 mg = 100000 ants
=> Maximum 105 ants
Now if one ant is of 5 mg:
1g = 1000mg = 1000/5 = 200 ants
100g = 20000 ants
Minimum 20,000 ants
Hence the range of ants to eat is 20,000-1,00,000 ants.
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Which equation represents the graph of function j?
The required equation that represents the graph is j(x) = (-x + 4)¹/². Option D is correct.
What is a parabola?A parabola is a cross-section cut out of the cone and represented by an equation x = y².
here,
The given graph is of the left parabola,
-x = y²
When we translate the above expression 4 units right we get the graph,
So
-x + 4 = y²
put y = j(x)
-x + 4 = j(x)²
j(x) = [-x + 4]¹/²
Thus, the required equation that represents the graph is j(x) = (-x + 4)¹/². Option D is correct.
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Please help me with the following question.
a) The point estimate of the population mean is given as follows: 3.2.
b) The standard error of the sample mean is given as follows: 0.16.
c) The interpretation of the 95% confidence interval is that we can be 95% confidence that the mean number of children that females would like to have is between 3.04 and 3.36. (option D).
d. It is not plausible that the population mean is of 2, as 2 falls outside of the confidence interval. (option A).
How to obtain the features?The point estimate of the confidence interval is given by half the sum of the bounds, hence:
(3.04 + 3.36)/2 = 3.20.
The standard error of the sample mean is half the difference between the bounds, hence:
(3.36 - 3.04)/2 = 0.16.
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Please help me ASAP!
The reflection points of (-7, 8) across the x-axis and y-axis are (-7, -8) and (7, 8).
What is a reflection?A reflection is a type of transformation that involves flipping a shape, known as the preimage, over a line, known as the line of reflection, to produce a new shape (called the image). You can picture what would happen if you flipped the form over the line in order to graph a reflection.
Given:
A point (-7, 8).
Reflection rule about the x-axis:
(x , y) → (x, -y)
So, (-7, 8) → (-7, -8)
Reflection rule about the y-axis:
(x , y) → (-x, y)
So, (-7, 8) → (7, 8)
Therefore, all the required values are given above.
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A flyer posted at a market is a rectangular piece of paper that is 19 inches (in) long and 15 in. Wide. Find the area of the rectangle defined by this flyer
of the 400 employes 5% of them are manegers
Answer:
20%
Step-by-step explanation:
To answer this question we have to 5% of 400, this will give us the number of managers!
1) 5% of 400
To find 5% of 400 we have to do 5 × 400...5 × 400 = 2000Then 2000 ÷ 100...2000 ÷ 100 = 20%This gives us the answer!
Have a lovely day :)
select all the dxpressions equivalent to 7^-2 • 7^5 • 7^-3
The solution of the expression ( 7⁻² x 7⁵ x 7⁻³ ) is equal to 1.
What is an expression?The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.
Given that the expression is ( 7⁻² x 7⁵ x 7⁻³ ). The expression will be solved as below,
E = ( 7⁻² x 7⁵ x 7⁻³ )
E = 7⁽ ⁻²⁺⁵⁻³⁾
E = 7⁽⁻⁵⁺⁵⁾
E = 7⁰
E =1
Hence, the solution of the expression ( 7⁻² x 7⁵ x 7⁻³ ) is equal to 1.
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Is the relationship linear, exponential, or neither? X/-12 -6 0 6 y/9 12 20 40
Answer: The relationship between the variables x and y in the given data points is linear.
Step-by-step explanation: A linear relationship is one in which the change in the y-value (output) is always the same for a given change in the x-value (input), regardless of the starting point. In other words, the slope of the line is constant.
In this case, the slope of the line can be calculated by finding the difference in y-values for a given difference in x-values between two points. We can pick any two points, for example:
(X: -6, Y: 12) and (X: 6, Y: 20)
The slope can be calculated by:
m = (20 - 12) / (6 - (-6)) = 8/12 = 2/3
This means that for every 1 unit increase in x, y increases by 2/3 units.
This is a linear relationship.
In contrast, in an exponential relationship, the y-value increases (or decreases) at a constantly increasing (or decreasing) rate as the x-value increases.
someone help i dont get this math much at all- its about compound interest
[tex]{\Large \begin{array}{llll} y=ab^x \end{array}} \\\\[-0.35em] ~\dotfill\\\\ \begin{cases} x=5\\ y=7 \end{cases}\implies 7=ab^5 \\\\[-0.35em] ~\dotfill\\\\ \begin{cases} x=0\\[1em] y=\frac{1}{4} \end{cases}\implies \cfrac{1}{4}=ab^0\implies \cfrac{1}{4}=a(1)\implies \cfrac{1}{4}=a \\\\\\ \stackrel{\textit{substituting on the 1st equation}}{7=\left( \cfrac{1}{4} \right)b^5\implies 28=b^5}\implies \sqrt[5]{28}=b~\hfill \boxed{y\approx \cfrac{1}{4}(1.9473)^x}[/tex]
If a/2-b/3 = 1 what is 2a+3b in terms of b
If a/2-b/3 = 1, then we can write:
2(a/2-b/3) = 2
Combining like terms, we have:
a - b/3 = 1
Multiply both sides by 3 to get:
3a - b = 3
Now, we can add b to both sides of the equation:
3a = b + 3
Finally, we can divide both sides by 3 to get:
a = (b + 3)/3
Now we can substitute this value of a into the original equation
2a + 3b = 2(b + 3)/3 + 3b = 2b/3 + 6/3 + 3b = 2b + 2 + 3b = 5b + 2
So 2a+3b = 5b + 2 in terms of b
Question content area top
Part 1
A car moving at a constant speed passed a timing device at tequals
0.
After 9
seconds, the car has traveled 828
ft. Write a linear function rule to model the distance in feet d the car has traveled any number of seconds t after passing the timing device.
A linear function rule to model the distance in feet {d} the car has traveled any number of seconds {t} after passing the timing device is
d = 92t.
What are algebraic expressions?In mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.Mathematical symbols can designate numbers (constants), variables, operations, functions, brackets, punctuation, and grouping to help determine order of operations and other aspects of logical syntax.Given is that a car moving at a constant speed passed a timing device at t = 0 s. After 9s, the car has traveled 828 ft.
We can write the linear function as -
y = mx
Now, we can write the slope as -
{m} = (828/9) = 92
So -
d = 92t
Therefore, a linear function rule to model the distance in feet {d} the car has traveled any number of seconds {t} after passing the timing device is
d = 92t.
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Which transformations have been performed on the graph of f(x)=x√ to obtain the graph of g(x)=14x+3−−−−√+6? Select each correct answer. Responses reflect the graph over the x-axis reflect the graph over the x -axis translate the graph to the right translate the graph to the right stretch the graph away from the x-axis stretch the graph away from the x -axis translate the graph up translate the graph up compress the graph closer to the x-axis compress the graph closer to the x -axis translate the graph to the left translate the graph to the left translate the graph down
The transformations have been performed on the graph of f(x) = 3√x to obtain the graph of g(x)=1/4x+3√x+3+6 are respectively,
C. stretch the graph away from the x-axis
E. translate the graph to the left
G. translate the graph up
What are functions?Function is a relation between a set of inputs and a set of outputs which are permissible. In a function, for particular values of x we will get only a single image in y. It is denoted by f(x).
Given that,
Two functions,
f(x) = 3√x,
g(x)=1/4x+3√x+3+6
Graph is attached,
the steps of transformation are,
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Answer:
compress the graph closer to the x-axis
translate the graph up
translate the graph to the left
Step-by-step explanation:
I took the test on k12 trust me.
Hi! Can someone please help with this question? I'm really confused on how exactly to find the force of magnitude
The magnitude and direction of the force C are 93.853 pounds-force and 281.237°, respectively.
How to find the magnitude and direction of a force in a 3-vector system
In this problem we find the case of a system at equilibrium and formed by 3 vectors, of which we must determine the magnitude and direction of a force must be determined. Vectors are described by two features: (i) Magnitude, (ii) Direction.
The magnitude is obtained by Pythagorean theorem:
F = √(x² + y²)
The direction is determined by inverse trigonometric functions:
θ = tan⁻¹ (y / x)
Besides, the system can be described physically by Newton's laws and mathematically by vector sum:
F₁(x, y) + F₂(x, y) + F₃(x, y) = (0, 0)
First, determine the vector associated to force C:
F₃(x, y) = - F₁(x, y) - F₂(x, y)
F₃(x, y) = - (- 92 · cos 45°, 92 · sin 45°) - (54 · cos 30°, 54 · sin 30°)
F₃(x, y) = - (- 46√2, 46√2) - (27√3, 27)
F₃(x, y) = (46√2, - 46√2) - (27√3, 27)
F₃(x, y) = (46√2 - 27√3, - 46√2 - 27)
Second, calculate the magnitude of force C:
F₃ = √[(46√2 - 27√3)² + (- 46√2 - 27)²]
F₃ ≈ 93.853
Third, determine the direction of force C:
θ = tan⁻¹ [(- 46√2 - 27) / (46√2 - 27√3)]
θ ≈ 281.237°
To learn more on Newton's laws: https://brainly.com/question/13678295
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Answer:
F₃ = 94 lb at 78.8° below the +x axis
Step-by-step explanation:
You want the magnitude of force F₃ that makes the sum of forces be zero.
Sum of forcesAs you have already noted, the sum of forces is zero when the system is at equilibrium.
F₁ +F₂ +F₃ = 0
F₃ = -(F₁ +F₂)
The forces F₁ and F₂ can be added by adding their horizontal and vertical components.
F₁ = 92(cos(135°), sin(135°)) ≈ (-65.0538, 65.0538)
F₂ = 54(cos(30°), sin(30°)) ≈ (46.7654, 27)
Then the sum of forces is ...
F₁ +F₂ ≈ (-18.2884, 92.0538) . . . . . sum of corresponding parts
MagnitudeAs we noted above, F₃ is the opposite of the sum, so is ...
F₃ = (18.2884, -92.0538)
The magnitude is found using the Pythagorean theorem:
|F₃| = √(18.2884² +(-92.0538)²) ≈ √8808.3677 ≈ 93.8529
The magnitude of F₃ is about 94 lb.
DirectionThe components of F₃ tell you the force is in the 4th quadrant. The ratio of the x- and y-components is the tangent of the angle:
θ = arctan(y/x) = arctan(-92.0538/18.2884) = arctan(-5.03345)
θ ≈ -78.763°
In the first attachment, the sum of forces F₁ +F₂ is shown by the black arrow. The direction of F₃ will be the opposite of that arrow's direction, so will be down to the right, about 78.8° below the +x axis. The second attachment shows the magnitude and direction of F₃, where 0° is the direction of the +x axis.
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Additional comment
For finding the magnitude of the sum of two forces, the Law of Cosines is another way to do it. To use that, you need to know the angle between the two forces. That's the angle at lower right inside the triangle shown in the first attachment. It is 75°. Then the magnitude is ...
|F₃| = √(54² +92² -2·54·92·cos(75°)) ≈ √8808.37 ≈ 93.853 . . . . lb
This math can be simpler than working with the x- and y-components of the forces.
The angle of F₃ is another matter. Finding that requires solving the force triangle for one of the other interior angles, then adding the angles in the appropriate way.
For example, the angle at the origin can be found from the Law of Sines as ...
α = arcsin(92/93.853·sin(75°)) ≈ 71.237°
Adding this to the angle of the red vector (30°) gives the resultant angle relative to the +x axis of 101.237°. The direction of F₃ is opposite this, so is ...
101.237° -180° = -78.763° . . . . as above
As you can see from the attachments, a vector calculator or spreadsheet is a useful tool for finding sums of forces from their magnitude and direction.
Just to be clear, the conversion between polar and rectangular forms is ...
(x, y) = r(cos(θ), sin(θ))
r = √(x² +y²)
θ = arctan(y/x) . . . . . with attention to quadrant
Spreadsheets and some calculators have an ATAN2(x, y) function that takes the signs into account when it computes the angle. When working with angles, make sure the calculator's angle mode is set to degrees or radians appropriately. (Spreadsheets usually use radians.)
