The Laplace transform of the given integral function is 1/s +4 / (s²+16) .
The integral transform, commonly known as the Laplace transform in mathematics, converts a function of either a real variable t in the time domain into a function of something like a complex variable s.
The Laplace transform is equal to the integral for the suitable functions
[tex]{\displaystyle {\mathcal {L}}\{f(t)\}(s)=\int _{0}^{\infty }f(t)e^{-st}\,dt.}[/tex]
Now we will use this to find the suitable Laplace transform of the trigonometric function:
(sin 2t-cos 2t)²
= sin² 2t + cos² 2t - 2sin 2tcos 2t
= 1 - sin 4t
Now we will use the Laplace transform of the function.
L [1 - sin 4t] = L[1] - L[sin 4t]
Now L[1] = 1/s
L[sin 4t] = 4/ (s²+4²) = 4 / (s²+16)
Hence the Laplace transform will be
L [1 - sin 4t] = 1/s +4 / (s²+16)
Pierre-Simon Laplace invented the complex frequency domain, often known as the s-domain or the s-plane. There are numerous uses for the transform, a method for solving differential equations, in both science and engineering.
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Find function which gives the slope of the line tangent to j(x).
j(x)=4x55−x4+x2
A. 3x4−12x3+2x
B. 16x3−12x2+2
C. 4x4−4x3+2x
D. 4x4−4x3+2
Please help me thank you so much!
Answer:
please write it more clearly or take a pic
Amount Desired at End of Period
$17,600.00
Length of Time
7
1. Period Used
2. Rate Used
23. PV factor used
3 4. PV of amount desired at end of period
Rate
2%
Compounded
Quarterly
Required:
Complete the following using the information above and the present value Table 12.3
or the present value table in the Business Math Handbook or the present value
formula to answer the following:
Note: Use cells A2 to D3 from the given information to complete this question.
A percentage is a number or ratio expressed as a fraction of . It is often denoted using the percent sign, "%" and PV factor used is 0.62026 .
Hence,
The amount desired at end of a period is $9400.
The length of time is 4 years .
The rate is 2%.
Compounded is monthly.
The period used is 48.
The rate used is 1%.
The PV factor used is 0.62026 .
The PV of the amount desired at the end of the period is $5830.45
What is the percentage?
A percentage is a number or ratio expressed as a fraction of . It is often denoted using the percent sign, "%".
Here from the question,
PV factor = (1 + i) ----(1)
where, i = 12/12 % , i =1
and
n = 4(12)
n = 48
Substituting the values in the equation , we get
PV factor = (1 + 0.01)^ -48
PV factor = 0.62026
Hence,
the amount desired at end of a period is $9400.
The length of time is 4 years.
The rate is %.
Compounded is monthly.
The period used is 48 .
The rate used is 1%.
The PV factor used is 0.62026.
The PV of the amount desired at the end of the period is $5830.45
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help please
thank you
have a great day
How can you stay safe as you evacuate during a flood? Select the three correct answers:
A, C, & D
Moving furniture is not beneficial in a flood situation.
A, C and D
hope this helps!
how many craft sticks will be left over if 9 friends equally share a package of 85 craft sticks
Answer:
4 craft sticks
Step-by-step explanation:
Assuming that none of the craft sticks can be split in order to equally share the whole package, then the most craft sticks each person could have would be 9 because 9*9=81. This means that there would be 4 craft sticks left over because 85-81=4
Determine the intercepts of the line.
Presley has (9x-10) bracelets and sells (4x + 5). How many
bracelets does Presley have left? Write an expression
to show the difference.
Presley have 1 bracelets left and the expression which shows the difference is (9x - 10) - (4x + 5) .
What is linear polynomial equation?
Any polynomial written as the equation p(x) = ax + b, with a and b being real numbers and a 0, is referred to as a linear polynomial. The largest exponent of the variable in a linear polynomial, or one, is known as the degree of the variable.
If n elements are given and x element is subtracted from the n elements, hence the remaining element is y, then expression can be expressed by n- x = y.
We have,
(9x - 10)
(4x + 5)
Initially Presley has (9x - 10) bracelets and she sells (4x + 5), hence we have to calculate the remaining bracelets.
Therefore,
(9x - 10) - (4x + 5)
By simplifying the above equation we get,
= 9x - 10 - 4x + 5
= 5x -5
x = 5 / 5
∴ x = 1
Hence, the Presley have 1 bracelets left.
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write a linear equation that psses theough the point (2,-9) and has a slope of -5 in slope-intercept form
The linear equation that passes through the point (2,-9) and has a slope of -5 in slope-intercept form is y = -5x = 1
How to represent linear equation?Linear equation can be represented in different form such as slope intercept form, point slope form, general form and standard form.
Hence, the linear equation in slope intercept form is as follows;
y = mx + b
where
m = slopeb = y-interceptTherefore, the line passes through (2,-9) and has a slope of -5 .
Hence,
y = -5x + b
let's find the y-intercept using (2, -9)
-9 = -5(2) + b
-9 = -10 + b
b = -9 + 10
b = 1
Therefore, the linear equation is y = -5x + 1
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Mara solved an exponential equation by using logarithms. This is her work.
Latex: 7 \cdot 3^x=189
7
⋅
3
x
=
189
7
⋅
3
x
=
189
Latex: 3^x=27
3
x
=
27
3
x
=
27
Latex: \log _3\!(3^x)= \log _3\!27
log
3
(
3
x
)
=
log
3
27
log
3
(
3
x
)
=
log
3
27
Latex: x \log _3\!3=9
x
log
3
3
=
9
x
log
3
3
=
9
Latex: x \cdot 1=9
x
⋅
1
=
9
x
⋅
1
=
9
Latex: x=9
x
=
9
x
=
9
Review Mara's work in steps 3 and 4. (Hint: There is one mistake in those steps.)
a. Be sure to explain what she did and why it was correct or incorrect for Step 3.
b. Be sure to explain what she did and why it was correct or incorrect for Step 4.
c. Provide Mara with feedback on what the mistake was and how to fix it.
a) The mistake that mara made in step 3 is that; she didn't apply the basic rule of logarithm which should have given the expression log 3^x = x log 3
b) The mistake that mara made in step 4 is that; you must eradicate the log at the same time and as such it should be x log 3 = 3log 3
c) The mistake she made throughout is not applying the basic rule of logarithm.
How to solve Exponential Equations using logarithm?
She is trying to solve the exponential function 7 x 3^x = 189 with the following steps;
Step 1. 7 x 3^x = 189
Step; 2. 3^x = 27; This step is correct because she got it by using division property of equality to divide both sides by 7.
Step 3; log^3 (^3) = log^27; This step is incorrect because from basic rules of logarithm, we know that; log 3^x = x log 3
Step 4. xlog^33=9; This is incorrect because you cannot remove the log on one side of the equation without doing the same on the second side. Thus, what she she should have had here is;
x log 3 = 3log 3
Step 5. x * 1 = 9; This is wrong because dividing both sides by log 4 gives; x = 3
Step 6. x = 9; This is wrong because x = 3
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Complete question is;
Mara solved an exponential equation by using logarithms. This is her work.
1. 7 x 3^x = 189
2. 3^x = 27
3. log^3 (^3) = log^27
4. xlog^33=9
5. x * 1 = 9
6. x = 9
Review Mara's work in steps 3 and 4. (Hint: There is one mistake in those steps.)
a. Be sure to explain what she did and why it was correct or incorrect for Step 3.
b. Be sure to explain what she did and why it was correct or incorrect for Step 4.
c. Provide Mara with feedback on what the mistake was and how to fix it.
Value of x in 4,5,x,480
Step-by-step explanation:
you need to give us also some context.
because that sequence can be anything.
but I suspect you mean
4 : 5 = x : 480
0.8 = x / 480
x = 480 × 0.8 = 384
85 POINTS + BRAINLEIEST PLEASE NEED THIS DONE SOON!
Aurora is planning to participate in an event at her school's field day that requires her to complete tasks at various stations in the fastest time possible. To prepare for the event, she is practicing and keeping track of her time to complete each station.
The x-coordinate is the station number, and the y-coordinate is the time in minutes since the start of the race that she completed the task.
(1, 2), (2, 4), (3, 8), (4, 16)
Part A: Is this data modeling a linear function or an exponential function? Explain your answer. (2 points)
Part B: Write a function to represent the data. Show your work. (4 points)
Part C: Determine the average rate of change between day 2 and day 4. Show your work. (4 points)
A. The data modeling the relation is an exponential function.
B. The function is: y = 2^x.
C. The rate of change from x = 2 to x = 4 is of 4.
What is an exponential function?The definition of an exponential function is presented as follows:
[tex]y = ab^x[/tex]
In which the variables of the function are listed as follows:
a is the numeric value of the function when the input is of x = 0.b is the rate of change of the function, which is the constant by which y is multiplied when x is increased by one.From this data-set, when x increases by one, y is multiplied by 2, hence the rate of change is:
b = 2.
When x is increased by n, the rate of change is:
b^n = 2^n.
Hence, when x is increased by 2, from 2 to 4, in item c, the rate of change is:
2² = 4.
When x = 1, the output is the output at x = 0 multiplied by 2, hence the coefficient a of the function is given as follows:
a = 2/2 = 1.
Then the exponential function is:
[tex]y = 2^x[/tex].
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Why should there be a number corresponding to the length of every line we draw?
Number lines are significant because they depict numbers as they appear in daily life.
What is number line?
A number line is a representation of a graduated straight line in elementary mathematics that serves as a visual representation of the real numbers. It is assumed that every point on a number line corresponds to a real number, and that vice versa.
Research has revealed that number lines are crucial because they foster sound mental number sense and arithmetic procedures.
They assist in providing a mental approach for addition and subtraction. Number lines are crucial, we can all agree on that.
Number lines are significant because they depict numbers as they appear in daily life.
Primarily because they make it possible for negative integers to be represented in a meaningful fashion.
The ability to display all real numbers, even enigmatic irrational numbers such π, -π, √2, -√ 2, etc., was a secondary but no less significant result.
Hence, number lines are significant because they depict numbers as they appear in daily life.
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a nutrition label on a protein bar shows that the bar contains 7% of the daily recommended amount of carbohydrates. there are 20 grams of carbohydrates are recommended in the protein bar. how many grams of carbohydrates ar recommended per day? round your answer to the nearest whole. PLEASE HELP WITH N EXPLANATION
The daily amount in grams of the recommended carbohydrates is 2587.15 grams
How to solve for the amount of recommended carbohydrateThe amount of daily recommended carbohydrate is solved by dividing the quantity of carbohydrate in the protein bar by the percentage contained in the bar
The problem deals with percentage and 7% is written as
7%
= 7 percent
= 7 / 100
= 0.07
The factor 0.07 of the daily recommended amount of carbohydrates gives 20 grams of carbohydrate
let the daily recommended amount of carbohydrates be x
0.07 * x = 200
0.07x = 200
x = 200 / 0.07
x = 2587.15 grams
The daily recommended amount of carbohydrates is 2587.15 gram
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The Taylors have recorded their weekly grocery expenses for the past 16 weeks and determined that the mean weekly expense was $86.60. Later, Mrs. Taylor discovered
that 1 week's expense of $89 was incorrectly recorded as $33. What is the correct mean?
The correct mean is $. (Round to the nearest cent as needed.)
Answer: The correct mean weekly grocery expense for Taylor is $62.51
How to find mean of a discrete data?
Suppose the data values be .
Then, their mean is evaluated as:
where n = number of observations.
For the given condition, Taylor recorded the weekly expenses for 12 weeks. Therefore, we get n = 12
Let the real weekly expenses for Taylor be
Let observation is misinterpreted as T
Then, the mean of that misinterpreted set of data would be
Since we're given that:
Therefore, we get the mean of original weekly expenses as:
Therefore, the correct mean weekly grocery expense for Taylor is $62.51
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Step-by-step explanation:
What is the mean of these numbers? 53 29 47 36 65
he box is 3 inches by 4 inches by 5 inches. A second box is
4 inches by 4 inches by 4 inches. Explain how to decide
which box holds more.
Answer:
4x4x4
Step-by-step explanation:
3x4x5= 60
4x4x4= 64
64 is a higher volume than 60
Answer:
In order to find out which box can hold more, we can find the respective volumes of the boxes.
Volume of first box
= 3 inches × 4 inches × 5 inches
= 60 inches³
Volume of second box
= 4 inches × 4 inches × 4 inches
= 64 inches³
∴Since the second box has a greater volume than the first box, the former can hence hold more than the latter.
What is the largest integer that is less than √83-√35?
Answer:
3
Step-by-step explanation:
√83-√35 = 3.1943537960446828393782978131270521416836379374706155296172187959...
Step-by-step explanation:
we need to remember the squared numbers of the baud integers :
1² = 1
2² = 4
3² = 9
4² = 16
5² = 25
6² = 36
7² = 49
8² = 64
9² = 81
10² = 100
so, what squared integers are closest to 83 and 35 ?
well, 81 (9²) and 36 (6²).
so, the result has to be closest to 9 - 6 = 3.
83 is larger than 81 than 35 is smaller than 36. so, 3 is less than sqrt(83) - sqrt(35).
therefore, the correct answer is indeed 3.
Consider the equation and the following ordered pairs: (6,y) and (x,1).
y=−2x+5
The values of x and y are 2 and -7 respectively, this forms an ordered pair of (6,-7) and (2,1).
What are the the values of x and y to complete the given ordered pair?Given the equation and ordered pair the question;
y = -2x + 5Point: (6,y) Point; (x,1)To determine, the y-value, plug the x-value into the equation and solve for y.
y = -2x + 5
Plug in x = 6
y = -2( 6 ) + 5
y = -12 + 5
y = -7
Determine the x-value by plunging in the y-value into the equation and solve for x.
y = -2x + 5
Plug in y = 1
1 = -2x + 5
1 + 2x = 5
2x = 5 - 1
2x = 4
x = 4/2
x = 2.
Therefore, the ordered pair are (6,-7) and (2,1).
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Find the rectangular equation for the plane curve defined by the parametric equation
x=t+4, y=t^2
-infinity < t < infinity
The rectangular equation for the plane curve defined by the parametric equation x = t + 4, y = t² is; y = x² - 8x + 16
What is the Rectangular Equation?We are given the parametric equations as;
x = t + 4
y = t²
Now, for us to convert parametric equations to a rectangular equation (cartesian equation) means that we are solving for t in terms of x and then plugging it back into the y equation. Therefore, we have;
x = t + 4
t = x - 4
Thus;
y = (x - 4)²
Expanding this gives;
y = x² -4x - 4x + 16
y = x² - 8x + 16
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For a 14-person team, how does the actual weekly labor cost compare to the target?
$15 over target $300 over target $600 over target
$1,800 over target
$6,000 over target
The actual weekly labor cost compared to the target is 240 hours
What are Time and Work?
According to fundamental mathematical concepts, time may be described as the amount of time that a specific activity occurs, whereas work can be described as the collection of actions carried out in order to attain a specific activity or outcome. It should go without saying that time is needed to accomplish a task. It implies that time and work have a certain relationship.
The task completed is calculated as the sum of the number of people participating in the work and the number of days it took to finish. The fundamental time and work equation is W = N X D.
Target costing is a system under which a company plans in advance for the price points, product costs, and margins that it wants to achieve for a new product.
Given
Regular Rate $15.00/hr
Overtime Rate $22.50/hr
Targeted Labour Cost $12,000/wk
Labour Hours Needed 800/wk
According to the question:
Overtime means each employee can work beyond the input of 40 hrs. Per week.
Labor requirement = 800 hrs.
14 men labor capacity = 14× 40 = 560 hrs.
So overtime hours required = 800-560=240 hrs
Hence,
The actual weekly labor cost compared to the target is 240
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The school play ran for 3 nights. 185 tickets were sold for the first night. 160 tickets were sold for the second night. 192 tickets were sold for the third night. The tickets cost $4 each. What information is NOT necessary to calculate the total amount of money raised from ticket sales?
A) 192 tickets were sold the for the third night.
B) The school play ran for 3 nights.
D) 185 tickets were sold for the first night.
C) The tickets cost $4 each.
Answer:B
Step-by-step explanation:
Becauee it already says the first night how many tickets were sold also on the second and the third night. And if someone read the equation they would have known that the play went in for three nights.
Bonnie loves to order products online. She ordered 27 products from one company, but unfortunately, some items were back-ordered, so she received only 19 items. How many items were missing from her order? (Let m stand for the number of missing items.)
The number of items that are missing from the order if She ordered 27 products from one company, but unfortunately, some items were back-ordered, so she received only 19 items is 8.
What is subtraction?The action of subtracting a matrix, vector, or other quantity from another according to predetermined rules in order to find the difference.
Given:
The number of the ordered products, O = 27,
The number of the received order, R = 19,
If m stands for the number of missing items, then,
m = O - R,
m = 27 - 19
m = 8
Therefore, the number of items that are missing from the order if She ordered 27 products from one company, but unfortunately, some items were back-ordered, so she received only 19 items is 8.
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PLEASE HELP! ALGEBRA 1 HW I WILL GIVE BRAINLYEST FOR ANSWER!!
In the given equation [12.5x + 5y = C] the constant C is always 50 with different given values of x and y.
What do we mean by equations?A mathematical equation is a formula that uses the equals sign to represent the equality of two expressions. A mathematical statement that has an "equal to" symbol between two expressions with equal values is called an equation. As in 3x + 5 Equals 15, for instance. Equations come in a variety of forms, including linear, quadratic, cubic, and others.So, the values of C are:
Equation: 12.5x + 5y = CCalculate as follows:
(A) When x = -2 and y = 15.
12.5(-2) + 5(15) = CC = 50(B) When x = 0 and y = 10.
12.5(0) + 5(10) = CC = 50(C) When x = 2 and y = 5.
12.5(2) + 5(5) = CC = 50(D) When x = 4 and y = 0.
12.5(4) + 5(0) = CC = 50Therefore, in the given equation [12.5x + 5y = C] the constant C is always 50 with different given values of x and y.
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5- (8 - 6) + 3 times 4 +6
-----------------------------------------
5(4 -5)
The dash lines are for a fraction line. :)
The result of the fractional operation in this problem is given as follows:
-21/5 = -4.20.
How to solve operations with fractions?A fraction is represented by the division of a term x by a term y, as follows:
Fraction = x/y.
The terms that represent x and y are given as follows:
x, which is the top term of the fraction, is called the numerator.y, which is the bottom term of the fraction, is called the denominator.The numerator in this fraction is given as follows:
5 - (8 - 6) + 3 x 4 + 6.
The parenthesis and the multiplication have precedence, hence:
5 - (8 - 6) + 3 x 4 + 6 = 5 - 2 + 12 + 6 = 21.
The denominator in this fraction is given as follows:
5(4 - 5) = 5(-1) = -5.
The result is the division of the numerator by the denominator, hence:
21/(-5) = -21/5 = -4.20.
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What is the slope of this line?
O 3/2
O 2:3
0 −3/2
O I don't know.
Answer:
3/2
Step-by-step explanation:
the answer is 3/2 because you take the slope by using the equation y/x. I did this problem by starting prop the point (0,-6). I then counted for how many points I went up, how many did I go to the right or left. If it went to the right it’s positive, to the left it is negative. In this case it went to the right 2 times every time it went up 3. Meaning 3/2
The sum of two numbers is 19/24 and their difference is 11/24, what are the two numbers?
The value of the the two numbers are 5/8and 1/6
What is Simultaneous equation?Simultaneous equations are two or more algebraic equations that share variables e.g. x and y.
They are called simultaneous equations because the equations are solved at the same time.
if the first number is x and second number is y then
x+y= 19/24 equation 1
x-y= 11/24 equation 2
using elimination method, subtract equation 1 from 2
x-x+y-(-y)=19/24-11/24
2y= 8/24
2y=1/3
divide both side by 2
y= 1/3×1/2= 1/6
substitute 1/6 for y in equation 2
x+1/6=19/24
x= 19/24-1/6
x= 15/24
x= 5/8
Therefore the value of the two numbers is 5/8 and 1/6
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help please
what c=math ........
The value of c for the expression, -0.65(c-7) = 1.95, is 4.
According to the question,
We have the following expression:
-0.65(c-7) = 1.95
Now, 0.65 is in multiplication on the left hand side. So, it will be in the division on the right hand side. Note that the negative sign can also be moved to the right hand side.
c-7 = -1.95/0.65
c-7 = -3
Moving 7 from the left hand side will result in the change of the sign from minus to plus:
c = -3+7
c = 4
Hence, the value of c is 4 for the given expression.
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An economist wants to estimate the mean per capita income (in thousands of dollars) for a major city in Texas. Suppose that the mean income is found to be $20.5 for a random sample of 1190 people. Assume the population standard deviation is known to be $11. Construct the 85% confidence interval for the mean per capita income in thousands of dollars. Round your answers to one decimal place.
At an 85% confidence interval, the mean per capita income in thousands of dollars for the major city in Texas is $20.5 ± 0.459.
What is the confidence interval estimate?The confidence interval estimates the mean estimate by adding or subtracting the margin of error.
In random sampling, the margin of error represents the difference between the actual and projected results.
Mean income = $20.5
Sample size, n = 1,190
Standard deviation = $11
Confidence interval = 85%
Z-score for 85% confidence interval = 1.440
The margin of error = z-score x standard deviation/√n
= 1.440 x 11/√1,190
= 1.440 x 11/34.50
= 1.440 x 0.3188
= 0.459
= $459 (0.459 x $1,000)
Lower Limit = Mean - Margin of Error
= $20,500 - $459
= $20,041
= $20.041
Upper Limit = Mean + Margin of Error
= $20,500 + $459
= $20,959
= $20.959
Thus, for the Texas city, the mean per capita income is $20.5 ± 0.459.
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If semantics D=2x² X -
a trinomial in standard form.
Ox²-3x - 15
2
6x²-3x - 15
O3x²-3x + 15
O-2x² + x + 15
15find an expression that equals semantics-1D as
The expression that equals semantics -1 D is - 2x² + x + 15.
What is a trinomial?One or more terms in an algebraic expression each include variables and constants. These expressions utilize separators like +, -, and that are symbols or operations. An algebraic statement with variables and constants is a quadratic trinomial. It is written as ax² + bx + c, where a, b, and c are real non-zero values and x is the variable. The leading coefficient "a," linear coefficient "b," and additive constant "c" all refer to the same constant.
The given trinomial is D = 2x² - x - 15
Multiply both sides by -1 to find -1D
-1D = -( 2x² - x - 15) = 0
-1 D = - 2x² + x + 15
So, this is the trinomial equal to the semantics -1D.
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When a constant force acts upon an object, the acceleration of the object varies inversely with its mass. When a certain constant force acts upon an object with mass 3 kg, the acceleration of the object is 25 m/s^2. If the same force acts upon another object whose mass is 5 kg, what is this object's acceleration?
If the same force acts upon another object whose mass is 5 kg, the object's acceleration will be 1.667 m/s^2.
How can the acceleration be calculated?We were told that the constant force acts upon an object, and the acceleration of the object varies inversely with its mass, which can be interpreted as :
A = k/M
where M is the mass of the object.
A = acceleration
the k= proportionality constant
then we were told that mass is 3 kg, the acceleration of the object is 25 m/s^2
then substitute into the equation as:
25 =k*3
k= 25/3
then we were told that when mass is 5 kg, then acceleration will be ?
A= (25/3 )/5 = 1.667m/s^2.
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What are the solutions of this quadratic equation?
2x2 + 16x − 8 = 0
Answer:
[tex]x= -4[/tex] + [tex]2\sqrt{5}[/tex] and [tex]x= -4 -2\sqrt{5}[/tex]
Step-by-step explanation:
[tex]ax^{2}[/tex] + [tex]bx[/tex] - [tex]c = 0[/tex]
For this equation: [tex]a = 2, b = 16, c = -8[/tex]
[tex]2x^{2}[/tex] + [tex]16x[/tex] - [tex]8 = 0[/tex]
Step 1: Use quadratic formula with [tex]a=2, b=16, c=-8[/tex]
[tex]x=\frac{-b + - \sqrt{b^{2}-4ac } }{2a}[/tex]
[tex]x=\frac{-(16) + - \sqrt{16^{2}-4(2)(-8) } }{2(-2)}[/tex]
[tex]x=\frac{-16+- \sqrt{320} }{4}[/tex]
[tex]x= -4[/tex] + [tex]2\sqrt{5}[/tex] and [tex]x= -4 -2\sqrt{5}[/tex]
Hope this helps! :)