a) The work done is 3.3 J
b) The new force would stretch it 1.9 cm beyond its natural length.
What is Hooke's law?Hooke's law states that, the force of elasticity that tends to stretch a spring is directly proportional to the extension that is caused by the force as long as we do not by any means exceed the elastic limit of the material. This implies that the Hooke's law can only be found to hold when the elastic limit of the material has not been exceeded and the material has not become plastic.
Now;
F = Ke
W =1/2 Fe
F = 2W/e
W = work done
F = force exerted
e = extension
F = 2 * 23 /(44 - 30) * 10^-2
F = 328.6 N
a) To stretch 34 cm to 36 cm;
W = 1/2 * 328.6 N * 2 * 10^-2
W = 3.3 J
The work done is 3.3 J
b) F = Ke
328.6 N/(44 - 30) * 10^-2 = K
K = 2347 N/m
Then;
45 N = 2347 N/m * e
e = 45 N/ 2347 N/m
e = 0.019 m or 1.9 cm
New length = 30 cm + 1.9 cm = 31.9 cm
The new force would stretch it to a distance of 31.9 cm or 1.9 cm beyond its natural length.
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Perform the operation and write the result in the standard form.
(1 + 9i)(1 - 9i)
Answer:
10-18i
Step-by-step explanation:
1(1-9i)+9(1-9i)
1-9i+9-9i
1+9-9i-9i
10-18i
9x-9y-0
-3x+3y=0
elimination process
Answer:
(-10,-10)Step-by-step
explanation:
Yes 9x-9y=03x-4y=10In
elimination, we want both equations to have the same form and like terms to be lined up. We have that. We also need one of the columns with variables to contain opposites or same terms. Neither one of our columns with the variables contain this. We can do a multiplication to the second equation so that the first terms of each are either opposites or sames. It doesn't matter which. I like opposites because you just add the equations together. So I'm going to multiply the second equation by -3.I will rewrite the system with that manipulation:9x-9y=0-9x+12y=-30----------------------Add them up!0+3y=-30 3y=-30 y=-10So now once you find a variable, plug into either equation to find the other one.I'm going to use 9x-9y=0 where y=-10.So we are going to solve for x now.9x-9y=0 where y=-10.9x-9(-10)=0 where I plugged in -10 for y.9x+90=0 where I simplified -9(-10) as +90.9x =-90 where I subtracted 90 on both sides.x= -10 where I divided both sides by 9.The solution is (x,y)=(-10,-10)
Bill school is selling tickets to a fall musical. On thefirst day of ticket sales to school sold one adult ticket and 6 children tickets for a total of $52. The school took in $66 on the second day by selling 1 adult ticket and 8 child tickets. Find the price of an adult ticket
The price of an adult ticket is x= $10
What is mathematical expression?
A mathematical expression is defined as the collection of the numbers variables and functions by using signs like addition, subtraction, multiplication, and division.
Let the adult ticket be x
Let the children ticket be y
first day,
1*x + 6*y = 52
x + 6y = 52 equation 1
second day,
1*x + 8*y = 66
x + 8y = 66 equation 2
Solving both the equations
Subtracting equation 2 -equation 1, we get
x + 8y - x - 6y = 66 - 52
2y = 14
y = 7
putting the value of y in equation 1, we get
x + 6*7 = 52
x = 52 - 42
x = 10
Therefore, price of an adult ticket is x= $10
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28:32 simplified
Does any one know?
it will be 7:8
Step-by-step explanation:
28/4 32/4
7 8
Find the intervals where f(x) is increasing or decreasing: √x -2x. Ans: increasing (0, 1/4) Decreasing (1/4, ∞)
Answer:
[tex]\textsf{Increasing function}: \quad \left[0, \dfrac{1}{16}\right)[/tex]
[tex]\textsf{Decreasing function}: \quad \left(\dfrac{1}{16}, \infty\right)[/tex]
Step-by-step explanation:
Given function:
[tex]f(x)=\sqrt{x}-2x[/tex]
As a negative number cannot be square rooted, the domain of the function is restricted to [0, ∞).
[tex]\textsf{A function is \textbf{increasing} when the \underline{gradient is positive}}\implies f'(x) > 0[/tex]
[tex]\textsf{A function is \textbf{decreasing} when the \underline{gradient is negative}} \implies f'(x) < 0[/tex]
Differentiating produces an algebraic expression for the gradient as a function of x. Therefore, differentiate the given function:
[tex]\begin{aligned}f(x) & = \sqrt{x}-2x\\& = x^{\frac{1}{2}}-2x\\\implies f'(x) & = \dfrac{1}{2}x^{\left(\frac{1}{2}-1\right)}-2x^{(1-1)}\\ & = \dfrac{1}{2}x^{-\frac{1}{2}}-2x^0\\ & = \dfrac{1}{2\sqrt{x}}-2\end{aligned}[/tex]
Increasing function
To find the interval where f(x) is increasing, set the differentiated function to more than zero and solve for x:
[tex]\begin{aligned}f'(x) & > 0\\\implies \dfrac{1}{2\sqrt{x}}-2 & > 0\\\dfrac{1}{2\sqrt{x}} & > 2\\\ \dfrac{1}{2} & > 2\sqrt{x}\\\dfrac{1}{2 \cdot 2} & > \sqrt{x}\\ \dfrac{1}{4} & > \sqrt{x}\\ \sqrt{x} & < \dfrac{1}{4}\\\left(\sqrt{x}\right)^2 & < \left(\dfrac{1}{4}\right)^2\\ x & < \dfrac{1}{16}\end{aligned}[/tex]
As the domain is restricted, the function is increasing when:
[tex]\textsf{Solution}: \quad 0 \leq x < \dfrac{1}{16}[/tex]
[tex]\textsf{Interval notation}: \quad \left[0, \dfrac{1}{16}\right)[/tex]
Decreasing function
To find the interval where f(x) is decreasing, set the differentiated function to less than zero and solve for x:
[tex]\begin{aligned}f'(x) & < 0\\\implies \dfrac{1}{2\sqrt{x}}-2 & < 0\\\dfrac{1}{2\sqrt{x}} & < 2\\\ \dfrac{1}{2} & < 2\sqrt{x}\\\dfrac{1}{2 \cdot 2} & < \sqrt{x}\\ \dfrac{1}{4} & < \sqrt{x}\\ \sqrt{x} & > \dfrac{1}{4}\\\left(\sqrt{x}\right)^2 & > \left(\dfrac{1}{4}\right)^2\\ x & > \dfrac{1}{16}\end{aligned}[/tex]
Therefore, the function is decreasing when:
[tex]\textsf{Solution}: \quad x > \dfrac{1}{16}[/tex]
[tex]\textsf{Interval notation}: \quad \left(\dfrac{1}{16}, \infty\right)[/tex]
Note: The answer quoted in the original question is incorrect for the quoted function (please refer to the attached graph for proof).
Differentiation Rules
[tex]\boxed{\begin{minipage}{4.8 cm}\underline{Differentiating $ax^n$}\\\\If $y=ax^n$, then $\dfrac{\text{d}y}{\text{d}x}=nax^{n-1}$\\\end{minipage}}[/tex]
514 gram in kg convert into
Answer:
514 grams is equal to 0.514 kilograms
Find the lateral area of this square based pyramid. base is 10 ft. and slant is 10 ft.
The lateral area of the square pyramid that has a base of 10ft and height of 10 ft is calculated as: 200 ft²
How to Determine the Lateral Surface Area of a Square Pyramid?A square pyramid is a solid that has a square base and four triangular lateral faces.
The lateral area of the square pyramid is therefore the total area of the four triangular lateral faces of the square pyramid.
Area of one triangular lateral face = 1/2(base)(height)
Lateral area of the square pyramid = Total area of the four triangular lateral faces = 4 × 1/2(base)(height) = 2(base)(height)
We know the following:
Base = 10 ft
Height = 10 ft
Therefore:
Lateral area of the square pyramid = 2(10)(10)
Lateral area of the square pyramid = 200 ft²
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Graduation gift of $5,000 average 2.5% interest. 3. what will the total value be after 10 years simple interest?
Name three points that are collinear
Answer:
B, J, C.
Collinear points means the points are on the same straight line, which means they have the same gradient. B, J, C are the only points on the sane straight line.
O LINEAR EQUATIONS AND INEQUALITIES
Finding a percentage of a total amount: Real-world situations
Das
A file that is 244 megabytes is being downloaded. If the download is 18.5% complete, how many megabytes have been downloaded? Round your answer to the
nearest tenth.
megabytes
The size of the file that has been downloaded is 50 megabytes.
Given total size of the file is 244 megabytes
The percentage that completed the download till now = 18.5%
We have to determine the size of the file downloaded till now can be written as
= 18.5 % of 244
= 18.5 / 100 * 244
= 45.14 megabytes
≈ 50 megabytes
The size of the file that has been downloaded is 50 megabytes.
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f(x)=3x-3. find f(4)
Answer:
f(4)=9
Step-by-step explanation:
The given function is
F(x)=3x-3
so,
f(4)=3*4-3
f(4)=12-3
f(4)=9
putting 4 in place of x we get answer of the question.
Use the order of operations to simplify the expression.
5-8
8-5
+ (7 - 2²)
Answer:
2
Step-by-step explanation:
-3/3 + (7-2^2) = _
-1+3=2
Suppose you want to have $600,000 for retirement in 30 years. Your account earns 6% interest. How much would you need to deposit in the account each month?
To have $600,000 for retirement in 30 years with 6% interest , we need to deposit $498.29 in the account each month.
As given in the question,
Final amount 'A'= $600,000
Time 't' = 30years
Rate of interest 'r'= 6%
Month =12
Let 'P' be the amount deposit in the account each month
[tex]A = \frac{(P(1+\frac{r}{m})^{mt}-1 )}{\frac{r}{m} }\\\\\implies 600,000 = \frac{(P(1+\frac{6}{12\times 100})^{12\times 30}-1 )}{\frac{6}{12\times 100} }\\\\\implies 600,000 \times \frac{1}{200}= P (\frac{12.06}{12})^{360}-1 \\\\\implies 3000 +1 = P(1.005)^{360} \\\\\implies P = \frac{3001}{6.02258} \\\\\implies P = \$498.29[/tex]
Therefore, to have $600,000 for retirement in 30 years with 6% interest , we need to deposit $498.29 in the account each month.
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Which transformation would take Figure A to Figure B?
Answer:
Reflection over y- axis
Note: Enter your answer and show all the steps that you use to solve this problem in the space provided.
Solve the following equation algebraically. Show your work.
17=−13−8x
Answer:
-15/4 = x
Step-by-step explanation:
17 = -13 -8x
Solving for x
Add 13 to each side
17 +13 = -13+13-8x
30 = -8x
Divide each side by -8
30/-8 = -8x/-8
Simplify by dividing the top and bottom by 2
-15/4 = x
Please help meeee!!!!
Answer:2
Step-by-step explanation: x+1+2x=3x+1 3x+1=7 3x=7-1 x=6/3 x=2
hope it helps
Answer:
3
Step-by-step explanation:
x+1+2x=7
variables should be on the left and the whole number on the right.
something like this: x+2x=7-1
simplify the equation: 3x=6
find x: x= 6/3=2
so u know x is 2
then substitute the 2 into x. so 2+1 =3#
Your answer is three.
A storage locker measures 8 feet wide,
12 feet deep, and 9 feet high. The
monthly rental price for the locker
is $3.60 per cubic yard. How much
does it cost to rent the locker each
month? Explain.
Simplify the expression −7+ −5−40 ×−8
The value of the given expression when simplified is equal to 318.
What is an Expression?In mathematics, an expression is defined as a set of numbers, variables, and mathematical operations formed according to rules dependent on the context.
The given expression can be simplified using the PEMDAS as shown below.
-7 + 5 - 40 × -8
As per the PEMDAS multiplication should be solved first,
= -7 + 5 + 320
Further, solve addition,
= -7 + 5 + 320
= -7 +325
= 318
Hence, the value of the given expression when simplified is equal to 318.
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The number of words in books are discrete or continuous
Aubrey worked at three part-time jobs last week. At one job, she worked 15 hours at a salary of S15 per hour, at another she worked 10 hours at S14 per hour,
and at the third she worked 11 hours at $21 per hour. What was her mean hourly wage?
Which could be a possible value of x for the expression below to be a rational number? √9x+4
X=4
X=13
X=14
X=16
Determine the relationship between the quantities on the given graph.
Wages Earned ($)
OA. The hourly rate depends on the wages earned.
B.
The time worked depends on the wages earned.
C.
The wages earned depends on the time worked.
The time worked depends on the hourly rate.
O D.
Total Wages
Time Worked (hours)
The wages earned depends on the time worked is the correct relationship between the quantities on the given graph that means option C is correct
The graph given in the question shows the time worked on x axis and wages earned on y axis and a ray staring from the origin and moving upward
from the graph we can say that when time worked is zero then wages earned is zero. As the time worked is increasing the wages earned is also increasing .
Hence, it can be said that The wages earned depends on the time worked is the correct relationship between the quantities on the given graph that means option C is correct
The correct question is -Determine the relationship between the quantities on the given graph.
Total Wages
Wages Earned ($)
Time Worked (hours)
OA. The hourly rate depends on the wages earned.
OB. The time worked depends on the wages earned.
OC. The wages earned depends on the time worked.
OD. The time worked depends on the hourly rate.
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If the graph of the parent function f(x) = x is 7 units up and stretched vertically by a factor of 3
The transformed function can be seen in the image below, and the rule is:
g(x)= x/3 + 7
How to get the transformed function?
Here we have the parent function, and we want to apply a translation of 7 units up and stretch it vertically by a scale factor of 3
First, we need to apply the translation, remember that a vertical translation of N units is written as:
g(x) = f(x) + N
If we want the translation to be upwards, then we need to use a positive value of N, so in this case we wil have:
g(x) = f(x) + 7
And now we apply a stretch of scale factor 3, this means that we need to divide the variable inside of the function by 3, so we get:
g(x) = f(x/3) + 7
This will give:
g(x)= x/3 + 7
Where we use the fact that f(x) = x
The graph of this function can be seen below.
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How much will a person pay for 6.7 pounds of bananas at a price of $0.64 per pound?
Answer:
Price per pound = $0.64
which means one pound of banana costs 0.64$.
so,If 1 pound costs 0.64$ then 6.7 pounds would cost:
1 pound = $0.64
6.7 pounds= 0.64× 6.7
that is equal to $4.288.
Step-by-step explanation:
Price per pound = $0.64
which means one pound of banana costs 0.64$.
so,If 1 pound costs 0.64$ then 6.7 pounds would cost:
1 pound = $0.64
6.7 pounds= 0.64× 6.7
that is equal to $4.288.
Amelia has 120 ten-dollar bills and 75 twenty-dollar bills. What is the ratio of ten-dollar bills to twenty-dollar bills
Simplify your answer.
Enter your answer as a fraction.
●
please help
Answer:
24/15
Step-by-step explanation:
120 : 75 =
120/5 : 75/5 =
24 : 15 =
24/15
Answer:
8 : 5 or 8/5
Step-by-step explanation:
starts as 120 : 75
divide both by 5
= 24 : 15
divide both by 3
= 8 : 5 or 8/5
you just need to get them down to the smallest they can. in this case it is 8 and 5. for every 8 $10 bills there are, you have 5 $20 bills.
Ellen wanted to buy the following items: A DVD player for $49.95 A DVD holder for $19.95 Personal stereo for $21.95. Does Ellen have enough money to buy all three items if she has $90?
Answer: no she dosen't
Step-by-step explanation:
If you were to add up all three numbers
49.95+19.95+21.95=91.85
Which means she is $1.85 short to buy all of the items
7th grade question
2. Mateo is draining a pool at a rate of 1/8 of a gallon of water every 1/2 hour.
If he continues to drain the pool at this rate, how much water will be
drained in 1 hour?
A.4 gallons
B.1 gallon
C. 1/2 gallon
D.1/4 gallon
Answer:
1/4 gallon
Step-by-step explanation:
Just multiply the numerator and denominator of the given rate by 2:
2(1/8) gallon 1/4 gallon
------------------ = ---------------- = 1/4 per gallon
2(1/2) hour 1 hour
Calculate the area of one triangle so that you can begin building the tabletop .What is the area of each triangle in square inches
A triangle in which one of the interior angles is 90° is called a right triangle. The longest side opposite to the right angle is the hypotenuse and the two arms of the right angle are the height and the base.
The area of each triangle is 200 square inches.
What is a right triangle?A triangle in which one of the interior angles is 90° is called a right triangle. The longest side opposite to the right angle is the hypotenuse and the two arms of the right angle are the height and the base.
We have,
The area of a right triangle is given by:
= 1/2 x base x height
We have from the figure,
Base = 20 inches
Height = 20 inches
Area = 1/2 x 20 x 20
Area = 10 x 20
Area = 200 square inches
Thus the area of each triangle is 200 square inches.
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The complete question is:
You work as an assistant to a carpenter who designed the tabletop below. He tells you that each shape is a right triangle, and each is the same size. You now need to calculate the area of one triangle so that you can begin building the tabletop. What is the area of each triangle in square inches?
A. 200 square inches
B. 400 square inches
C. 570 square inches
D. 2,800 square inches
E. 5,600 square inches
2x - 7y=1
4x - 14y= 22
elimination process
Answer:
No solution
Step-by-step explanation:
Let's solve your system by elimination.−2x+14y=−29;x−7y=19Multiply the second equation by 2, then add the equations together.(−2x+14y=−29)2(x−7y=19)
Becomes
−2x+14y=−292x−14y=38Add these equations to eliminate x:0=9
HELP PLEASE
Graph the point (-2,3) and 3 more points using a slope of -1/2
The linear equation that represents the point (-2,3) and 3 more points with a slope of -1/2 is y = -1/2x + 2
How to graph the point (-2,3) and 3 more points using a slope of -1/2?The given parameters are
Slope, m = -1/2
Point, (x1, y1) = (-2, 3)
The linear equation is calculated as:
y = m(x - x1) + y1
Substitute the known values in the above equation
y = -1/2(x + 2) + 3
Expand
y = -1/2x - 1 + 3
Evaluate the sum
y = -1/2x + 2
This means that the linear equation that represents the point (-2,3) and 3 more points with a slope of -1/2 is y = -1/2x + 2
See attachment for the graph of the point and the three other points
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