Stretched 1 cm beyond its natural length, a rubber band exerts a restoring force of magnitude 2 newtons. Assuming that Hooke's Law applies, answer the following questions:
(a) How far will a force of 3 newtons stretch the rubber band?
(b) How much work does it take to stretch the rubber band this far?
A) The distance that a force of 3 newtons would stretch the rubber band is; 0.015 m
B) The amount of work it takes to stretch the rubber band this far is; 0.0225 J
How to solve Hooke's Law?
From Hookes's law, as long as the elastic limit is not exceeded the extension is directly proportional to the force applied.
F = Ke
Where;
F = force
K = force constant
e = extension
Thus, for a restoring force of magnitude 2 newtons ;
2 N = K(1 × 10⁻²) m
K = 2 N /(1 × 10⁻²) m
K = 200 N/m
a) For a force of 3 newtons, we have;
3N = 200 N/m × a
Where a is the extension in meters
a = 3N/200 N/m
a = 0.015 m
b) The formula to find the work done is;
P.E = ¹/₂Ke²
P.E = ¹/₂ * 200 * 0.015²
P.E = 0.0225 J
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What is the slope of y = arcsin(x) when x=0.4?
(You can compute arcsin(x) = sin-1(x) by pressing the “inverse” or “second function key”then pressing the “sin" key. Do this calculation in degrees, so arcsin(1)=90.)
Answer: about 0.41
Step-by-step explanation:
Use calculator
[tex]arcsin=sin^{-1}x\\\\\boxed{sin^{-1}(0.4) = 0.41151684}[/tex]
Please type the answers please help
Answer:
Step-by-step explanation:
哇，我喜歡吃很多食物，因為我喜歡並喜歡它。
Wa, wǒ xǐhuān chī hěnduō shíwù, yīnwèi wǒ xǐhuān bìng xǐhuān tā.
Helpppppop
h(x)=x^2-6
f(x)=4x+6
Evaluate f(h(3))
Answer:
18
Step-by-step explanation:
tbh I kinda forgot how to do this but ill try,
input 3 into the f(x)
4(3)+6=12+6=18
Find the value of x.
to
75°
125°
x =
Answer:
USE AIR MATH!!
Step-by-step explanation:
hope that helps
Please help me with this, I need help like URGENT please
Answer:
1. y= = 0.5 (2, 0.5)
2. y= 0 (4, 0)
3. y= -0.5 (6, 0.5)
Step-by-step explanation:
To get your answer, you would want to plug in the x-coordinates into the equation and solve for y.
the numbers being multiplied in a product are called
Answer:factors
Step-by-step explanation:
Como puedo resolver estas funciones y saber su tipo?
Round the decimal to the given place value.
124.123474
hundred-thousandth
Answer: 124.12347
Step-by-step explanation:
Evaluate the expression when m= -4
m2 +6m +9
Answer:
41
Step-by-step explanation:
because if m=-4 that means (-4)2+6(-4)+9=41
Last week, a chocolate shop sold 9 ounces of white chocolate. It sold 9 9/10 times as much milk chocolate as white chocolate. How many ounces of milk chocolate did the shop sell?
please answer asap
Solving the Question
We're given:
9 ounces of white chocolate sold[tex]9\dfrac{9}{10}[/tex] times as much milk chocolate as white chocolate soldIf the shop sold " [tex]9\dfrac{9}{10}[/tex] times as much milk chocolate as white chocolate", we must multiply [tex]9\dfrac{9}{10}[/tex] by the amount of white chocolate sold to find the amount of milk chocolate sold.
Multiply [tex]9\dfrac{9}{10}[/tex] by 9 ounces:
[tex]9\dfrac{9}{10}\times9[/tex]
Convert the fraction into an improper fraction:
[tex]=\dfrac{99}{10}\times9[/tex]
Multiply:
[tex]=\dfrac{891}{10}[/tex]
AnswerThe shop sold [tex]\dfrac{891}{10}[/tex] ounces of milk chocolate.
What inequality is shown by a number line that shows 12 to the right of −2?
The inequality shown by a number line which describes that 12 is to the right of -2 is; 12 > -2.
What inequality is shown by the number line that shows that 12 is to the right of 2?It follows from the task content that the inequality which represents the number line as described in the task content is to be determined
On this note, it follows that since, numbers are arranged from left to right in increasing order on the number line, then;
Since 12 is to the right of -2, the inequality which represents the situation is; 12 > -2.
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16 40/50 in decimal form
[tex]\huge\textsf{Hey there!}[/tex]
[tex]\mathsf{16 \dfrac{40}{50}}[/tex]
[tex]\mathsf{= \dfrac{16\times50 + 40}{50}}[/tex]
[tex]\mathsf{= \dfrac{800 + 40}{50}}[/tex]
[tex]\mathsf{= \dfrac{840}{50}}[/tex]
[tex]\mathsf{= 840\div50}[/tex]
[tex]\mathsf{= 16.8}[/tex]
[tex]\huge\textbf{Therefore, your answer should be:}[/tex]
[tex]\huge\boxed{\mathsf{16.8}}\huge\checkmark[/tex]
[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]
Identify a pattern in each list of numbers. Then use this pattern to find the next number.
5, 12, 33, 96, 285, ___
=====================================================
Explanation:
The given sequence is 5, 12, 33, 96, 285, ...
The jump from 5 to 12 is +7The jump from 12 to 33 is +21The jump from 33 to 96 is +63The jump from 96 to 285 is +189The sequence of increases is: 7, 21, 63, 189
Then notice,
The jump from 7 to 21 is "times 3"The jump from 21 to 63 is also "times 3"The jump from 63 to 189 is also "times 3".Assuming this pattern keeps up, the next increment will be 189*3 = 567
We add this increment to the last term of the original sequence
285+567 = 852
The sequence is now 5, 12, 33, 96, 285, 852, ...
Choose all degrees of rotation that will carry the regular pentagon onto itself.
A. 72°
B. 90°
C. 108°
D. 144°
E. 216°
Answer:
A. 72°
D. 144°
E. 216°
Step-by-step explanation:
I just answered this.
in short : we rotate each vertex on a circle arc. the center of that circle being P.
so, at the end of every 1/5 of the circle arc there is a vertex of the polygon.
therefore, with every 1/5 of a full circle rotation we move the pentagon visually onto itself.
that is starting at
360/5 = 72°
and then every additional 72°
144°
216°
288°
360°
so, A, D and E are correct
Pls help it’s due soon
f (a) = 3a + 2, When
f(a) = 11
Answer:
3
Step-by-step explanation:
Think of "f(a)" like "y" in this context. You can set that equal to 11 and solve for a:
f(a) = 3a + 2
11 = 3a + 2
9 = 3a
3 = a
Please explain this
Determine the domain and range of the graph
Ryan collects rainwater in a barrel for his garden. The barrel is filled with 18 gallons of water. Ryan used 9.7 gallons to water his garden in June and 3 and one eighth gallons in July. How much water is left in the barrel?
24.575 gallons
5.175 gallons
3.168 gallons
3.125 gallons
The quantity of water left in the barrel is 5.175 gallons. The correct option is the second option 5.175 gallons
Calculating quantityFrom the question, we are to determine how much water is left in the barrel
From the given information,
"The barrel is filled with 18 gallons of water"
and
"Ryan used 9.7 gallons to water his garden in June"
After this time,
The quantity of water that would be left in the barrel will be 18 gallons - 9.7 gallons
= 8.3 gallons
Then,
3 and one eighth gallons in July
3 and one eighth = 3 1/8 = 3.125 gallons
The quantity of water that would be left is 8.3 gallons - 3.125 gallons
= 5.175 gallons
Hence, the quantity of water left in the barrel is 5.175 gallons. The correct option is the second option 5.175 gallons
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Answer:
b
Step-by-step explanation:
What is the slope of the line represented by the equation y = -x +?
0-1/2
HELP
in the equation y= -x-1/2
the slope is -1/1 which can also be shown as -1.
asha saves coins in a jar. The table shows how the amount of money was in the jar at the end of every three-month period. A line of best fit for this
ata is B= 0.45m + 1.93.
Month, m
Balance, B
($)
3
6
9
3.24 4.63 5.97 7.26
12
Which value is the best estimate of the amount of money in the jar at the end of the first month?
A $0.45
OB. $1.08
OC. $1.93
OD. $2.3
If A line of best fit for the data is B= 0.45m + 1.93. The value that is the best estimate of the amount of money in the jar at the end of the first month is: D. $2.38.
Best estimate of the amount of moneyGiven:
B= 0.45m + 1.93.
Where:
m= 1 month (First month)
Hence:
B= 0.45(1) + 1.93
B= 0.45+ 1.93
B=$2.38
Therefore if A line of best fit for the data is B= 0.45m + 1.93. The value that is the best estimate of the amount of money in the jar at the end of the first month is: D. $2.38.
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Calculators were purchased at $100 per dozen and sold at $30 for three calculators. What is the profit on six dozen calculators?
The profit is $
Answer:
30x100= 3000
Step-by-step explanation:
Use units to help you answer the question. If necessary, round your answer to two decimal places.
An acre is equal to 43,560 square feet, and there are 5280 feet in a mile. If a farm has the shape of a rectangle measuring 0.9 miles by 1.5 miles, what is the area of the farm in acres?
The area of the farm in acres is 864 acres.
How to find the area of a farm?An acre is equal to 43,560 square feet, and there are 5280 feet in a mile.
Therefore,
1 mile = 5280 feet's
The farm has the shape of a rectangle measuring 0.9 miles by 1.5 miles. Therefore, let's convert to feet's
1 mile = 5280 feet's
0.9 miles = ?
cross multiply
length = 0.9 × 5280 = 4752 feet
1 mile = 5280 feet's
1.5 miles = ?
width = 1.5 × 5280 = 7920 feet's
Hence,
area of the farm = 4752 × 7920
area of the farm = 37635840
Therefore, the area of the farm in acres can be calculated as follows:
43560 ft = 1 acre
37635840 ft = ?
cross multiply
area of farm = 37635840 / 43560
area of the farm = 864 acres.
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If Thomas has 92 donuts and the box requires 3 donuts each box, once each donut is put in the boxes how many donuts would be left over?
Answer:
2
Step-by-step explanation:
Take 92 and divide by 3
3*30 = 90
92-90 = 2
There are 2 donuts left over
If anyone can help me to solve this!!
Answer:
[tex]\begin{array}{|l|l|c|c|c|}\cline{1-5} \textbf{Equation} & \textbf{Standard Form} & \textbf{a} & \textbf{b} & \textbf{c}\\\cline{1-5} \text{1.}\:\:x^2+x=20 & x^2+x-20=0 & 1 & 1 & -20\\\cline{1-5} \text{2.}\:\:4x^2-2x=28 \phantom{)))}& 4x^2-2x-28=0 \phantom{)))}& 4 & -2 & -28\\\cline{1-5} \text{3.}\:\:5x^2=225 & 5x^2-225=0 & 5 & 0 & -225\\\cline{1-5} \text{4.}\:\:x^2-x=36 & x^2-x-36=0 & 1 & -1 & -36\\\cline{1-5} \text{5.}\:\:3x^2-4=7x & 3x^2-7x-4=0 & 3 & -7 & -4 \\\cline{1-5}\end{array}[/tex]
Step-by-step explanation:
Standard form of a quadratic equation:
[tex]\boxed{ax^2+bx+c=0}[/tex]
Question 1
Given:
[tex]x^2+x=20[/tex]
Rearrange to standard form by subtracting 20 from both sides:
[tex]\implies x^2+x -20=20-20[/tex]
[tex]\implies x^2+x -20=0[/tex]
Therefore:
a = 1b = 1c = -20Question 2
Given:
[tex]4x^2-2x=28[/tex]
Rearrange to standard form by subtracting 28 from both sides:
[tex]\implies 4x^2-2x-28=28-28[/tex]
[tex]\implies 4x^2-2x-28=0[/tex]
Therefore:
a = 4b = -2c = -28Question 3
Given:
[tex]5x^2=225[/tex]
Rearrange to standard form by subtracting 225 from both sides:
[tex]\implies 5x^2-225=225-225[/tex]
[tex]\implies 5x^2-225=0[/tex]
Therefore:
a = 5b = 0c = -225Question 4
Given:
[tex]x^2-x=36[/tex]
Rearrange to standard form by subtracting 36 from both sides:
[tex]\implies x^2-x-36=36-36[/tex]
[tex]\implies x^2-x-36=0[/tex]
Therefore:
a = 1b = -1c = -36Question 5
Given:
[tex]3x^2-4=7x[/tex]
Rearrange to standard form by subtracting 7x from both sides:
[tex]\implies 3x^2-4-7x=7x-7x[/tex]
[tex]\implies 3x^2-4-7x=0[/tex]
[tex]\implies 3x^2-7x-4=0[/tex]
Therefore:
a = 3b = -7c = -4Real number root for V-49
Step-by-step explanation:
there is no real number solution for the square root of a negative number.
a sqare root multiplied by itself had to deliver exactly the number inside the square root.
so for sqrt(-49), what can be the answer ?
which number multiplied by itself gives -49 ?
it any negative number at that.
because
a × a = a²
and
-a × -a = a² but definitely not -a².
we get a negative number only, when we multiply a positive number with a negative number or vice versa.
the only solution is complex or imaginary (based on the imaginary number i):
i² = -1
i = sqrt(-1)
so, sqrt(-49) = sqrt(49 × -1) = 7×sqrt(-1) = 7i
but again, no real solution.
Evaluate
3(x+4)(x+1)
(x+2)(x-2)
for x = 4.
Answer:
1440
Step-by-step explanation:
3(4+4)(4+1)(4+2)(4-2)
3*8*5*6*2
1440
5 divisible my 3 and 9
Answer:
5 is not divisible by 3 and 9 .
Mustafa's soccer team is planning a school dance as a fundraiser. The DJ charges $200 and decorations cost $100.
The team decides to charge each student $5.00 to attend the dance. If n represents the number of students attending
the dance, which equation can be used to find the number of students needed to make $1,500 in profit?
Answer:
Step-by-step explanation:
Mustafa's soccer team is planning a school dance as a fundraiser. The DJ charges $200 and decorations cost $100.
The team decides to charge each student $5.00 to attend the dance. If n represents the number of students attending
the dance, which equation can be used to find the number of students needed to make $1,500 in profit?
Answer:
Step-by-step explanation:
This article is about the basic inequality {\displaystyle z\leq x+y}{\displaystyle z\leq x+y}. For other inequalities associated with triangles, see List of triangle inequalities.
Three examples of the triangle inequality for triangles with sides of lengths x, y, z. The top example shows a case where z is much less than the sum x + y of the other two sides, and the bottom example shows a case where the side z is only slightly less than x + y.
In mathematics, the triangle inequality states that for any triangle, the sum of the lengths of any two sides must be greater than or equal to the length of the remaining side.[1][2] This statement permits the inclusion of degenerate triangles, but some authors, especially those writing about elementary geometry, will exclude this possibility, thus leaving out the possibility of equality.[3] If x, y, and z are the lengths of the sides of the triangle, with no side being greater than z, then the triangle inequality states that
{\displaystyle z\leq x+y,}z\leq x+y,
with equality only in the degenerate case of a triangle with zero area. In Euclidean geometry and some other geometries, the triangle inequality is a theorem about distances, and it is written using vectors and vector lengths (norms):
{\displaystyle \|\mathbf {x} +\mathbf {y} \|\leq \|\mathbf {x} \|+\|\mathbf {y} \|,}\|\mathbf {x} +\mathbf {y} \|\leq \|\mathbf {x} \|+\|\mathbf {y} \|,
If the tangent line to y = f(x) at (6, 4) passes through the point (0, 3), find f(6) and f'(6).
f(6) =
f'(6) =
Answers:
f(6) = 4
f ' (6) = 1/6
===========================================================
Explanation:
f(6) = 4 since the point (6,4) is on the f(x) curve. This is where the tangent is touching.
The tangent line also goes through (0,3)
Let's find the slope of the line through those two points.
[tex](x_1,y_1) = (6,4) \text{ and } (x_2,y_2) = (0,3)\\\\m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}\\\\m = \frac{3 - 4}{0 - 6}\\\\m = \frac{-1}{-6}\\\\m = \frac{1}{6}\\\\[/tex]
The slope of the tangent line is 1/6. This is the value of f ' (6) because the derivative measures the tangent at the given x value. It's useful to determine the instantaneous rate of change.
