The length of the ramp is 161.62 inches when the barrel turns 47 times in being rolled up the ramp.
What is the Circumference of a circle?The Circumference of a circle is defined as the product of the diameter of the circle and pi.
C = πd
where 'd' is the diameter of the circle
The circumference of the circular base of the barrel is given by the formula C = πd, where C is the circumference and d is the diameter of the base.
In this case, d = 1.1 inches, so C = π1.1 inches = 3.46 inches.
Since the barrel turns 47 times, the distance it travels is 47 times the circumference of the base,
47 × 3.46 inches = 161.62 inches
Therefore, the length of the ramp is 161.62 inches.
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Find the general solution of the given differential equation. (x + 1) dy + (x + 2)y = 8xe^-x y(x) = __
Give the largest interval over which the general solution is defined. (Think about the implications of any singular points. Enter your answer using interval notation.) ___
Determine whether there are any transient terms in the general solution. (Enter the transient terms as a comma-separated list; if there are none, enter NONE.)
______
The general solution of the given differential equation is y(x) = C₁e^-x + 4xe^-x. The largest interval over which the general solution is defined is (-∞, ∞). There are no transient terms in the general solution.
The differential equation given can be rearranged into the form dy/dx + (x + 2)/(x + 1)y = 8xe^-x, which is a linear first order differential equation. Using the integrating factor method, an integrating factor of e^(x + 1) can be used to obtain the general solution y(x) = C₁e^-x + 4xe^-x.
The integration constant C₁ can be determined by supplying the appropriate initial conditions. As the equation is a linear first order differential equation, the general solution is valid over the entire domain of x, which is (-∞, ∞). As the equation does not involve any terms that provide a particular value for y at any point in the domain, there are no transient terms in the general solution.
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To the nearest pound, Tim has £8
To the nearest 50p, Sue has £4. 50
Work out the maximum possible total amount of money.
Give your answer in pounds (£).
The maximum possible total amount of money would be = 13.23 £
What is Linear Equation ?
Linear Equation can be defined as the equation in which the highest degree of the variable is one.
Given,
To the nearest pound, tim has £8
To the nearest 50p, sue has £4.50
so, to the nearest pound, tim has £8
=> 7.5 ≤ Tim has < 8.5
sue has £4.50
to the nearest 50 p
=> 4.25 ≤ Sue < 4.75
=> possible total amount of money
= 7. 5 + 4.25 ≤ Amount < 8.5 + 4.75
=> 11.75 ≤ Amount < 13.25
maximum possible total amount of money would be less than 13.25
and in term of paisa maximum < 4.75 = 4.74
and maximum less than < 8.5 = 8.49
Hence maximum possible total amount of money would be = 13.23 £
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Please help me really fast
Answer:
Step-by-step explanation:
(0,-7) is the correct one. How I got this answer is cheese.
Why is triangle always 180 degrees?
Triangle is always 180 degrees because the sum of all angles in a triangle is 180 degrees. This is known as the "Triangle Angle Sum Theorem." The theorem states that the sum of all angles in a triangle is equal to 180 degrees.
1. A triangle is a three-sided polygon with three angles.
2. The sum of the three angles in any triangle must be 180 degrees.
3. This is known as the Triangle Angle Sum Theorem.
4. The Triangle Angle Sum Theorem states that the sum of the angles in a triangle must equal 180 degrees.
5. It does not matter which angles the triangle has, the sum will always equal 180 degrees.
6. This theorem is based on the fact that the sum of the angles in any triangle is equal to two right angles or 180 degrees.
7. The Triangle Angle Sum Theorem can be proven by drawing a triangle, and then measuring and adding the three angles.
8. The sum of the three angles will always equal 180 degrees.
9. Therefore, triangle is always 180 degrees.
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The regular polygon below is to be rotated about its center. Which angle of rotation
would carry the figure onto itself?
Answer choices:
324°
150°
225°
300°
The shape of a decagon will remain the same when it is rotated through
its angle of rotational symmetry.
How to find the rotation?
The rotation about the center will carry a regular decagon back to itself is 36°.
Note the following
The angle of rotational symmetry of a decagon is the smallest angle that a decagon can be rotated by such that the image formed by the rotation coincide with the preimage;
A decagon has 10 sides, the interior angle of a regular decagon is given as follows;
Each interior angle = (n-2)*180/10 = 144⁰
A decagon has a reflective symmetry, therefore, the lines of symmetry joining opposite vertices are straight lines.
The number of diagonals in a decagon = 5
Rotating through the vertex and opposite vertex of the diagonals gives the number of image of the rotation that is similar to the preimage of a decagon as ten.
Therefore, a rotation of (360/10) = 36⁰, about the center will carry a regular decagon back to itself.
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45 POINTS -Find the perpendicular line. Don’t explain
By analytical geometry, the line y = - 2 · x - 1 represents a line perpendicular to the line shown in the picture. (Correct choice: C)
How to find the equation of a line perpendicular to another line
According to analytical geometry, lines are described by polynomials of the form:
y = m · x + b
Where:
m - Slopeb - Interceptx - Independent variable.y - Dependent variable.And the equation of the perpendicular line pass through a point of original line and is related to the slope of the line by following relationship:
m · m' = - 1
Where:
m - Slope of original line.m' - Slope of perpendicular line.First, determine the slope and intercept of the original line:
(x, y) = (0, 1)
1 = m · 0 + b
b = 1
(x, y) = (2, 0)
0 = m · 2 + b
2 · m + b = 0
m = - b / 2
m = - 1 / 2
Second, calculate the slope of the perpendicular line:
m' = 1 / (- 1 / 2)
m' = - 2
Third, we conclude by discarding options that the equation of the perpendicular line is y = - 2 · x - 1.
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Two ferries travel across a lake 50 miles wide. One ferry goes 5 miles per hour slower than the other. If the slower ferry leaves 1 hour before the faster and arrives at the opposite shore at the same time as the other ferry, what is the speed of the slower ferry
The first ferry's speed is 18.5 mph and the second ferry, which is slower, travels at 13.5 mph.
How to find the calculation?Let x represent the first ferry's speed.
The second, slower ferry's speed is then x-5 (since 5 miles per hour slower)
First ferry time equals distance/speed equals
50/x
Time spent on the second ferry:
50 / x - 5
The difference in times is 1 hour because the second ferry departs an hour earlier.
50 / x - 5 - 50/x = 1
50x - 50(x - 5) = x (x - 5 )
250 = x² - 5x
x² - 5x - 250 = 0
(x - 10 )(x + 5) = 0
x = 18.5 - 13.5
Speed can never be detrimental.
Therefore, the first ferry's speed is 18.5 mph.
and the second ferry, which is slower, travels at 13.5 mph.
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What is a 120 angle called?
An angle that measures 120 degrees is called an obtuse angle.
An obtuse angle is defined as an angle that measures greater than 90 degrees but less than 180 degrees. It is formed by the intersection of two lines that are not collinear, that is, they do not lie on the same line, and the angle is greater than a right angle but less than a straight angle.
An obtuse angle is represented by an arc with a curved arrow on one end, pointing in the direction of the other end.
It's important to keep in mind that the term obtuse angle is just a classification based on the measure of the angle, which is greater than 90 degrees but less than 180 degrees, and it's not a specific angle measure, it could be any angle that is in that range.
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Help!! Stuff about triangles
Answer:
3
Step-by-step explanation:
Since [tex]\angle A \cong \angle A[/tex] by the reflexive property and [tex]\angle ABC \cong \angle ADE[/tex] since they are both right angles, [tex]\triangle ABC \sim \triangle ADE[/tex] by AA.
It follows that:
[tex]\frac{x}{9}=\frac{5}{9+6} \implies x=3[/tex]
Olivia tries to cut a piece of metal 45 inches long the piece of metal ends up being 43. 5 inches long what is the approximate orecent error in this situation
When Olivia tries to cut a piece of metal 45 inches long, the piece of metal ends up being 43.5 inches long, then there is an approximate percent error of 3.33% in this situation.
Therefore the answer is 3.33%.
To calculate the approximate percent error in this situation, we can use the formula:
Percent Error = (|Experimental Value - Theoretical Value| / Theoretical Value) x 100
In this case, the experimental value is 43.5 inches and the theoretical value is 45 inches. Plugging these values into the formula, we get:
Percent Error = (|43.5 - 45| / 45) x 100
= (1.5 / 45) x 100
= 0.033 x 100
= 3.33%
So the approximate percent error in this situation is 3.33%.
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3. Find the values of a and b. 36° 113° O
The measure of angles a and b is 144° and 67° respectively.
What is quadrilateral?There are four sides, four vertices, and four angles in a closed quadrilateral. It has a polygonal shape. It is produced by joining four non-collinear points. The total internal angle of a quadrilateral is always 360 degrees.
The English word quadrilateral is derived from the Latin words quadra, which means four, and latus, which means sides. Each of a quadrilateral's four sides does not always have to be the same length.
Given a quadrilateral,
in which opposite sides are parallel,
so, When a transversal cuts between two parallel lines, the interior angles on the same side of the transversal are additional to 180°.
36° + a° = 180°
and 113° + b° = 180°
a° = 180° - 36° = 144°
and b° = 180° - 113°
b° = 67°
Hence the values of a° is 144° and b° is 67°.
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3) Breanna thought of a number, subtracted 4 from it, and then multiplied her answer by 3. She got
a final number of 24. What was her starting number?
The quotient of 25 and 5 increased by 3
Answer: 8
Step-by-step explanation: Based on the given conditions, formulate 25/5+3 Reduce the sum or difference: to 8 therefore the answer is 8
Answer:
down below
Step-by-step explanation:
The quotient means the total amount that comes from dividing two things. In this case, the problem is asking for 25 and 5 to be divided. 25 divided by 5 is 5. You can check this by multiplying 5 and 5 to get 25. So, you know it's right. Now, take 5 and add 3 to it. 5 + 3 = 8. So, the answer is 8.
Hope this helps! :)
Q 23
Regina writes the expression y + 9
Which expression is equivalent to the one Regina writes?
A) (9. 3 • 4) + y
B 9+ y (3 = 4)
© (y + 9)(3 = 4)
None of these
The expression written by Regina is y + 9, which means adding nine to some number y. None of the given expressions are equivalent to this expression.
The expression written by Regina is y + 9, which means adding nine to some number y. None of the given expressions are equivalent to this expression. In order for two expressions to be equivalent, they must have the same value when the same values are plugged into them. For example, if y is equal to 5, then y + 9 would be equal to
14, while (9. 3 • 4) + y
would be equal to
27, (9+ y (3 = 4))
would be equal to 17, and
(y + 9)(3 = 4)
would be equal to 21. As these values are not equal, the given expressions are not equivalent to the one written by Regina.
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Figure ABCD is a parallelogram if point C lies on the line y=-1 what is the x vale of point C
The value of x of point C is 4. The coordinate of C is (4,-1).
What is the coordinate of a point?
The coordinates represent the location of a point in the 2D coordinate plane with respect to the origin. A point's x-coordinate is its perpendicular distance from the y-axis as measured along the x-axis. A point's y-coordinate is the perpendicular distance from the x-axis measured along the y-axis.
The distance between points A and B is 4 units.
The opposite sides of a parallelogram are equal and parallel.
To make parallelogram, the point C lies on the left side of point D.
The distance between point C and D must be 4 unit.
The coordinates of C is (4,-1).
The x value of point C is 4.
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One of the legs of a right triangle measures 2 cm and its hypotenuse measures 5 cm.
Find the measure of the other leg. If necessary, round to the nearest tenth."
When the hypotenuse of a right triangle measures 5 cm and one of its legs measures 2 cm, [tex]\sqrt{21}[/tex] is the measurement of the other leg.
what is Pythagoras theorem ?Perpendicular, Base, and Hypotenuse are the names of this triangle's three sides. The Pythagorean Theorem demonstrates how to calculate the side lengths of a right triangle by adding the areas of three intersecting squares. As the foundation for more intricate trigonometry theories like the Pythagorean theorem's opposite, this theorem is a very helpful tool. Given a triangle ABC with sides measuring a, b, and c, and the equation a2 + b2 = c2, Make another triangle with sides of lengths a and b and a right angle.
given
by Pythagoras theorem
[tex]c^{2} = a^{2} + b^{2} \\5^{2} = 2^{2} + b^{2} \\5^{2} - 2^{2} = b^{2} \\25 - 4 = b^{2} \\21 = b^{2} \\b =\sqrt{21}[/tex]
When the hypotenuse of a right triangle measures 5 cm and one of its legs measures 2 cm, [tex]\sqrt{21}[/tex] is the measurement of the other leg.
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how do i solve this problem 5.50h=44
Answer:
h = 8
Step-by-step explanation:
5.50h=44
Divided both sides by 5.50
h = 8
Let's check
5.50(8) = 44
44 = 44
So, h = 8 is the correct answer!
The equations represent the heights, y, of the flowers, in inches, after x days. Which ordered pair (1,2.2)(1 ,2.5) or (0 ,1) is a solution to the system? Will the flowers ever be the same height? Explain. The 2 equations are y= 1.5x+1 and y= 1.2x+1
Since both of the flower will be y = 1 at x = 0, yes, the flowers will be the same height at x = 0. And (0,1) is the solution to the system of equation
How to Know Solution to a System of EquationTo know the solution of a system of equation, the two equation can be solved simultaneously.
Given the 2 equations y = 1.5x + 1 and y = 1.2x + 1
Equate the two equations to get x
1.5x + 1 = 1.2x + 1
collect the like terms
1.5x - 1.2x = 1 - 1
0.3x = 0
x = 0
Substitute x in any of the equation.
y = 1.5(0) + 1
y = 1
Yes! The flower will be of the same height at x = 0.
Therefore, (0,1) is the solution to the system of equation. And the flower will be of the same height at x = 0.
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Kourtney and Kayla are sisters who are taking the same classes this semester: MAT 003, CHM 131/3131A, and ACA 122. If kourtney earns a pee a P in MAT 003, a B in CHM 131A, and an A in ACA, then what will her GPA be?
A. 3. 5
B. 3. 2
C. 2. 58
D. 3. 8
the GPA for the current semester will be 3.5.
What is GPA?
A metric used to assess your performance throughout the course of your complete degree program is your grade point average.
The average grade point average (GPA) is a figure that represents your typical performance in classes over the course of a semester, term, or year. In line with how much you raise your overall grade point average over your time at the university, your typical GPA score will fluctuate (or, in some cases, how much you fall behind).
A pass grade is a P, an A is a grade of excellent performance worth 4 points per credit, and a B is a grade of good performance worth 3 points per credit. The grade averages do not take P grade into account.
MAT 003, CHM 131a, and ACA 122 each have three, one, and two credits. Thus, the final score is 3 + 1 + 1 = 5. P in MAT 003, B in CHM 131a, and A in ACA 122 are the grades she receives.
GPA can be calculated by
GPA = ( 3 × 1 + 4 × 1)/ 5
GPA = ( 3 + 4)/ 5
GPA = 3.5
Hence the GPA for the current semester will be 3.5.
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Stacy wants to buy a tree to decorate her apartment. Her living room has 8 foot high ceilings. The height of each tree she is interested in buying is given below. Which tree(s) can she buy so that they fit in her living room? Choose all that apply
A. 108 inches
B. 114 inches
C. 94 inches
D. 79 inches
or other you can type what you got
Answer:
C And D
Step-by-step explanation:
94 Inches Is 7.8 Feet Tall & 79 Inches is 6.5 Feet Tall
Answer:
C and D
Step-by-step explanation:
You should start by changing the inches to feet
(there are 12 inches in foot [ 12 inch = 1 foot ])
A. 9 foot
B. 9.5
C. about 7 feet
D. about 6 feet
C and D are correct. Hope this helps!
A line is parallel to y = 4x + 11 and
intersects the point (-2, 4). What is the
equation of this parallel line?
y = [?]x + [ ]
Hint: Use the Point-Slope Form: y - y₁ = m(x − x1)
Then write the equation in slope-intercept form.
Enter
Answer:
y=4x+12
Step-by-step explanation:
if a line is parallel to another they have the same slope ,,
y=mx+c
where m represents the slope
and c represents the intercepted part of y axis
so the slope equals 4 from y=4x+11
to find the intercepted part c ,, substitute by the given point in the equation y=mx+c
(-2,4),, and slope is 4
4= 4×-2+c
4= -8+c
c= 12
so the equation is
y=4x+12
Answer:
y =4x-18
Step-by-step explanation:
y +2 = 4(x - 4)
y +2 =4x-16
y = 4x-18
Pepito bought 2 t-shirt at 149.95 each and a pair of pants for php 30.75, if her money was a 200 pesos bill. How much was her change?
If pesos had it would be so pesos have 169.25 dollars left 200-30.75=169.25
how to get the Y intercept when you don't have a 0 X coordinate?
Answer: You plug in y as 0 into your equation.
Step-by-step explanation:
Do the above thing OK.
Consider rigid-body physics in a higher or lower dimension than three. How many coordinates are required to specify the location and orientation of a rigid body:If the space is two-dimensional?a. 2b. 3c. 4d. 5
In two-dimensional space, only two coordinates are required to specify the location and orientation of a rigid body.
In two-dimensional space, a rigid body can only move in two directions (up/down and left/right) and rotate around a single axis. As a result, only two coordinates are needed to specify the location and orientation of a rigid body in two-dimensional space. The two coordinates needed to specify the rigid body's position are the x-coordinate and y-coordinate, which define the position of the body in the plane. The orientation of the rigid body can be determined by determining the angle between the x-axis and the body's orientation, which is referred to as the angle of rotation. The combination of these two coordinates (position and rotation) specify the full state of the rigid body in two-dimensional space.
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Using a number line, find both the intersection and the union of the following
intervals:
[1, 5] and (0,8]
pls help !
Answer:
The union of the intervals is (0,8]
The intersection of the intervals is [1,5]
Hope this helped!
Write 4.2 as a mixed number and as an improper fraction.
Write your answers in simplest form.
0
improper fraction: 0
mixed number:
믐
8 0.8
X
As a mixed number, 4.2 can be written as 4 + 2/10.
As an improper fraction, 4.2 can be written as 21/5.
Define Fraction.Any number of equal parts is represented by a fraction, which also represents a portion of a whole. A fraction, such as one-half, eight-fifths, or three-quarters, indicates how many components of a particular size there are when stated in ordinary English.
What is a mixed fraction?A mixed fraction is one that is represented by both its quotient and remainder. A mixed fraction is, for instance, 2 1/3, where 2 is the quotient and 1 is the remainder. An amalgam of a whole number and a legal fraction is a mixed fraction.
Since 4 + 2/10=4.2 so as a mixed number, 4.2 can be written as 4 + 2/10.
Also, 21/5=4.2 so, as an improper fraction, 4.2 can be written as 21/5.
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Find the values of x and y in parallelogram PQRS.
PT =y. TR = 3x + 1, QT = 3y. TS = 5x + 11
x=
y=
PLEASE HELPPP!!!!
In the parallelogram PQRS, x = 2 and y=7
Parallelogram:
A parallelogram is a quadrilateral with two pairs of parallel sides. A parallelogram has opposite sides of equal length and opposite angles of equal length. Also, the interior angles on the same side of the horizontal line are supplementary angles. The sum of all interior angles is 360 degrees. A three-dimensional shape whose faces are parallelograms is called a parallelepiped. The area of a parallelogram depends on its base (one of its parallel sides) and its height (height drawn from top to bottom). The perimeter of a parallelogram depends on the length of its four sides.
Given that
PT=y, TR=3x+1, QT=3y, TS=5x+11
The diagonals of a parallelogram bisect each other
PT = TR and QT = TS
y = 3x+1 and 3y = 5x+11
Now,
We have a system of equations
Multiply the first equation by 3
3y = 9x+3 and 3y = 5x+11
Set them equal
9x + 3 = 5x + 11
⇒ 9x - 5x = 11 -3
⇒ 4x = 8
⇒ x =2
Now,
Putting the value of x =2 in equation :
y = 3x+1
=3(2)+1
=7
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Write two equations that can be solved using the double 7+7
Using doubles plus one fact the sum of 7 + 7 is equal to 15 it is done by simply adding 1 to the given number.
What is Doubles plus ?When we add two of the same number, we add using the “doubles fact”. For example, 1 + 1 and 2 + 2 are both doubles facts. Look at the example below: 4 + 4 = 8 is a doubles fact. Doubles fact can help us know other additional strategies like doubles plus one
A double is a number or an amount that is twice as large as the given number or amount. So, if we multiply a number by 2 or if we add a number to itself we say that the number is doubled
The sum of 7 + 7 can be determined by using doubles plus one fact as:
Simply add 1 in 7 + 7 to get the result required.
Therefore by using doubles plus one fact the sum of 7 + 7 is equal to 15.
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Michael's pumpkin farm sold 75 pumpkins on October 24 that day they made $600. What did Michael charge for each pumpkin?
Answer:
$8.
Step-by-step explanation:
right!!
How do you tell if something is a difference of squares?
A binomial is a difference of squares if both terms are perfect squares. Remember that we might first need to filter out a common element.
what is perfect square ?Perfect squares result from squaring an integer. One such example is the number 81, which is a perfect square since it can be derived by squaring 9: 99=81. 144 is a perfect square since it can be generated by squaring the number 12, which results in 12. 169 is a perfect square since it can be squared to produce the number 13. mathematics-specific language Informally: When an integer (a "whole") number, whether positive, negative, or zero, is multiplied by itself, the result is referred to as a square number, a perfect square, or simply "a square". Accordingly, all square numbers are 0, 1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144, and so on.
given
A binomial is a difference of squares if both terms are perfect squares. Remember that we might first need to filter out a common element.
If a binomial is found to be a difference of squares, it is factored into two binomials. the first being the first term's square root less the second term's square root.
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