An inclined plane of length 8 m is used to lift the load 2 m, using the same effort.
A ramp that helps lift and lower heavy things is called an inclined plane. It is a flat surface that is positioned against a horizontal surface at an angle other than a right angle.
Work is defined as the use of force to move an object over a distance. It is derived as the product of displacement (d) and force (F). Work is given by W = F×d = 25 N×d.
When a body is lifted, we can express work as W = m×g×h where g is gravity and h is height. And the force is written as F = m×g where m is the mass of an object. Then, W = F×h
Calculating the work done to lift the load to 2 m, we get,
W = 100 N×2 m = 200 Nm.
Substitute this value in W = F×h, we get,
200 Nm = 25 N×d
Divide both sides by 25 N, and we get,
[tex]\begin{aligned}\frac{\mathrm{200\;Nm}}{\mathrm{25\;N}}&=\frac{\mathrm{25\;N\times d}}{\mathrm{25\;N}}\\d&=\mathrm{8\;m}\end{aligned}[/tex]
The value is 8 m. Therefore, the first statement is correct.
The complete question is -
To lift a load of 100 N a distance of 1 m an effort of 25 N must be applied over an inclined plane of length 4 m. What must be done to lift the load 2 m, using the same effort?
A. Use an inclined plane of length 8 m.
B. Use an inclined plane of length 2 m.
C. Use an inclined plane of length 10 m
D. Use an inclined plane of length 16 m.
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What is the length of the radius of a circle given the equation x² y² 8?
The length of the radius of a circle with the equation x² + y² = 8 is 2√2 units .
In the question ,
it is given that ,
the equation of the circle is ⇒ x² + y² = 8 ,
we know that the general equation of the circle is given as x² + y² = b² ;
and "b" is the radius of circle ,
On comparing both the equations ,
we get ,
b² = 8
Simplifying the above equation further ,
we get ,
b = √8 = √2 × 2 × 2
the radius "b" is
b = 2√2 units .
Therefore , the length of the radius of the circle is 2√2 units .
The given question is incomplete , the complete question is
What is the length of the radius of a circle given the equation x² + y² = 8 ?
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Solve the equation for v.
0.5v + 0.04 < 1.14
v > 2.2
v < 2.2
v > 2.4
v < 2.4
Answer:
v < 2.2
Step-by-step explanation:
0.5v < 1.14 – 0.04
0.5v < 1.1
v < 1.1/0.5
v < 2.2
pls mark as brainliest
which racing organization saw its television ratings increase 28% over 2021 to a season average of 1.2 million viewers?
Answer:
Formula 1 Racing
Step-by-step explanation:
How do you calculate raw score in grades?
Raw score can be computed by using arithmetical operations such as addition, subtraction, multiplication, and division.
This can be done by hand or by using a calculator or a computer program. Additionally, statistical methods such as mean, median, mode, and standard deviation can be used to compute raw data. Raw data can also be influenced in many ways.
For example, data can be organized, filtered, and sorted into categories or hierarchies. Data can also be visualized in graphs, charts, and diagrams to make patterns and trends feasible to understand. Statistical methods such as correlation and regression can also be used to analyze and interpret raw data. Additionally, data can be combined with other data sets to create new insights and relationships. Finally, machine learning and predictive analytics can be used to make predictions about future outcomes based on existing data.
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There are about 2.54 centimeters in 1 inch. if a segment is 2.7 centimeters long, how many inches is it, rounded to the nearest hundredth?
Answer: 1.06 cm
Step-by-step explanation:
Take 2.7 divided by 2.54 = 1.062cm
Rounded the nearest hundredth, so it will be 1.06 cm
Write an equation for the line that passes through the given point and is
parallel to the graph of the given equation.
3x + 4y = 12; (−4, 7)
I forgot how to do this. :|
Answer:
3x + 4y = 16
Step-by-step explanation:
3x + 4y = 12
3(-4) + 4(7) = -12 + 28 = 16
Answer: 3x + 4y = 16
37(2x-14)+x=15-(-9x-5)
Answer:
Step-by-step explanation:
To find value of X ,first solve LHS
37*2x-37*14 =74x-518 +x
=75x-518
Now solve RHS
135x+75
Now equate LHS=RHS
75x-518=135x+75
75x-135x=75+518
-60x=593
x= -593/60
=-9.88
How many types of quadrilaterals can be possible class 9?
There are six types of possible quadrilaterals namely trapezium, parallelogram, rectangle, rhombus, square, and kite.
Explanation:
Different types of possible quadrilateral :
There are six types of possible quadrilateral.Possible quadrilaterals are trapezium , parallelogram, rectangle, rhombus, square, and kite.Trapezium is a quadrilateral with one pair of opposite sides.Parallelogram is a quadrilateral with both the pairs of opposite sides parallel to each other.Rectangle is a parallelogram with all the angles equal to 90°.Rhombus is a parallelogram with congruent pair of opposites sides.Square is a rhombus with each angle 90°.Kite is a quadrilateral with pair of congruent adjacent sides.Therefore, there are six types of possible quadrilateral : trapezium, parallelogram, rectangle, rhombus, square, and kite.
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make a scatterplot of weight versus desired weight. describe the relationship between these two variables.
The relationship between the variable is the direction, strength, and linearity .
Scatterplots can be used when one continuous variable is under the control of the experimenter and the other is dependent on it, or when both continuous variables are independent. When one parameter is systematically increased and/or decreased by the other, it is called the control parameter or independent variable and is usually plotted along the horizontal axis. Measured or dependent variables are usually plotted along the vertical axis. In the absence of a dependent variable, any type of variable can be plotted on any axis and the scatter plot he only shows the degree of correlation (not causality) between the two variables.
Scatterplots can suggest different types of correlations between variables with specific confidence intervals. If the dot pattern slopes downwards from the lower left to the upper right, this indicates a positive correlation between the investigated variables. If the dot pattern slopes from top left to bottom right, it indicates a negative correlation. You can draw a line of best fit (also called a "trend line") to explore the relationship between variables. The formula for correlation between variables can be determined by established best-fit methods. For linear correlation, the optimal procedure is called linear regression, which guarantees a correct solution in finite time. There is no one-size-fits-all procedure that guarantees the correct resolution in any relationship. Scatterplots are also very useful for seeing how two comparable data sets match up to show non-linear relationships between variables.
Desired Weight:
A standardized table of desirable (or ideal) weight for adult height is based on life expectancy. Both malnutrition and obesity are associated with an increased risk of early death. A desirable weight corresponds to a body mass index (ratio of weight in kg/height in m2) between 20 and 25. Ideal weight charts based on actuarial data were first published in 1942 by the Metropolitan Life Assurance Company of New York and were replaced in 1959 by charts of average and desirable weights.
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Solve the following system of equations. Show your work.
−2x+5y=−2
4x−10y=4
Solution:
Equations −2x+5y=−2 and 4x−10y=4 have no solution.
Define no solution.An inconsistent system is a set of equations that cannot be solved. Although a system of linear equations typically has a single solution, it occasionally may have infinite or no solutions (parallel lines) (same line). The solution set refers to all possible answers to an equation or inequality. The no solution symbol,, is used to indicate that there is no solution to an equation or inequality. None Found: There are no solutions when the lines that make up a system are parallel because the two lines have no points in common.
Given,
Equations,
−2x+5y=−2 .. Equation 1
4x−10y=4 .. Equation 2
Multiplying equation 1 by 2
-4x + 10y = -4
4x - 10 y = 4
-----------------
0
Equations −2x+5y=−2 and 4x−10y=4 have no solution.
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SOLVING WORD PROBLEMS INVOLVING QUADRATIC INEQUALITIES:
As an architect, your job is to fulfill the requirements of the client. You are demanded by your client to have a plan or sketch in planting a garden and surrounding it with decorative stones. The desired length of the lot is 15 meters longer than its width. The area of the rectangular plot should not be more than 126 m^2.
Solution:
-15/2+√31.(3/2)i is the width of the garden.
What is Area of Rectangle?The area of Rectangle is length times of width.
Given,
As an architect, your job is to fulfill the requirements of the client.
You are demanded by your client to have a plan or sketch in planting a garden and surrounding it with decorative stones.
Let width be x
The desired length of the lot is 15 meters longer than its width.
Length =x+15
The area of the rectangular plot should not be more than 126 m²
Area=Length×width
126=x(x+15)
126=x²+15x
x²+15x-126=0
Apply it in Quadratic formula.
x=-b±√b²-4ac/2a
a=1, b=15 and c=-126.
x=-15±√15²-4(1)(-126)/2(1)
x=-15/2+√31.(3/2)i.
Hence, the width of the garden is -15/2+√31.(3/2)i.
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There is a spider in an infinite two-dimensional grid. You have absolutely no idea where she is. The only thing you know is that in each second she moves in the same direction. Unfortunately, you do not know the direction: it can be left, right, up or down. In each second, you can put your finger on one point in the grid. Devise a strategy to catch the spider after finitely many steps
The strategy to catch the spider is elaborated out here.
The best strategy for catching the spider after infinitely many steps is to start at one point in the grid and then move in a clockwise spiral, expanding your search area every time you move. As you move, you can use a combination of visual and physical cues, such as vibrations and sound, to detect the spider's presence. This method will ensure that the spider will eventually be caught in a finite amount of time. Additionally, if the spider changes directions, your search will be able to adjust to that change, as you will be able to detect it in the spiral pattern.
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what’s the biggest number 7.06 or 7.9
Answer:
7.9
Step-by-step explanation:
7.06<7.9
Find the roots and the vertex of the quadratic on a calculator. Round all values to 3 decimal places (if necessary).
y = 3xsquared - 18x - 263
Please answer quickly I’ll mark you brainlist
The vertex of the equation is (3, -290). Then the solutions of the equation will be 99.67 and -93.67.
What is the equation of the parabola?Let the point (h, k) be the vertex of the parabola and a be the leading coefficient.
Then the equation of the parabola will be given as,
y = a(x - h)² + k
The equation is given below.
y = 3x² - 18x - 263
Convert the equation into vertex form, then we have
y = 3x² - 18x - 263
y = (√3x)² - 2 · √3x · 3√3 + 27 - 27 - 263
y = 3(x - 3)² - 290
Then the solution of the equation will be given as,
3(x - 3)² - 290 = 0
3(x - 3)² = 290
x - 3 = ± 96.67
x = 3 ± 96.67
x = 3 + 96.67, 3 - 96.67
x = 99.67, -93.67
The vertex of the equation is (3, -290). Then the solutions of the equation will be 99.67 and -93.67.
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Help please im not the smartest kid
Answer:
No, it's doesn't mean you are not smart. Just maybe you need to focus on learning most of the things to solve in math, you need to start with what is given to you.
Here given to you that every scale of 2 in = 8ft in actual truck.
So in order to know what 6in equals. Break down 6 into something you can use which is 2in = 8ft
6 = 2 + 2 + 2
So 6in = 8ft + 8ft + 8ft
Which can be simplified to 6ft = 24 ft.
Answer:
24
Step-by-step explanation:
8 divided by 2 is 4 and 4 times 6 equals 24. Or you could do 6 divided by 2 equals 3 and 8 times 3 equals 24.
how many different three-letter words (including nonsense words) are there in which successive letters are different?
16250 many different three-letter words—including nonsense words—have different letters in the next position.
Given that,
We have to find how many different three-letter words—including nonsense words—have different letters in the next position.
We know that,
The number of alphabets are 26
First letter has 26 choices.
Second letter can not be same has first letter so 25 choices.
Third letter can not be same has second letter so 25 choices.
So,
Total words = 26×25×25=16250
Therefore, 16250 many different three-letter words—including nonsense words—have different letters in the next position.
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A certain fossil of a beetle contains 15% as much carbon as a living beetle. The age of the fossil can be found using carbon dating.
Calculate the age of this fossil given that the half life of carbon-14 is 5715 years.
Answer:
Hope this helps you!
Step-by-step explanation:
The age of this fossil can be calculated using the following formula:
Age = (5715 years) * ln(1/0.15) / ln(2)
Age = 81,922 years
please help before i cry
Answer:
Don't overthink it.
[tex]V=\frac{1}{3} Ah[/tex] is the same as [tex]V=\frac{Ah}{3}[/tex]
Multiply both sides by 3
3V = A * h
Then get A by itself by dividing both sides by h.
[tex]A = \frac{3V}{h}[/tex]
Answer:
I think it's A= lw
Step-by-step explanation:
The question says to rearrange the formula to highlight the base area, and the formula to finding the base area of a pyramid is A = l w (length multiplied by width)
If the simple interest on $6,000 for 9 years is $4,320, then what is the interest rate?
Answer:
6.48%
Step-by-step explanation:
a six-sided die (with numbers 1 through 6) and an eight-sided die (with numbers 1 through 8) are rolled. what is the probability that exactly one 6 is rolled? express your answer as a common fraction.
When a six-sided die and an eight-sided are rolled then the probability that exactly one 6 is rolled is 1/4.
Given, a six-sided die (with numbers 1 through 6) and an eight-sided die (with numbers 1 through 8) are rolled.
we have to find the probability that exactly one 6 is rolled.
First we have to check the total number of outcomes on rolling both the dices.
Now, the total number of outcomes be, 48
As, we the favorable outcomes be, the outcome with exactly one 6 on the dices.
Favorable Outcomes = { (1,6) , (2,6) , (3,6) , (4,6) , (5,6) , (6,1) , (6,2) , (6,3) , (6,4) , (6,5) , (6,7) , (6,8)}
The total number of favorable outcomes be, 12
So, the probability that exactly one 6 is rolled is
P(E) = Number of favorable outcomes / Total number of outcomes
P(E) = 12/48
P(E) = 1/4
Hence, the probability that exactly one 6 is rolled is 1/4.
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How do you calculate the slope ratio of a ramp?
In order to calculate the slope ratio of a ramp, divide the difference between the elevations of two points by the distance between them, then multiply the quotient by 100, the resultant figure is the slope ratio.
What is the slope of a line?
The slope or gradient of a line in mathematics is a number that defines both the direction and the steepness of the line. The tangent relation or the height-to-distance ratio helps to determine the slope of the line.
The difference between the elevations is also called as the rise. And the distance between the points is known as the run.
Thus, we can also say that,
Slope ratio= rise / run x 100.
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help please
Rewrite 16x4y3 − 32x3y4 using a common factor.
2x4y4(8 − 16x)
2x3y3(8y − 16x)
8x4y3(2 − 4y)
8x3y3(2x − 4y)
Answer:
Step-by-step explanation:
o find the vertex of f(x)=x2−8x+7 , there are several things you can do. You could complete the square to get the equation into vertex ...
A nack bar ell 2 ize of nack pack. A large nack pack i $5 and a mall pack i $3. In one day the nack bar old 60 nack pack for a total of 220. How many mall mack pack did the nack bar ell
The supplied statement states that there are 20 large snacks and 40 little snacks.
In arithmetic, what are mixtures?When two separate answers to a problem are combined, a new, complete solution is produced. Setting up a table will facilitate resolving these issues.
What are combinations and mixtures?Alignment allows us to determine the ratio in which the ingredients/items have been combined and at what price they are offered to generate profit or face loss. A mixture, as the name implies, is combining two or more things together.
Briefing:
Total number of snacks = 60
Total earnings = $220
If only tiny snacks are sold, the total cost would be $180 (60 x 3).
Earnings difference = 220 - 180 = $40
$5 - $3 = $2 is the difference in the cost of the snack.
Number of Large snacks = $40 ÷ 2 = 20
Small snack count is 60 - 20 = 40.
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how many ways are there to make an r-arrangement of pennies, nickels, dimes, and quarters with at least one penny and an odd number of quarters? (coins of the same denomination are identical).
There are 26¹⁰ - 4 × (25)¹⁰ + 2 × (24)¹⁰ + 22¹⁰ exponential generating Function to make an arrangement of Pennies, nickels, dimes and quarters with at least one penny and an odd number of quarters.
Exponential generating Function:
An exponential generator provides a way to encode a sequence as the coefficients of a power series. This encoding helps in many ways.
Therefore, According to the Question:
The exponential generating function is,
G(x) = (x¹/1! + x²/2! + ...)(x¹/1! + x³/3! + x⁵/5! +...)(x°/0! + x¹/1! + x²/2! + ...)²
where the first factor describes the pennies, the second describes the quarters, and the last describes nickels and dimes.
We want the coefficient of Xˣ /r!.
Using exponential identities we get,
G(x) = [tex]e^{x} - 1 (\frac{e^{x} - e^{-x} }{2} ) (e^{x} )^2[/tex]
= [tex]\frac{1}{2} (e^{4x} -e^{2x} -e^{3x} + e^{x}[/tex]
and the coefficient is
[tex]\frac{1}{2} (4^r -2^r -3^r +1)[/tex]
The generating function is
G(x) = (x¹/1! + x²/2! + ...)⁴(x°/0! + x¹/1! + x²/2!+...)²² = ()⁴,
and we again want the coefficient of X¹⁰/10!.
Multiplying we get,
G(x) = [tex](e^{4x} - 4e^{3x} + 2e^{2x} + 1)e^{22x}[/tex]
= [tex]e^{26x} - 4e^{25x} + 2e^{24x} +e^{22x}[/tex]
so the coefficient of X¹⁰/10! is
26¹⁰ - 4 × (25)¹⁰ + 2 × (24)¹⁰ + 22¹⁰
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a drawer contains ten socks with one pair of each of the following colors: brown, black, blue, green, and white. how many socks must be removed from the drawer to guarantee that at least two socks of the same color have been removed?
6 socks must be removed from the drawer to guarantee that at least two socks of same color have been removed.
Given,
It makes no difference how many socks there are; what matters is how many different colours of socks there are, as there are five different colours.
So, if 6 socks are taken from the drawer, it is almost certain that at least two of them will be the same colour.
Because, after taking 5 socks, you will either have a match or a difference. To ensure a matching pair, add one more sock.
You have a pair if the first five are the same colour. If none of the first five socks match, the sixth sock will match one of the first five.
So with 6 socks, you are guaranteed that at least 2 of them will be the same color.
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What is the greatest common factor of 45, 50, 84?
Answer:
1
Step-by-step explanation:
there's no common factor between them
Priya can type 575 words in 25 minutes. She starts typing a report at 1035 hours and finishes at 1128 hours. Assuming she types non-stop at her usual rate and does not make any mistakes, find the number of words in the report.
Answer:
128,340 words
Step-by-step explanation:
find how many hours he typed by subtracting 1035 from 1128. 1128-1035=93hoursthen turn the hours into minutes. 93*60=5,580minutesnext find out how many sets of 575 words she typed by dividing 5,580 by 25. 5,580/25=223.2then finally multiply 223.2 by 575 to get your answer of 128,340. 223.2*575=128,340wordsMultiply −12y(9y − 7). I need this ASAP!
Answer: -108y^2 + 84y
Step-by-step explanation:
y^2 is y squared
give me brainiest! :D
The required simplified solution of the given expression is -108y² + 84y.
What is simplification?The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.
here,
Given expression,
= −12y(9y − 7).
Simplify,
Applying distributive property,
= -12y×9y - 12y(-7)
= -108y² + 84y
Thus, the required simplified solution of the given expression is -108y² + 84y.
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X=
2 Michael bakes a soft pretzel and a loaf of bread. Use the system of equations to
find c, the amount of flour, in cups, needed for the soft pretzel, and b, the amount
of flour, in cups, needed for the loaf of bread. Show your work.
b = 24c
5
16+ 4c = 2/
SOLUTION
The value of b is 3.
The value of c is 1/8.
What is an equation?An equation is a mathematical statement that is made up of two expressions connected by an equal sign.
Example:
2x + 5 = 9 is an equation.
We have,
Two equations given are:
b = 24c ____(1)
(1/4)b + 4c = 5/4 _____(2)
Putting (1) in (2) we get,
(1/4)24c + 4c = 5/4
6c + 4c = 5/4
10c = 5/4
c = 5/40
c = 1/8
Putting c = 1/8 in (1) we get,
b = 24/8
b = 3
Thus,
b = 3.
c = 1/8.
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Barb was going to buy a shirt which was originally priced for $20. There was a price tag on the shirt that said $12. What percentage was the shirt marked down?
A. 40%
B. 60%
C. 1.33%
D. 1.67%
Answer:
60%
Step-by-step explanation:
The problem is basically saying:
12 is what percent of 20, which we can make this into a solvable equation:
12 is what percent of 20
12 = ?% x 20
Now to solve by dividing 12 by 20
12/20 = 0.6
Multiply 0.6 by 100 to get 60%