A cart is pushed up a ramp with a force of 250 N. The ramp sits at a 28° angle with the horizontal.A, Determine the components of the vector representing the force.B. Describe what would happen if the angle of the ramp was decreased?
Answers
We have a cart that is pushed up a ramp, and we have that the force is 250 N. We also know that the ramp sits at 28 degrees with the horizontal. Then we can draw the situation as follows:
Therefore, we can find the components of the force by finding the measures of x and y using trigonometric ratios (sine and cosine) as follows:
Component x of the forceWe can find this component as follows:
\(\begin{gathered} cos(28^{\circ})=\frac{x}{250N} \\ \\ cos(28^{\circ})250N=x \\ \\ x=cos(28^{\circ})250N=220.736898215N \\ \\ x=220.736898215N \end{gathered}\)Component y of the forceIn this case, instead of using cosine, we have to use the sine function to find the y component of the force:
\(\begin{gathered} sin(28^{\circ})=\frac{y}{250N} \\ \\ 250Nsin(28^{\circ})=y \\ \\ y=250Nsin(28^{\circ})=117.367890696N \\ \\ y=117.367890696N \\ \end{gathered}\)Therefore, the components of the vector representing the force are as follows:
\(\langle220.736898215,117.367890696\rangle\)If we round the results to the nearest hundredth, we can rewrite the components as follows:
\(\langle220.74,117.37\rangle\)What would happen if the angle of the ramp was decreased?
We can use a smaller angle to see what would happen in this case. We can determine what would happen if the angle of the ramp were 15 degrees with the horizontal. We have a similar representation as before:
We can see that the component y would decrease, and the x component will increase - we need to remember that the sum of both components needs to be equal to 250N, and we can check this as follows:
\(\begin{gathered} x=cos(15^{\circ})250N=241.481456572N \\ \\ y=sin(15^{\circ})250N=64.7047612756N \end{gathered}\)Therefore, in summary, we have:
Part A: The components of the vector representing the force are:
\(\begin{gathered} \langle220.736898215,117.367890696\rangle \\ \\ \text{ If we round this result to the nearest hundredth, we have:} \\ \\ \langle220.74,117.37\rangle \\ \end{gathered}\)Part B: We have checked that if the angle of the ramp was decreased, then the component x of the vector would increase (in measure), and the component y of the vector would decrease (in measure) - we need to remember that the sum of both components needs to be equal to 250N.
Related Questions
3. The value of x varies directly with y,
and when x = 21, y=3.
Find the value of x if y= 10.
Answers
Answer:
70
Step-by-step explanation:
First you want to find the amount of x per 1 y so you divide 21 by 3 to get when x = 7 y = 1. Now you can just multiply 10 by 7 to get 70.
I hope this helps!
Select the correct answer. Simplify the following algebraic expression. √45x^5 A. 9x²√5x OB. 91³√5x² О с. 3x²√5x OD. 3r³√5x²
please help me and can you explain how you got your answer
Answers
The simplified form of the given algebraic expression is 3x²√5x. The correct option is с. 3x²√5x
Simplifying an algebraic expressionFrom the question, we are to simplify the given algebraic expression.
The given expression is
√45x^5
First, we will write the given expression properly
The expression written properly is
√45x⁵
Simplifying
√45 × √x⁵
√9×5 × √x⁴×x
√9 × √5 × √x⁴ × √x
3 × √5 × x² × √x
3 × x² × √5 × √x
3x² × √5×x
3x² × √5x
3x²√5x
Hence, the simplified expression is 3x²√5x
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-8/9 / -2/3 x -4 1/2
Answers
Answer:
- 14/3
Step-by-step explanation:
-8/9 * 3/-2 * -7/2
-24/-18 * -7/2
4/3*-7/2
-28/6
= - 14/3
The hypotenuse of a right triangle is three times the length of one of its legs. The length of the other leg is four feet. Find the lengths of the three sides of the triangle. For non-integer answer(s), round your answer(s) to the nearest tenth.
Answers
Hello!
It is given information that this triangle is a right triangle, meaning that the Pythagorean Theorem can apply here.
\(a^2+b^2=c^2\)
We can set the length of a leg as an unknown variable \(x\).
\(x^2+4^2=(3x)^2\)
Remember that it is the whole \(3x\) term being squared, meaning that it'll simplify to \(9x^2\), not \(3x^2\).
\(x^2+16=9x^2\)
\(8x^2=16\)
\(x^2=2\)
\(x=\sqrt{2}\)
This means we can plug back in to find the sides.
The hypotenuse would be \(3\sqrt{2}\), or 4.2.
And the legs would be 1.4 and 4, respectively.
Hope this helps!
Pls answer this fast
Answers
Answer: C
Step-by-step explanation:
1. divide 3 by 2 to find out how many pounds of blueberries she picked each day. 3/2 is 1.5
2. multiply 1.5 by 16 to convert to ounces. 1.5x16 is 24.
3. she picked 24 ounces of blueberries each day.
6. Which two expressions are
are equivalent?
A. 5x -5 and 51x-5)
B. 5(x-5) and 5x – 25
C. 5x - 1 and 5x -5)
D. 5xix - 1) and 5x -5
HELPPPLP
Answers
Answer:
B
Step-by-step explanation:
5•x=5x
5• (-5)=-25
5x-25 and 5(x-5) are equivalent
Answer:
awnsrer is b 5(x-5) and 5x - 25
ALGEBRA please put a very small explanation to the awnser
Answers
Certainly! The problem can be solved using the Pythagorean theorem,
which states that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.
In this case, the ladder acts as the hypotenuse, and we need to find the length of the vertical side (height) it reaches up the wall.
The ladder forms the hypotenuse, and its length is given as 12 meters. The distance from the foot of the ladder to the base of the wall represents one side of the triangle, which is 4.5 meters.
By substituting the given values into the Pythagorean theorem equation: (12m)^2 = h^2 + (4.5m)^2, we can solve for the unknown height 'h'.
Squaring 12m gives us 144m^2, and squaring 4.5m yields 20.25m^2. By subtracting 20.25m^2 from both sides of the equation, we isolate 'h^2'.
We then take the square root of both sides to find 'h'. The square root of 123.75m^2 is approximately 11.12m.
Therefore, the ladder reaches a height of approximately 11.12 meters up the wall.
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Find the value of x, 6,4, 3x, 4x+1
Answers
Answer:
If two chords intersect in a circle, then the product of the segments of one chord equals the product of the segments of the other chord.
6(3x) = 4(4x + 1)
18x = 16x + 4
2x = 4
x = 2
The ratio of the number of student in mr. Moore’s class compared to the number of student in miss Henry’s class is 5:4. The ratio of the number students in miss Henry’s class compared to the number of students on mr. Wilson’s class is 8:9. What is the ratio of number of students in mr. Moore’s class to mr. Wilson’s class?
Answers
Answer:
10:9
Step-by-step explanation:
First ratio is 5:4. 4 is equal to Henry class
If you múltiply the ratio by 2 you get
10:8, This ratio can be compared because now Henry class has 8
2(5:4)
10:8
8:9
Meaning that the answer is 10:9
The require ratio of number of students in Mr. Moore's class to Mr. Wilson's class is 10:9
What is Ratio?The ratio can be expression as how many times one number contain another number.
For example, If any bag contain 4 apples and 8 oranges then the ratio of apple to orange is 4:8 while the ratio of the orange to the apple is 8:2
How to find ratio?Consider M denote the number student present in the Mr. Moore's class
similarly H denote the number of student in miss Henry's class and W denote the number of student present in Mr. Wilson's class
then we have given that
M : H = 5 : 4 or
\(\frac{M}{H} = \frac{5}{4}\)
Also we have H : W = 8 : 9
\(\frac{H}{W} = \frac{8}{9}\)
Now multiply these two equations we have
\(\frac{M}{H}\times \frac{H}{W}=\frac{5}{4}\times\frac{8}{9}\)
\(\frac{M}{W}= \frac{10}{9}\)
The ratio of number of student in Mr. Moore's class to Mr. Wilson's class is 10:9
This is the conclusion to the answer.
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Neil needs to mail a USB drive to a friend. He uses 43-cent stamps and 8-cent stamps to pay $2.01 in postage. How many of each stamp did Neil use?
Answers
The cost of the each stamp is a 4$ and the 9$.
According to the statement
We have to find that the cost of the each stamp.
So, For this purpose, we know that the
The cost function can be used to find the average cost, which is the average amount of money it costs to produce a unit.
From the given information:
Neil needs to mail a USB drive to a friend. He uses 43-cent stamps and 8-cent stamps to pay $2.01 in postage.
Then
48x + 7y = 255
let the value of the two unknowns.
Then
If x = 1, then y = 29.57, which is not a whole number.
If x = 2, then y = 122.71, which is not a whole number.
If x = 3, then y = 15.86, which is not a whole number.
If x = 4, then y = 9, which a a whole number. This is a solution
And we know that the answer will be in a whole number.
So, The cost of the each stamp is a 4$ and the 9$.
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At the beginning of 2002, an ice cream shop claimed to have "nearly 1,020 different ice cream flavors." Assuming that you could choose from 1,020 different flavors, that you could have your ice cream in a cone, a cup, or a sundae, and that you could choose from a dozen different toppings, how many different desserts could you have?
Answers
Answer:
36720 different desserts
Step-by-step explanation:
(1020x3)x12=36720
NEED HELP WITH THIS MATH QUESTION QUICK!
Answers
Answer:
\(\textsf{The quotient is $\boxed{10}\;x+\boxed{16}$}\)
\(\textsf{The remainder is $\boxed{28}\:x^2+\boxed{10}\:x+\boxed{22}$}\)
Step-by-step explanation:
Definitions
Dividend: The polynomial which has to be divided.
Divisor: The expression by which the dividend is divided.
Quotient: The result of the division.
Remainder: The part left over.
Long Division Method of dividing polynomials
Divide the first term of the dividend by the first term of the divisor and put that in the answer.Multiply the divisor by that answer, put that below the dividend and subtract to create a new polynomial.Repeat until no more division is possible.Write the solution as the quotient plus the remainder divided by the divisor.Given:
\(\textsf{Dividend}: \quad 10x^4-14x^3-10x^2+6x-10\)
\(\textsf{Divisor}: \quad x^3-3x^2+x-2\)
Therefore:
\(\large \begin{array}{r}10x+16\phantom{)}\\x^3-3x^2+x-2{\overline{\smash{\big)}\,10x^4-14x^3-10x^2+6x-10\phantom{)}}}\\{-~\phantom{(}\underline{(10x^4-30x^3+10x^2-20x)\phantom{-b)}}\\16x^3-20x^2+26x-10\phantom{)}\\-~\phantom{()}\underline{(16x^3-48x^2+16x-32)\phantom{}}\\28x^2+10x+22\phantom{)}\\\end{array}\)
Solution:
\(10x+16+\dfrac{28x^2+10x+22}{x^3-3x^2+x-2}\)
\(\textsf{The quotient is $\boxed{10}\;x+\boxed{16}$}\)
\(\textsf{The remainder is $\boxed{28}\:x^2+\boxed{10}\:x+\boxed{22}$}\)
Some pens are shared among three students anne,lucy, and John.Anne gets 5 times many pens as lucy, and lucy gets 2 pens less than john. Suppose John gets x pens, how many pens does anne get in terms of x
Answers
Using a system of equations, it is found that Anne gets 5x - 10 pens.
What is a system of equations?A system of equations is when two or more variables are related, and equations are built to find the values of each variable.
In this problem, we consider that John gets x pens.
Lucy gets 2 pens less than john, hence:
L = x - 2.
Anne gets 5 times many pens as lucy, hence:
A = 5L = 5(x - 2) = 5x - 10.
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for every 2 cars you wash your friend washes 3. you wash a total of 8 cars. how many does your friend wash?
Answers
Answer:
12
Step-by-step explanation:
A box of crackers contains 16 1/2 ounces. A serving of crackers is 1 1/2 ounces. How many servings are in the box of crackers?
Answers
Answer:
11 servings
Step-by-step explanation:
16.5/1.5=11
For the function f(x)=x+4−−−−−√
, the average rate of change to the nearest hundredth over the interval 2 ≤ x ≤ 6 is
Answers
The average rate of change of the function f(x) = √(x+4) over the interval 2 ≤ x ≤ 6 is approximately 0.29 to the nearest hundredth.
To find the average rate of change of the function f(x) = √(x+4) over the interval 2 ≤ x ≤ 6, we need to calculate the change in the function divided by the change in the input variable over that interval.
The change in the function between x = 2 and x = 6 is:
f(6) - f(2) = √(6+4) - √(2+4) = √10 - √6
The change in the input variable between x = 2 and x = 6 is:
6 - 2 = 4
So, the average rate of change of the function over the interval 2 ≤ x ≤ 6 is:
(√10 - √6) / 4
To approximate the answer to the nearest hundredth, we can use a calculator or perform long division to get:
(√10 - √6) / 4 ≈ 0.29
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Sheila bought a box of 25 headbands. When she arranged the headbands by color, she saw that 4 were green, 4 were red, 13 were blue, and 4 were pink. What is the percent of blue headbands she bought?
Answers
If you choose 5 persons at random from 8 MALES AND 9 FEMALES. What is the probability that 3 are male and 2 are female?
Answers
We can conclude after answering the provided question that So the probability that 3 are male and 2 are female 0.325 or 32.5%.
What is probability?Probability is a measure of how likely an event is to occur. It is represented by a number among both 0 and 1, with 0 representing an unlikely event and 1 representing an unavoidable event. Switching a fair penny and coin flips has a likelihood of 0.5 or 50% because there are two equally likely outcomes. (Heads or tails). Probability theory is a branch of mathematics that studies happenings rather than there own properties. It is applied in many fields, including statistics, financial management, science, and engineering.
\(C(17,5) = 17! / (5! * (17-5)!) = 6188.\\C(8,3) = 8! / (3! * (8-3)!) = 56\)
The number of ways to choose 2 females out of 9 is given by the combination formula:
\(C(9,2) = 9! / (2! * (9-2)!) = 36\)
The total number of ways to choose 3 males and 2 females is the product of these two combinations:e
C(8,3) * C(9,2) = 56 * 36 = 2016
Therefore, the probability that 3 are male and 2 are female is:
P(3M,2F) = 2016 / 6188 ≈ 0.325
So the probability that 3 are male and 2 are female is 0.325 or 32.5%.
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Answer the filling questions in your own words.
1. Which figure above is a line segment?
2. Which figure above is a ray?
3. Explain, in detail, the differences between a line, a line segment, and a ray.
Answers
A line has no endpoints (line FG), a line segment has two endpoints (line segment AB), and a ray has one endpoint (ray CD).
What is a Line Segment?A line segment can be described as a line having two definite endpoints.
What is a Ray?A ray is a part of a line that has just one fixed endpoint and extends in the opposite direction of the endpoint to infinity.
What is a Line?A line has no endpoint. It extends in opposite directions to infinity.
1. The figure that is a line segment is the green figure. (line segment AB).
2. The blue figure is a ray (ray CD)
3. The red figure is a line (line FG).
In summary, a line has no endpoints (line FG), a line segment has two endpoints (line segment AB), and a ray has one endpoint (ray CD).
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Select the correct answer.
Each statement describes a transformation of the graph of f(x) = x. Which statement correctly describes the graph of g(x) if g(x) = f(x - 11)?
A. It is the graph of f(x) where the slope is increased by 11.
It is the graph of f(x) translated 11 units to the left.
It is the graph of f(x) translated 11 units up.
It is the graph of f(x) translated 11 units to the right.
B.
C.
OD.
Answers
The correct answer is C. It is the graph of f(x) translated 11 units to the left.
The correct answer is:
C. It is the graph of f(x) translated 11 units to the left.
When we have a function of the form g(x) = f(x - a), it represents a horizontal translation of the graph of f(x) by 'a' units to the right if 'a' is positive and to the left if 'a' is negative.
In this case, g(x) = f(x - 11), which means that the graph of f(x) is being translated 11 units to the right. However, the answer options do not include this specific transformation. The closest option is option C, which states that the graph of g(x) is translated 11 units to the left.
The graph of f(x) = x is a straight line passing through the origin with a slope of 1. If we apply the transformation g(x) = f(x - 11), it means that we are shifting the graph of f(x) 11 units to the right. This results in a new function g(x) that has the same shape and slope as f(x), but is shifted to the right by 11 units.
Therefore, the correct answer is C. It is the graph of f(x) translated 11 units to the left.
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A center pivot irrigation system provides water to a sector shaped field, find the area of the field if 0=140 degrees and r= 40 yd
Answers
The area of the sector is approximately 1954.77 square yards.
A circular sector, also known as a circle sector or a disc sector (symbol:), is a piece of a disc (a closed region bordered by a circle) encompassed by two radii and an arc. The smaller area is known as the minor sector, and the bigger is known as the major sector.
Any point on the circle outside of the sector can be connected to the arc's endpoints to produce half of the central angle.
We know that the area of a circle is πr² and the area of the sector of a circle with angle θ is given by θ/360 πr² .
Area of the sector
= 140°/360° × π × 40²
= 1954.7687... square yards.
≈ 1954.77 square yards.
Therefore the area of the sector is approximately 1452.113 square yards.
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What is the area of the square that measures 3.1 m on each side
Answers
The area of the square with a side length of 3.1 meters is 9.61 square meters.
To find the area of a square, we need to multiply the length of one side by itself. In this case, the square has a side length of 3.1 m.
Area of a square = side length × side length
Substituting the given side length into the formula:
Area = 3.1 m × 3.1 m
To perform the calculation:
Area = 9.61 m²
It's worth noting that when calculating the area, we are working with squared units. In this case, the side length is in meters, so the area is expressed in square meters (m²). The area represents the amount of space enclosed within the square.
Remember, to find the area of any square, you simply need to multiply the length of one side by itself.
The area of the square with a side length of 3.1 meters is 9.61 square meters.
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Pedro wants to grow tomatoes and herbs so he can make his own fresh pizza sauce. Pedro's planter box is seven feet long and four feet wide on the inside. Pedro fills the planter box with soil to a height of two feet. What is the volume of soil in Pedro's planter box?
Answers
According to the question the volume of soil in Pedro's planter box is 56 cubic feet (ft³).
What is volume?Volume is a measure of the amount of space that a three-dimensional object occupies or contains. It is measured in units of cubic centimeters (cm3), cubic meters (m3) or liters. Volume is an important concept in many areas of mathematics, including geometry, calculus and physics. It is also a key concept in many other disciplines, including engineering, architecture and the sciences. Volume is an important property of a solid object, and it is often used to quantify the size or capacity of an object. Volume can be calculated by multiplying the length, width and height of an object. It can also be calculated using the formula for the volume of a cylinder, cone, sphere or other shapes.
To calculate this, we need to multiply the length of the planter box (7 ft) by the width (4 ft) by the height of the soil (2 ft). This gives us the following equation: 7 ft x 4 ft x 2 ft
= 56 ft³.
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Select all the correct answers.
A frozen yogurt shop weighs customers' cups on a scale to determine how much they will pay for their yogurt. The scale
rounds weights to the nearest tenth of an ounce. A weight of 10 ounces or more costs at least $3.
Which of the following weights of yogurt cups would cost at least $3?
10.1 oz
9.67 oz
D 9.87 oz
0 10.0 OZ
10.02 oz
09.05 oz
09.98 oz
Answers
Any weight 10 ounces or more would cost at least $3
Choose all the ones that are 10.0 or greater. Since the scale rounds to the nearest tenth, if the tenths number is 9 and the hundredths number is at least 5 this would round up to 10.
Answers:
10.1 oz
10.0 oz
10.02 oz
9.98 oz
Read the question .
The weight above 10ounces Costs atleast 3$
So select all the weights above 10Oz
They are
10.1Oz10.02Oz10.0OzLeila has a deck of 10 cards numbered 1 through 10 . She is playing a game of chance.
This game is this: Leila chooses one card from the deck at random. She wins an amount of money equal to the value of the card if an even numbered card is drawn. She loses $6 if an odd numbered card is drawn.
(a) Find the expected value of playing the game.
(b) What can Leila expect in the long run, after playing the game many times?
(She replaces the card in the deck each time.)
Leila can expect to gain money.
Leila can expect to lose money.
Leila can expect to break even (neither gain nor lose money).
Answers
a. The expected value is $12
b. She is expected to win money
What is the expected value of playing the game?To find the expected value of playing the game, we need to calculate the average value of the winnings or losses.
(a) Expected Value:
The probability of drawing an even-numbered card is 5/10 (since there are 5 even-numbered cards out of 10), and the probability of drawing an odd-numbered card is also 5/10.
If Leila draws an even-numbered card, she wins an amount equal to the value of the card. So the expected value of winning is:
(5/10) * (2 + 4 + 6 + 8 + 10) = (5/10) * 30 = 15/10 = $15
If Leila draws an odd-numbered card, she loses $6. So the expected value of losing is:
(5/10) * (-6) = -3
To find the overall expected value, we subtract the expected value of losing from the expected value of winning:
Expected value = (15) + (-3) = 12
Therefore, the expected value of playing the game is $12
(b) In the long run, after playing the game many times, Leila can expect to lose money. Since the expected value is positive $12 , on average, she will win $12 per game.
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Consider the graph of function f below. A diagonal curve declines through (negative 6, 7), (negative 5, 5), (negative 4, 3), (negative 3, 1), (3, negative 1, negative 3), (0, negative 5) and (1, negative 7) on the x y coordinate plane. The function g is a transformation of f. If g has a y-intercept at -1, which of the following functions could represent g? A. g(x) = f(x) - 1 B. g(x) = f(x + 4) C. g(x) = f(x - 1) D. g(x) = f(x) + 4
Answers
The function g(x) is defined as follows:
D. g(x) = f(x) + 4.
What is a translation?A translation happens when either a figure or a function is moved horizontally or vertically on the coordinate plane.
The four translation rules for functions are defined as follows:
Translation left a units: f(x + a).Translation right a units: f(x - a).Translation up a units: f(x) + a.Translation down a units: f(x) - a.The y-intercept for each function is given as follows:
f(x): y = -5.g(x): y = -1.Meaning that g(x) is a translation up four units of function f(x), hence it is defined as follows:
g(x) = f(x) + 4.
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Answer: D
Step-by-step explanation:
The function g(x) is defined as follows:
D. g(x) = f(x) + 4.
What is a translation?
A translation happens when either a figure or a function is moved horizontally or vertically on the coordinate plane.
The four translation rules for functions are defined as follows:
Translation left a units: f(x + a).
Translation right a units: f(x - a).
Translation up a units: f(x) + a.
Translation down a units: f(x) - a.
The y-intercept for each function is given as follows:
f(x): y = -5.
g(x): y = -1.
Meaning that g(x) is a translation up four units of function f(x), hence it is defined as follows:
g(x) = f(x) + 4.
given f(x)= -6x+1 find f(3x+1)
Answers
Answer:
f(3x + 1) = - 18x - 5
Step-by-step explanation:
Substitute x = 3x + 1 into f(x), that is
f(3x + 1)
= - 6(3x + 1) + 1 ← distribute and simplify
= - 18x - 6 + 1
= - 18x - 5
Need help will give brainliest
Answers
The equation formed after the transformations is given as follows:
\(g(x) = \frac{1}{6}\sqrt{x + 3}\)
How to obtain the function?The parent function in this problem is defined as follows:
\(f(x) = \sqrt{x}\)
For the vertical shrink by a factor of 1/6, the function is multiplied by 1/6, hence it is given as follows:
\(g(x) = \frac{1}{6}\sqrt{x}\)
For the translation left 3 units, we have that x -> x + 3, hence:
\(g(x) = \frac{1}{6}\sqrt{x + 3}\)
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How would I solve for x? Write an explanation thx.
Answers
Answer:
Step-by-step explanation:
For any quadrilateral the sum of all the angles equal 360 so you can add all angles and set =360
x + 2x +3x 3x = 360 >This is your equation, combine like term
9x = 360 >Divide both sides by 9
x = 40
I NEED HELP PLEASE, THANKS! :)
Answers
Answer:
-0.4
Step-by-step explanation:
Since x=4 is not a critical point, you can simply evaluate the function. You can do this in your head.
(2√4 -6)/(9 -4) = (2·2 -6)/5 = -2/5 = -0.4