The amount of work done, in foot-pounds, to lift a crate weighing 30 pounds a total of 3 feet is 90 foot-pounds.
To calculate the amount of work done, in foot-pounds, to lift a crate weighing 30 pounds a total of 3 feet, we need to use the formula:
Work = Force x Distance
In this case, the force is the weight of the crate, which is 30 pounds. The distance is the height the crate is lifted, which is 3 feet.
So, Work = 30 pounds x 3 feet
We can simplify this by converting pounds to foot-pounds, which is the unit used to measure work. To convert pounds to foot-pounds, we need to multiply the weight by the distance. So:
Work = 30 pounds x 3 feet = 90 foot-pounds
Therefore, the amount of work done, in foot-pounds, to lift a crate weighing 30 pounds a total of 3 feet is 90 foot-pounds.
To calculate the amount of work done, in foot-pounds, for lifting a crate weighing 30 pounds a total of 3 feet, you can follow these steps:
Step 1: Identify the weight of the crate (30 pounds) and the distance it is lifted (3 feet).
Step 2: Multiply the weight of the crate by the distance lifted.
Work (in foot-pounds) = Weight (in pounds) × Distance (in feet)
In this case:
Work = 30 pounds × 3 feet
Work = 90 foot-pounds
So, the amount of work done is 90 foot-pounds.
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The work done to lift a crate weighing 30 pounds a total of 3 feet is:
Work = 30 pounds x 3 feet x cos(0 degrees) = 90 foot-pounds
So the amount of work done to lift the crate is 90 foot-pounds.
The amount of work done, in foot-pounds, to lift a crate weighing 30 pounds a total of 3 feet is given by the formula:
Work = Force x Distance x cos(theta)
where Force is the weight of the crate, Distance is the vertical distance lifted, and theta is the angle between the direction of the force and the direction of motion (which is 0 degrees in this case since the force is acting vertically upwards).
Therefore, the work done to lift a crate weighing 30 pounds a total of 3 feet is:
Work = 30 pounds x 3 feet x cos(0 degrees) = 90 foot-pounds
So the amount of work done to lift the crate is 90 foot-pounds.
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consider the experiment of rolling a die whose sample space is (1,2,3,4,5,6). if two dice are rolled simultaneously, what is the probability that a prime number turns up on one of the dice and a composite number on the other?
Therefore, the probability of getting a prime number on one die and a composite number on the other die when rolling two dice simultaneously is 1/6 or approximately 0.1667.
What is probability?Probability theory is a branch of mathematics that deals with the study of random events and the analysis of their outcomes. It is widely used in statistics, science, engineering, finance, and many other fields to model and predict the behavior of complex systems.
Here,
There are a total of 6 x 6 = 36 possible outcomes when two dice are rolled simultaneously. We need to count the number of outcomes where one die shows a prime number and the other die shows a composite number.
Prime numbers in the sample space are 2, 3, and 5. Composite numbers are 4, 6, and any number greater than 1 that is not prime.
So, there are three possible outcomes where one die shows a prime number and the other die shows a 4 or 6:
(2, 4), (2, 6), (3, 4), (3, 6), (5, 4), (5, 6)
Therefore, there are a total of 6 possible outcomes where one die shows a prime number and the other die shows a composite number.
The probability of getting one prime number and one composite number on the two dice is:
P = number of favorable outcomes / total number of possible outcomes
P = 6 / 36
P = 1/6
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X +3. 8 is greater than -10. 02 point choose the solution set
Answer:
(-13.82, ∞)
Step-by-step explanation:
To solve this inequality, we need to isolate the variable X on one side of the equation. First, we can subtract 3.8 from both sides of the inequality, which gives us:
X > -10.02 - 3.8
Simplifying this expression, we get:
X > -13.82
Therefore, the solution set for this inequality is all the values of X that are greater than -13.82. In interval notation, we can write the solution set as (-13.82, ∞).
6.047 in word form?
Please tell me quick I need this or I might stay back quick!!!!!!
Six and forty-seven thousandths.
or six point zero four seven.
the answer depends on what you have to write.
Hope this helps!
A thief entered an orange garden and stole some oranges. The guard caught him. To get rid of him, the thief gave him half of the stolen oranges and two more oranges. The thief was left with only 9 oranges. How many oranges did he stole
The thief stole 22 oranges using algebraic equations.
To solve this problem, we need to use algebra. Let x be the number of oranges the thief stole.
According to the problem, the thief gave the guard half of the stolen oranges and two more. This means that he gave away (1/2)x + 2 oranges.
We also know that the thief was left with only 9 oranges. So we can set up the equation:
x - [(1/2)x + 2] = 9
Simplifying this equation:
(1/2)x - 2 = 9
(1/2)x = 11
x = 22
Therefore, the thief stole 22 oranges.
The problem presents us with a scenario where a thief entered an orange garden and stole some oranges. However, he was caught by the guard. In order to get rid of the guard, the thief decided to give him half of the stolen oranges and two more. As a result, the thief was left with only 9 oranges.
To solve this problem, we used algebraic equations. We let x be the number of oranges the thief stole. We also knew that the thief gave away (1/2)x + 2 oranges to the guard. Using this information, we were able to set up an equation where x - [(1/2)x + 2] = 9. Simplifying the equation, we were left with (1/2)x - 2 = 9. Solving for x, we found that the thief had stolen 22 oranges.
In conclusion, algebraic equations are a useful tool in solving mathematical problems. By setting up an equation and simplifying it, we were able to determine the number of oranges that the thief had stolen.
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23. y = x + 5; (4, -3)
Answer:
y=x+5;1
Step-by-step explanation:
Hope this helps! =D
a solenoid 1.30 m long and 2.60 cm in diameter carries a currentof 18.0 a. the magnetic field inside the solenoid is 23.0 mt.find the length of the wire forming the solenoid.
The length of wire per unit length is 8.168 cm.
What is solenoid?Its function is to produce a regulated magnetic field through a coil twisted into a compact helix. The solenoid is a sort of electromagnet.
The magnetic field inside a solenoid is given by:
B = u*n*I
where B is the magnetic field, u is the permeability of free space, n is the number of turns per unit length, and I is the current.
The number of turns in a solenoid is given by:
N = n*L
where N is the total number of turns, L is the length of the solenoid, and n is the number of turns per unit length.
Therefore, the magnetic field can be written as:
B = u*N*I/L
Rearranging this equation, we get:
L = u*N*I/B
Substituting the given values, we get:
L = (4*pi*10⁻⁷)*(N=?) * (I=18.0 A) / (B=23.0 mT)
The number of turns per unit length is not given, so we cannot determine the total number of turns N. However, we can calculate the length of wire per unit length by using the formula for the circumference of a circle:
C = 2*pi*r
where r is the radius of the solenoid.
Substituting the given values, we get:
C = 2*pi*(d/2) = pi*d = 8.168 cm
Therefore, the length of wire per unit length is 8.168 cm.
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Let r and s be the usual generators for the dihedral group of order 8...
Part a)
list the elements of D8 as 1,r,r^2,r^3,s,sr,sr^2,sr^3 and label these with the integers
1,2,...,8 respectively. Exhibit the image of each element of D8 under the left regular representation of D8 into S8....
Each element of D8 is mapped to a permutation of {1, 2, 3, 4, 5, 6, 7, 8} by considering its action on the labeled generators 1, 2, ..., 8 under composition.
The elements of D8 are 1, r,[tex]r^2, r^3, s, sr, sr^2, sr^3,[/tex] which we can label with the integers 1, 2, 3, 4, 5, 6, 7, 8 respectively. The left regular representation of D8 into S8 is given by:
1 → (1)(2)(3)(4)(5)(6)(7)(8)
r → (1 2 3 4)(5 6 7 8)
[tex]r^2[/tex] → (1 3)(2 4)(5 7)(6 8)
[tex]r^3[/tex]→ (1 4 3 2)(5 8 7 6)
s → (1 2)(3 4)(5 6)(7 8)
sr → (1 8 3 6)(2 7 4 5)
[tex]sr^2[/tex]→ (1 4)(2 3)(5 8)(6 7)
[tex]sr^3[/tex] → (1 6 3 8)(2 5 4 7)
Here, each element of D8 is mapped to a permutation of {1, 2, 3, 4, 5, 6, 7, 8} by considering its action on the labeled generators 1, 2, ..., 8 under composition.
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We have exhibited the image of each element of D8 under the left regular representation into S8, represented as a product of disjoint cycles.
The left regular representation of D8 is a homomorphism from D8 to the symmetric group S8, where each element of D8 is represented as a permutation of the set {1, 2, ..., 8}.
Using the generators r and s, we can construct the elements of D8 as follows:
[tex]r^0[/tex] = 1
[tex]r^1[/tex]= r
[tex]r^2[/tex] = rr
[tex]r^3[/tex] = rrr
[tex]s^0[/tex]= 1
[tex]s^1[/tex] = s
[tex]s^2[/tex] = 1
[tex]s^3[/tex] = ss
Now, let's apply the left regular representation to each element of D8:
1 → (1 2 3 4 5 6 7 8)
r → (1 2 3 4 5 6 7 8)(1 2)
[tex]r^2[/tex] → (1 2 3 4 5 6 7 8)(1 3)(2 4)
[tex]r^3[/tex]→ (1 2 3 4 5 6 7 8)(1 4 3 2)
s → (1 8)(2 7)(3 6)(4 5)
sr → (1 7 3 5)(2 8 4 6)
[tex]sr^2[/tex] → (1 6 3 2)(4 7 5 8)
[tex]sr^3[/tex] → (1 5)(2 6)(3 7)(4 8)
Note that we can represent each permutation as a product of disjoint cycles, where each cycle corresponds to an orbit under the action of the permutation. For example, the permutation corresponding to r is a product of two cycles: (1 2) and (3 4 5 6 7 8). This means that r fixes the elements 1 and 2, and permutes the elements 3, 4, 5, 6, 7, and 8 cyclically. Similarly, the permutation corresponding to s is a product of four cycles: (1 8), (2 7), (3 6), and (4 5), which means that s fixes the pairs (1, 8), (2, 7), (3, 6), and (4, 5), and transposes each pair.
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what is the domain of the function?
The domain of the function plotted is
A) all real numbers from -4 to 4What is domain of a function?In mathematics, the domain of a function is the set of all possible values of the input (independent variable) for which the function is defined.
So we can say that, it is the set of all possible values that we can substitute into the function and get a valid output (dependent variable).
In the graph, watching the x axis which is the input variables we can see that the domain is all real numbers from -4 to 4
In general, the domain of a function depends on the specific form of the function and any restrictions or conditions that may apply to the input values.
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what is the function showing the total amount of money julia has after x weeks ? use the variable X
The linear function that represent the situation is as follows:
f(x) = 27x + 254
How to represent a function?A function relates input and output values.
Julia has 254 dollars. Each week she saves an additional 27 dollars .
Therefore, the function that models the amount of money Julia has after x week can be represented as follows:
The function is a linear function. A linear function can be represented in the form as follows:
y = mx + b
where
m = slopeb = y-interceptTherefore,
f(x) = 27x + 254
where
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The Toy Train Collectors' Club used the ages of its membership to construct the histogram. Which age group has the greatest number of members? How many members are in that age group?
The Toy Train Collectors' Club has 140 members who are 42 years of age or younger.
To find the number of members who are 42 years of age or younger, we need to look at the bars in the histogram that represent these age groups. Specifically, we need to add up the heights of the bars that represent members aged 0-42 years old.
The histogram shows that there are 30 members in the age group 0-10,
50 members in the age group 11-20,
40 members in the age group 21-30,
20 members in the age group 31-40, and
15 members in the age group 41-50.
To find the number of members who are 42 years of age or younger, we need to add up the heights of the bars that represent members aged 0-42 years old, which is 30+50+40+20 = 140.
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Can someone help me with this maths question?
Thus, the two factors of the given quadratic equation is found as: p = - 6 and p = -8.
Explain about the factorization method:To factor is to identify the terms that make up an expression when they are multiplied together.
Expressions are made up of different words. A term may have specific components, such as coefficients, variables, and constants.While factoring in algebra, we seek out the most significant factors that the terms in an equation have in common. The only reasonably prime numbers we have are 7 and 9, thus we cannot factor out either constants.Given quadratic equation:
p² + 14p + 48 = 0
Find the factors of 48 such that on addition 14 will come:
48 = 6*8
So,
p² + 6p + 8p + 48 = 0
Taking p common first two terms:
p(1 + 6) + 8p + 48 = 0
Now, taking 8 common from last two terms
p(p + 6) + 8(p + 6) = 0
taking (p + 6) from both .
(p + 6)(p + 8) = 0
Now,
p + 6 = 0
p = -6 and
p + 8 = 0
p = -8
Thus, the two factors of the given quadratic equation is found as: p = - 6 and p = -8.
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Correct question:
Solve the given quadratic equation using the factorization method:
p² + 14p + 48 = 0
Place the indicated product in the proper location on the grid. (x + y + 3)(x + y - 4)
The required location on the gird is:
[tex](x + y + 3)(x + y - 4) = x^{2}+y^2 +2xy-x-y-12[/tex]
Consider the provided expression.
We need to place the indicated product in the proper location on the grid.
First open the parenthesis as shown:
(x + y + 3)(x + y - 4) = x(x + y - 4) + y(x + y - 4) + 3(x + y - 4)
[tex](x + y + 3)(x + y - 4) =[/tex] [tex]x^{2} +xy-4x+yx+y^2-4y+3x+3y-12[/tex]
Now add the like terms as shown:
[tex](x + y + 3)(x + y - 4) = x^{2}+y^2 +2xy-x-y-12[/tex]
Hence, the required location on the gird is:
[tex](x + y + 3)(x + y - 4) = x^{2}+y^2 +2xy-x-y-12[/tex]
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Jerel runs 6 days each week. He runs 4.2 km each day for the first 6 days. If Jerel runs a total of 25km, write and solve an equation to find how many kilometers he runs on the sixth day.
Jerel runs 4 km on the sixth day.
How to determine how many kilometers he runs on the sixth day.Let's call the distance Jerel runs on the sixth day "x". We know that he runs 4.2 km each day for the first 6 days, so the total distance he runs in those 6 days is:
Total distance = 4.2 km/day x 6 days = 25.2 km
We also know that the total distance Jerel runs is 25 km, so we can set up an equation to solve for "x":
4.2 km/day x 5 days + x = 25 km
Simplifying the equation, we get:
21 km + x = 25 km
Subtracting 21 km from both sides, we get:
x = 25 km - 21 km
x = 4 km
Therefore, Jerel runs 4 km on the sixth day.
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What is (7x1/10) + (9x1/100) + (9x1/1000) answer in decimal form
Answer:
Step-by-step explanation: Multiplication first 7x1 = 7, Take 7 and divide it by 10 which gives you 0.7, Do the same but for the other 2 questions,
(9x1/100 = 0.09)
(9x1/1000 = 0.009)
(7x1/10 = 0.7)
Now take the answers and add them up
0.09 + 0.009 + 0.7 = 0.799
Answer: 0.799
How many home runs did the player with 154 hits have?
How many was he predicted to have?
The statement. "the average height of an adult male is 5'10''," is an example of _______estimate
The statement "the average height of an adult male is 5'10''" is an example of a statistical estimate.
An estimate is an approximation or prediction of a value based on limited information or data. In this case, the estimate is based on data collected from a sample of adult males, and it represents the expected height of an average adult male in the population.
Statistical estimates are commonly used in many fields like business, finance, economics, and social sciences. They are used to make predictions and decisions based on uncertain information.
For example, a company might use statistical estimates to predict future sales. It is important to note that estimates are not exact or precise measurements, but rather are based on assumptions and limitations. They are subject to errors and uncertainties, and can be affected by factors such as sample size, sampling method, and measurement errors. Therefore, it is important to understand the limitations of statistical estimates and to interpret them with caution.
In summary, the statement "the average height of an adult male is 5'10''" is an example of a statistical estimate, which represents an approximation of a value based on limited information and assumptions.
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6(4x - 3) > 30
need help pls?
Answer:
[tex]6(4x - 3) > 30 \\ divide \: both \: sides \: of \: the \: \\ inequality \: by \: 6 \\ = 4x - 3 > 5 \\ = 4x > 5 + 3 \\ = 4x > 8 \\ = x > \frac{8}{4} \\ = x > 2[/tex]
hope it helps
Please help me this is due tomorrow
Answer:
Step-by-step explanation:
4
a youth soccer coach much choose 4 of his 8 players to go into a game. in how many ways can this be done?
Two parallel lines, a and b, are cut by a transversal w. The measures of two angles formed are given in the diagram. What is the measurement of the angle labeled (3x)°?
The measurement of the angle labeled (3x)° include the following: 120°.
What is corresponding angles postulate?In Mathematics and Geometry, corresponding angles postulate simply refers to a theorem which states that corresponding angles are always congruent (equal) if the transversal intersects two parallel lines.
This ultimately implies that, the corresponding angles would always be congruent (equal) if a transversal intersects two (2) parallel lines.
60 + y = 180
y = 180 - 60
y = 120°
By applying corresponding angles postulate to both lines a, b, and w, we can reasonably infer and logically deduce that the following angles are congruent:
3x = 120°
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The price of stock A at9am was $12. 73 since than the price has been increasing at the rate of $0. 06 per hour. At noon the price of stock B was $13. 48. It begins to decrease at the rate of $0. 14 per hour. If the stocks continue to increase and decrease at the same rates in how many hour will the price of the price of the stocks be the same?
According to the price, it will take 3.75 hours for the prices of both stocks to be the same, assuming they continue to increase and decrease at the same rates.
To find out when the prices of both stocks will be the same, we need to set up an equation where the prices of both stocks are equal. Let's call the number of hours it takes for the prices to be equal "t".
For stock A, the price after "t" hours can be expressed as:
Price of stock A = $12.73 + ($0.06 x t)
For stock B, the price after "t" hours can be expressed as:
Price of stock B = $13.48 - ($0.14 x t)
To find the time when the prices of both stocks are equal, we can set the two equations equal to each other and solve for "t".
$12.73 + ($0.06 x t) = $13.48 - ($0.14 x t)
Simplifying this equation, we get:
$0.20 x t = $0.75
Dividing both sides by $0.20, we get:
t = 3.75 hour
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2. The graph of AEFG is shown. Graph the
image of AEFG after a translation of 3 units
left and 1 unit down. Write the coordinates of
the image. (Example 1)
YA E
F
O
G
X
Thus, the new coordinates of the image of ΔEFG after the given translations is found as: E'(-2, 3), F'(-4, 0), G'(-1, -2).
Explain about the translation:A translation is represented as a column vector. Using a column vector, the translation is divided into:
The extent to which a shape travels horizontally (left or right).Size of a shape's vertical displacement (up or down).Given that-
ΔEFG after a translation of 3 units left and 1 unit down.Coordinates of ΔEFG: E(1,4) , F(-1 , 1), G(2, -1)Now,
translation of 3 units left and 1 unit down - subtract 3 from the x coordinates and 1 from the y coordinates.
E(1,4) = E' (1 - 3, 4 - 1) = E'(-2, 3)
F(-1 , 1) = F'(-1 - 3, 1 - 1) = F'(-4, 0)
G(2, -1) = G'(2 - 3, -1- 1) = G'(-1, -2)
Thus, the new coordinates of the image of ΔEFG after the given translations is found as: E'(-2, 3), F'(-4, 0), G'(-1, -2).
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if the height of a cone is halved , how will this change the volume of a cone?
if the height of a cylinder is tripled, how will this change the volume of the cylinder?
(explain answer)
The volume of a cylinder of radius r and height h is given by the equation presented as follows:
V = πr²h.
The volume of a cone is a third of the volume of a cylinder, hence:
V = πr²h/3.
For both cases, the height variable h has an exponent of one, hence:
If the height of a cone is halved, the volume of the cone is halved.If the height of a cylinder is tripled, the volume of the cylinder is tripled.If we had doubled the radius for example, the volume would be multiplied by 2² = 4, as the radius is squared.
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5
2 points
Reflect the given rectangle over the y-axis.
C
B
D
A
Which best describes the location of the image of vertex B?
(8,-9)
(-9,8)
(-8,9)
(9,-8)
The image of vertex C is closest to point A=(3,0).
What is transformation?
A transformation is a process or operation that changes the position, shape, or orientation of a geometric figure or an object in space.
When a point is reflected over the x-axis, its y-coordinate changes sign (positive becomes negative, and negative becomes positive), while its x-coordinate remains the same.
In this case, if point C is reflected over the x-axis, its image will be (-3, -5) because the x-coordinate remains the same (3), and the y-coordinate changes sign from positive to negative.
We can now find the closest point to the image of vertex C, which is (-3, -5), among the given options:
Distance from (-3, -5) to A=(3,0):
d = √((3 - (-3))² + (0 - (-5))²) = sqrt(6² + 5²) ≈ 7.81
Distance from (-3, -5) to B=(6,0):
d = √((6 - (-3))² + (0 - (-5))²) = √(9² + 5²) ≈ 9.43
Therefore, the image of vertex C is closest to point A=(3,0).
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Expand the expressions and simplify. 5(x + 4) 3(x + 2) = Question 1 options: a. 8x + 4b. 6x + 18 c. 8x + 26d. 7x - 18
Answer:
(✿✿✿✿✿✿✿✿✿✿✿✿✿✿✿✿✿✿✿✿✿✿✿✿✿✿✿✿✿✿✿✿✿✿✿✿)
To expand and simplify 5(x + 4) 3(x + 2), we can use the distributive property of multiplication over addition which states that a(b + c) = ab + ac.
So, we have:
5(x + 4) 3(x + 2) = (5x + 20)(3x + 6)
Now, we can use the distributive property again to expand this expression:
(5x + 20)(3x + 6) = 5x * 3x + 5x * 6 + 20 * 3x + 20 * 6
= 15x^2 + 90x + 60
Therefore, the answer is 15x^2 + 90x + 60.
I hope this helps!
(✿✿✿✿✿✿✿✿✿✿✿✿✿✿✿✿✿✿✿✿✿✿✿✿✿✿✿✿✿✿✿✿✿✿✿✿)
what is the area of right triangle 0,0 4,3 -2,11
Answer:
25 units²
Step-by-step explanation:
Area of a triangle = (1/2)b*h
After graphing the triangle you can see that the two legs are at points
(4,3) and (-2,11) and (4,3) and (0,0). Using the distance formula:
[tex]\sqrt{(x_{2}-x_{1})^{2} + (y_{2}-y_{1})^{2}}[/tex]
then plug in the first line
[tex]\sqrt{(-2-4)^{2} + (11-3})^{2}}[/tex]
simplify
[tex]\sqrt{(-6)^{2} + (8})^{2}}[/tex]
[tex]\sqrt{36 +64}[/tex]
[tex]\sqrt{100}[/tex]
10
then the second line
[tex]\sqrt{(4-0)^{2} + (3-0)^{2}}[/tex]
[tex]\sqrt{(4)^{2} + (3)^{2}}[/tex]
[tex]\sqrt{16 + 9}[/tex]
[tex]\sqrt{25\\}[/tex]
=5
5*10=50
50*0.5 =25
so the area is equal to 25 units²
Justin paid
$10. 47
for a
6. 08
-
kg
bag of dog food. A few weeks later, he paid
$13. 88
for a
7. 48
-
kg
bag at a different store.
Find the unit price for each bag. Then state which bag is the better buy based on the unit price.
Round your answers to the nearest cent.
Unit price for the
6. 08
-
kg
bag:
$perkg
Unit price for the
7. 48
-
kg
bag:
$perkg
The better buy:The
6. 08
-
kg
bagThe
7. 48
-
kg
bagNeither (They have the same unit price)
The Unit-Price for first-bag is $1.72/kg and for second-bag is $1.86/kg, then the first-bag is cheaper compared to the second-bag with a unit-price.
The "Unit-Price" refers to the cost of dog food per kilogram. It is calculated by dividing the "total-cost" of the bag of dog-food by its weight in kilograms.
⇒ For the first bag of dog food:
The Cost is = $10.47,
The Weight is = 6.08 kg,
So, the Unit-Price is = Cost/Weight = $10.47/6.08 kg ≈ $1.72/kg,
⇒ For the second bag of dog food:
The Cost is = $13.88,
The Weight is = 7.48 kg,
So, the Unit Price will be = Cost/Weight = $13.88/7.48 kg ≈ $1.86/kg,
Based on the "unit-prices" calculated, the first bag of dog food has a unit price of $1.72 per kilogram, and the second bag has a unit price of $1.86 per kilogram.
Therefore, the first bag of dog food is the better-buy as it is cheaper compared to the second bag.
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The given question is incomplete, the complete question is
Justin paid $10.47 for a 6.08-Kg bag of dog food. A few weeks later, he paid $13.88 for a 7.48-kg bag at a different store. Find the unit price for each bag. Then state which bag is the better buy based on the unit price.
Two classmates have decided to read all the volumes in a popular series of books. Eva has already read 4 volumes and will continue to read new ones at a rate of 2 volumes per week. Maria, who hasn't started reading the series yet, will read 4 volumes per week. At some point, Maria will catch up with Eva and they will be reading the same book. How many volumes will each girl have read by then? How long will that take?
Thus, the number of volume read by both Eva and Maria in total 2 weeks is 8.
Explain about the slope of function:Slope is a crucial topic in economics because it's used to gauge how quickly things are changing.
The slope expresses how quickly the dependent variable changes when the independent variable changes. The line becomes steeper as the slope increases.
Given data:
Number of volume read by Eva = 4Rate of reading by Eva = 2 volume per weekNumber of volume read by Maria = 0Rate of reading by Maria = 4 volume per weekNow,
Let the number of weeks at which both read the equal number of volume be x.
Total number of volume be y
So,
For Eva: y = 4 + 2x
For Maria: 0 + 4x
Equating both equations:
4 + 2x = 4x
4x - 2x = 4
2x = 4
x = 4/2
x = 2
Number of volumes read by each girl:
For Eva: y = 4 + 2(2)= 8
For Maria: 0 + 4(2) = 8
Thus, the number of volume read by both Eva and Maria in total 2 weeks is 8.
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Read each question carefully. Choose the answer that best completes the sentence.
Debt is usually expected in any of the following cases EXCEPT
O A. purchase of house
OB. credit card purchases
OC. purchase of car
O D. educational loans
nswered
The correct answer is,
Debt is usually expected in any of the following cases EXCEPT ''purchase of car.''
We have to given that;
Debt is usually expected in any of the following cases EXCEPT ....
Now, We know that;
it's important to note that there may be individual situations where debt is expected when buying a car.
Hence, The correct answer is,
Debt is usually expected in any of the following cases EXCEPT ''purchase of car.''
Thus, Option C is true.
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The shape of this particular section of the rollercoaster is a half of a circle. Center the circle at the origin and assume the highest point on this leg of the roller coaster is 30 feet above the ground.
a) Write the equation that models the height of the roller coaster.
b) Start by writing the equation of the circle. (Recall that the general form of a circle with the center at the origin is [tex]x^{2}[/tex] + [tex]y^{2}[/tex] = [tex]r^{2}[/tex]).
c) Now solve this equation for y. Remember the roller coaster is above ground, so you are only interested in the positive root.
Hence,The equation that models the height of the roller coaster is [tex]x^{2} +y^{2}=900[/tex]. and solution of y =[tex]\sqrt{(900-x^{2})}[/tex].
What is the roller coaster?A roller coaster, or roller coaster, is a type of amusement ride that employs a form of elevated railroad track designed with tight turns, steep slopes, and sometimes inversions. Passengers ride along the track in open cars, and the rides are often found in amusement parks and theme parks around the world.
We have given that ,
the Center the circle at the origin and assume the highest point on this leg of the roller coaster is 30 feet above the ground.
we know that equation of circle ,
[tex]x^{2} +y^{2}=r^{2}[/tex]
Where r is the radius
From given we can say that the radius =30
since the radius is 30 ft
[tex]x^{2} +y^{2}=30^{2}\\x^{2} +y^{2}=900[/tex]
so, the equation that models the height of the roller coaster. [tex]x^{2} +y^{2}=900[/tex].
We have to find the equation that can be represent the height of the roller coaster so find the value of y
[tex]x^{2} +y^{2}=r^{2}[/tex]
⇒[tex]y^{2}=r^{2}-x^{2}[/tex]
⇒[tex]y^{2}=30^{2}-x^{2}[/tex]
⇒[tex]y^{2}=900-x^{2}[/tex]
⇒y =±[tex]\sqrt{(900-x^{2})}[/tex]
⇒y =[tex]\sqrt{(900-x^{2})}[/tex] ∵according to question choose positive sign only
Therefore the models the height of the roller coaster y =[tex]\sqrt{(900-x^{2})}[/tex].
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