The position, s(t), of the particle at time t if initially s(0) = 3 is (2) s(t) = 10 - 7 cos(t) - 6 sin(t).
To find the position, s(t), of the particle at time t, we need to integrate the velocity function, v(t), with respect to time:
s(t) = ∫ v(t) dt
Since the velocity function is v(t) = 7 sin(t) - 6 cos(t), we have:
s(t) = ∫ (7 sin(t) - 6 cos(t)) dt
Integrating each term separately, we get:
s(t) = -7 cos(t) - 6 sin(t) + C
where C is the constant of integration.
To find the value of C, we use the initial condition s(0) = 3:
s(0) = -7 cos(0) - 6 sin(0) + C = -7 + C = 3
C = 10, and the position function is:
s(t) = -7 cos(t) - 6 sin(t) + 10
Rewriting this equation in the form of answer choices, we get:
s(t) = 10 - 7 cos(t) - 6 sin(t)
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The position, s(t), of the particle at time t, given the initial condition s(0) = 3 and the velocity v(t) = 7sin(t) - 6cos(t), is s(t) = 9 - 7sin(t) - 6cos(t).
To find the position, we integrate the velocity function with respect to time. Integrating the velocity function v(t) = 7sin(t) - 6cos(t) gives us the position function s(t).
The indefinite integral of sin(t) is -cos(t), and the indefinite integral of cos(t) is sin(t). When integrating, we also take into account the initial condition s(0) = 3 to determine the constant term.
Integrating the velocity function, we get:
s(t) = -7cos(t) - 6sin(t) + C
To determine the constant term C, we use the initial condition s(0) = 3:
3 = -7cos(0) - 6sin(0) + C
3 = -7(1) - 6(0) + C
3 = -7 + C
C = 10
Substituting the value of C back into the position function, we obtain:
s(t) = 9 - 7sin(t) - 6cos(t)
Therefore, the position of the particle at time t, with the initial condition s(0) = 3, is given by s(t) = 9 - 7sin(t) - 6cos(t).
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A cooking group made 240 oz of spaghetti sauce to sell at a county fair. The group can pour the sauce into small jars that hold 8 oz and large jars that hold 16 oz. The group leader made a sketch to show the line representing the different combinations of jar sizes the group can use. The x-axis represented the number of small jars and the y-axis represented the number of large jars. The group leader labeled only the intercepts.
The points that the cooking group leader did label are (0,15) and (30,0). Thus, the correct answer is C.
As your first step, find the function that best represents x and y:
x is the number of 8-ounce jars x.y is the number of 16-ounce jars.Hence, the function is:
8x + 16y = 240The group leader labeled (0,15) on the y-axis, which means that when the number of small jars is 0, the group can use 15 large jars. This means that 15 large jars can hold 240 oz of spaghetti sauce, which is true since:
8x + 16y = 240(15x0) + (16x15) = 2400 + 16 x 15 = 24015 x 15 = 240The group leader also labeled (30,0) on the x-axis, which means that when the number of large jars is 0, the group can use 30 small jars. This means that 30 small jars can hold 240 oz of spaghetti sauce, which is true since:
8x + 16y = 240(8x30) + (16x0) = 2408 x 30 + 0 = 2408 x 30 = 240The function that represents this line is 8x + 16y = 240, where x is the number of small jars and y is the number of large jars. The line passes through (0,15) and (30,0) as the two intercepts.
This question should be written as:
A cooking group made 240 oz of spaghetti sauce to sell at a county fair. The group can pour the sauce into small jars that hold 8 oz and large jars that hold 16 oz. The group leader made a sketch to show the line representing the different combinations of jar sizes the group can use. The x-axis represented the number of small jars and the y-axis represented the number of large jars. The group leader labeled only the intercepts. Which points did the group leader label?
A. (0,8) and (16,0) B. (0,30) and (15,0) C. (0,15) and (30,0) D. (0,16) and (8,0)The correct answer is C.
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What is the additive inverse of 924?
The Additive Inverse of 924 is -924
⇒ The number that, when added to 924, will result in a sum of zero is the additive inverse of 924. The formula to solve the issue where x is the additive inverse of 924 is as follows:
924 + x = 0
⇒ When we solve the preceding equation for x, we obtain x = -924. As a result, the answer to the question "What is the additive inverse of 924?" is -924.
∴Therefore Additive Inverse of 924 = -924
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The point of intersection of angle bisectors of a triangle is called .
A . circumcentre
B. incentre
C. orthocentre
D. centroid
The point of intersection of a triangle's angle bisectors is known as the incentre.
What exactly is an incentre?The incentre is the point where the triangle's three angle bisectors meet at a single point. For more understanding, draw a triangle. Name each angle with A, B, and C. Place P in the triangle's center. The point that connects A to P, B to P, and C to P is the angle bisector of a triangle. Point P is the intersection of all of the lines mentioned above. The explanation leads us to the conclusion that the incenter is the center of the triangle pointed out by P.Then, what is the explanation of the other options?The point of intersection where the three perpendicular bisectors meet or intersect is called the circumcenter.The point of intersection where the three triangle’s altitudes meet or intersect is called the orthocentre. The point of intersection where the triangle’s three median values meet or intersect is called the centroid. The letter G is usually used to denote the centroid.Learn more about incentre in triangle:
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The height of a kicked ball can be modeled by the quadratic function h = - 0 .01x^2 + 1.18x + 2. The horizontal distance traveled by the ball in feet is represented by x, and h is the height of the ball in feet. Approximately how far does the ball travel horizontally by the time it hits the ground?
The horizontal distance covered by the ball is 119.5 ft.
What is a quadratic equation?It is a polynomial with a degree of 2 or the maximum power of the variable is 2 in quadratic equations. It has two solutions as its maximum power is 2.
Given that the height of a kicked ball can be modeled by the quadratic function h = - 0 .01x² + 1.18x + 2. The horizontal distance traveled by the ball in feet is represented by x, and h is the height of the ball in feet.
The horizontal distance covered by the ball will be calculated as,
h = - 0 .01x² + 1.18x + 2
Equate h to zero and solve for the distance x,
- 0.01x² + 1.18x + 2 = 0
Use the quadratic formula,
[tex]x=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]
[tex]x = \dfrac{-1.18\om\sqrt{(1.18^2)-(4\times(-0.01)\times2}}{2\times-0.01}[/tex]
[tex]x=\dfrac{-1.18\pm\sqrt{1.4+0.08}}{-0.02}[/tex]
x = ( -1.18 - 1.21 ) / 0.02
x = 119.5 ft
The horizontal distance will be 119.5 ft.
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The number of calls received by an office on Monday morning between 8:00 AM and 9:00 AM has a mean of 2. Calculate the probability of getting no more than 4 calls between eight and nine in the morning. Round your answer to four decimal places
The probability of getting no more than 4 calls between eight and nine in the morning is 0.9473
How to calculate the probability of getting no more than 4 calls?
This is a Poisson distribution problem with a mean of 2.
In a Poisson distribution, the probability that X successes is given by:
P(X = x) = [e^(-λ) × λˣ] / x!
where x is the number of successes
e = 2.71828 is the Euler number
λ is the mean
The number of calls received by an office on Monday morning between 8:00 AM and 9:00 AM has a mean of 2 i.e. λ = 2
P(X ≤ 4) = ([e⁻²× 2⁰]/0!) + ([e⁻²× 2¹]/1!) + ([e⁻²× 2²]/2!) + ([e⁻²× 2³]/3!) + ([e⁻²× 2⁴]/4!)
P(X ≤ 4) = 0.9473
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What is the percent of increase from 5 to 7?
The percentage increse in value from 5 to 7 is 40 %
What is Percentage ?A percentage is a ratio or fraction where the full value is always 100. Sam, for instance, would have received 30 out of a possible 100 points if he had received 30% on his arithmetic test. In ratio form, it is expressed as 30:100 and in fraction form as 30/100.
Finding the percentage of a whole in terms of 100 is what percentage calculation refers to. A percentage can be found in one of two ways:
use the unitary approach.by adjusting the fraction's denominator to 100.It should be noted that when the denominator is not a factor of 100, the second technique of percentage calculation is not applied. In these situations, we employ the unitary technique.
The initial value is 5
Final value = 7
Increse in value 7-5 = 2
Percentage increse is [tex]\frac{2}{5}* 100 = 40 \ \% \\[/tex]
The percentage increse in value from 5 to 7 is 40 %
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Anna and julia each take a bycicle trip. Anna ride 20 mile in 1 1/3 hour. Julia ride 246 mile in 16 hour. Which rider ha the lower unit rate? by how much?
Julia has lower rate than anna by 0.375 miles/ hour
A rate is a ratio that is used for comparing two different kinds of quantities which have different units. On the other hand, the unit rate illustrates how many units of quantity correspond to the single unit of another quantity. We say that when the denominator in rate is 1, it is called unit rate. In fact, unit rate is said to be the amount of something in each unit or per unit. Let us understand this using some examples:
40 miles/2 hours = 20 miles/hour, Unit rate is 20 miles per hour
160 words/4 minutes = 40 words/minutes, Unit rate is 40 minute per minute
To compare the unit rate of the two riders, we need to determine the number of miles per hour for each of them.
For Anna, the unit rate is 20 miles / 1 1/3 hour = 15 miles/hour.
For Julia, the unit rate is 246 miles / 16 hours = 15.375 miles/hour.
So, Julia has a lower unit rate than Anna by 0.375 miles/hour.
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What is the additive inverse of 4 (- 4?
The additive inverse of 4 is -4. This means that when 4 is paired with -4, the two numbers cancel each other out and the result is 0.
The additive inverse of a number is the opposite of that number. For example, the additive inverse of 4 is -4. This means that when two numbers are added together and one of them is 4 and the other is -4, the result will be 0. This is because the two numbers cancel each other out. The same is true for any number and its additive inverse. For example, 8 and -8 added together will also result in 0. Additive inverses are an important part of algebra and can be used to solve equations. By understanding the concept of additive inverses, you can easily manipulate equations and solve for unknowns. This is due to the fact that when two numbers are added together and one of them is the additive inverse of the other, the result will always be 0.
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The positive number a is 2,001% of the sum of the positive numbers b and c, and b is 87% of c. What percent of b is a?
Therefore , the solution of the given problem of percentage comes out to be percentage of b is 4301%.
A percentage is what?In mathematics, a percentage is a number of ratio that is stated as a portion of 100. Also occasionally used are the abbreviations "pct.," "pct," with "pc." To denote it, though, the percent symbol "%" is frequently employed. The % amount has no dimensions. Because percentages contain a numerator of 100, they are effectively fractions. A number should be followed by the % sign (%) to show that it represents a percentage. For instance, someone would receive a 75% grade if you properly solved 75 out of 100 questions on a test. To determine percentages, divide the amount of money by the total, and then multiply the result by 100. The percentage is calculated by multiplying the ratio (value/total) by 100%.
Here,
a =2001/100 * (b+c)
and
b= 87/100*c
thus putting value of b in a
=>a = 2001/100*(87/100*c + c)
=> a= 2001/100 * 187/87 * b
=>a/b = 374187 / 8700 * 100 = 4301%
and
Now percentage of b is 4301%.
Therefore , the solution of the given problem of percentage comes out to be percentage of b is 4301%.
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What is prime multiple of 10?
A multiple of 10 cannot be equals to a prime number. Multiple of 10 is always equals to a composite number.
As given in the question,
Multiple of a given number 10 are equals to :
10 , 20 , 30, 40, 50, ........, so on.
Prime number are those numbers which have only two factors one and the number itself.
Number 10 itself is not a prime number.
Factors of 10 are equals to :
1, 2, 5, 10
More than two factors.
All the Multiples of 10 cannot be a prime number as they have more than two factors.
Multiple of 10 represents the composite number.
Therefore, multiple of 10 cannot be equals to a prime number they are composite number.
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what does it mean to round to the nearest cent
Answer:
wrong - $32.547
right - $325.47
Step-by-step explanation:
Basically, if the number in the tens place (145) is 5 or higher the nearest would be the next ten or hundred up, if lower than 5 it goes back down.
Rounding cents is basically the same. as rounding Example:
$14.345
(This is not a vaild amount of money because once you reach a hundred cents you have another dollar. So you will move the decimal point over to the left.)
$143.45
More examples:
incorrect - $23.8678
correct - $2386.78
incorrect - $89.264
correct - $892.64
Rounding is something like rounding to the nearest ten or hundred here's an example:
14 to the nearest ten is 10
16 to the nearest ten is 20
284 to the nearest hundred is 300
104 to the nearest hundred is 100
(Hope this helps. Sorry if this confused you further)
Please help!! Find f(-3) - 2
Hint: find f(-3) first and then subtract 2.
The solution for f(-3) - 2 in the function when the function f(x) = 4 − (x + 3)⁵ is 2
How to determine the solution for f(-3) - 2 in the function?From the question, we have the following equation that can be used in our computation:
f ( x ) = 4 − ( x + 3 )^5
To make the equation legible, we need to rewrite it
So, we have the following representation
f(x) = 4 − (x + 3)⁵
Also from the question, we have
f(-3) - 2
This means that the value of x is -3, and we calculate f(x) when x = -3
Substitute the known values in the above equation, so, we have the following representation
f(x) - 2 = 4 − (x + 3)⁵ - 2
So, we have the following equation
f(-3) - 2 = 4 − (-3 + 3)⁵ - 2
There are constants to add or subtract to both sides of the equation
However, there is no factor to multiply or divide from both sides of the equation
So, we have the following representation
f(-3) - 2 = 4 − (0)⁵ - 2
Solving further, we have
f(-3) - 2 = 4 - 2
Evaluate the difference
f(-3) - 2 = 2
Hence, the solution is 2
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Complete question
Given that f ( x ) = 4 − ( x + 3 )^5
Find f(-3) - 2
Hint: find f(-3) first and then subtract 2.
Solve these simultaneous equations.
y=x
y=x²-6
Answer:
solutions for these simultaneous equations are x = 6 and y = x = 6, or x = 1 and y = x = 1
Step-by-step explanation:
To solve these simultaneous equations, we need to find the values of x and y that satisfy both equations.
Given:
y = x
y = x² - 6
We can substitute the first equation into the second:
x = x² - 6
we can subtract x from both sides to get:
0 = x² - 7x + 6
Then we can factor it:
(x-6)(x-1) = 0
Therefore x = 6 or x = 1
So the solutions for these simultaneous equations are x = 6 and y = x = 6, or x = 1 and y = x = 1
There are two solutions, (6,6) and (1,1)
Jean Junction i elling jean at 15% off the regular price the regular price i $25 per pair what i the dicount amount
The discount amount is $3.75 ($25 x 15% = $3.75).
1.Calculate the discount: Regular price x discount percentage = discount amount
2. Plug in the values: $25 x 15% = $3.75
3.The discount amount is $3.75.
The discount amount can be calculated by taking the regular price and multiplying it by the discount percentage. For example, if the regular price is $25, and the discount percentage is 15%, the discount amount can be calculated by multiplying the regular price by the discount percentage ($25 x 15% = $3.75). Therefore, the discount amount is $3.75. This calculation can be used to calculate the discount amount for any given regular price and discount percentage.
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What is the range of the given function?
((-2, 0), (-4, -3), (2, -9), (0, 5), (-5, 7))
A (x/x = -5, -4,-2,0,2)
B (uly = -9,-3,0,5, 7)
C lr=-9, -5,-4.-3,-2.0,2,5,7
D g1g=-9,-5,-4,-3,-2,0,2,5,7
Answer: B (-9, -3, 0, 5, 7)
Step-by-step explanation:
How many solutions does -3=2x²-8x+8 have
Answer:
no real solutions
Step-by-step explanation:
the easiest method would be to graph the equation and see how many intersection points with the x-axis there are; that represents the number of solutions
when we graph the equation we first want to add 3 to each side of the equation to get the following:
y = 2x²-8x+11
what we see is that the parabola does not intersect the x-axis at all; therefore, there are no 'real' roots or solutions
Answer:
Step-by-step explanation:
x =(4-√24)/4=1-1/2√ 6 = -0.225.
Rick melted a cube and made a cone with it. The amount of melted liquid left after making the cone wa 49 cm
The volume of the cube before it was melted is greater than 49cm^3
The amount of melted liquid left after making the cone is 49 cm^3.
A cone is a three-dimensional shape that has a circular base and a single vertex or point. The amount of liquid remaining after making a cone can be calculated by comparing the volume of the cone to the volume of the cube.
The volume of a cone can be calculated using the formula:
V = (1/3) * pi * r^2 * h
Where V is the volume of the cone, pi is a mathematical constant (approximately 3.14), r is the radius of the circular base, and h is the height of the cone.
However, we don't have information about the radius or height of the cone, we only know the volume of melted liquid left after making the cone is 49 cm^3.
We can use this information to determine the volume of the cube before it was melted and compare it with the volume of the cone.
The volume of a cube can be calculated using the formula:
V = s^3
Where V is the volume of the cube, s is the length of one side of the cube.
Let's call Vc the volume of the cube before it was melted and Vcon the volume of the cone
Vc - Vcon = 49 cm^3
Therefore, the volume of the cube before it was melted is greater than 49cm^3
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What is the best method to apply in solving the equation x² 9?
The best method to apply in solving the given equation x² = 9 is the factorization method.
Factorisation is defined as the breaking or deterioration of an entity (for example a number, a matrix, or a polynomial) into a product of another entity, or factors, which when multiplied together give the original number or a matrix, etc.
In x² = 9, we need to remove the power of 2 in order to separate just x.
This implies finding the square root √x² which is equal to x.
However, there are 2 possible answers to any square root, a positive or a negative answer.
x = √9
x = ± 3
0r we can solve this equation by the splitting method.
Rearrange the equation
x² = 9
(x - 3)(x + 3) = 0
On solving, we get
x = +3 and x = -3
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When writing a piecewise function from a graph how do you determine the domain of each rule?
When writing a piecewise function from a graph, the domain of each rule is determined by the x-values of the graph.
A piecewise function is a function that is defined by different rules for different ranges of the input (x-values). Each rule corresponds to a different interval of the domain.
To determine the domain of each rule when writing a piecewise function from a graph, you can use the following steps:
Identify the intervals of the x-axis where the graph changes behavior.
Write the domain of the function for each interval.
Write the rule for each interval of the domain.
For example, if a graph has a behavior change at x = 1, x = 3, and x = 5, then the domain of the function can be written as:
f(x) = {
y1, x < 1
y2, 1 ≤ x < 3
y3, 3 ≤ x < 5
y4, x ≥ 5
}
The domain for each rule is the interval of x-values between the changes in behavior. In this example, the first rule applies to x values less than 1, the second rule applies to x values between 1 and 3, the third rule applies to x values between 3 and 5, and the fourth rule applies to x values greater than or equal to 5.
Here, note that when writing a piecewise function, it is important to make sure that there are no gaps or overlaps in the domain of the function and that the x-values where the graph changes behavior are included in the domain of at least one of the rules.
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which pair of expressions are equivalent.
a) 3(x+ 2) and 3x + 2
b) 4d+ 2e and 8d +e
c) f+f+f+g and 3fg
d) b+b+ 3c and 2b +3c
Answer:
d) b+b+3c and 2b+3c
Step-by-step explanation:
b+b=2b
2b+3c=2b+3c
Greg’s parents bought a $350.00 savings bond when he was born. When he turns 3030, the bond’s value will have increased 125%. How much will the savings bond be worth on Greg’s thirtieth birthday?
Using percentages we know that the savings bond will be worth $787.5 on Greg's 30th birthday.
What is the percentage?In mathematics, a quantity or ratio known as A% stands for a percentage of 100.
There are several different ways to depict a dimensionless connection between two numbers, including ratios, fractions, and decimals.
To represent percentages, the symbol "%" is typically written after the number.
So, we know that:
The bond is $350.
The return is 125% when Greg turns 30.
Then, the amount after she turns 30 will be as follows:
350/100 * 125
437.5
Bonds value: 437.5 + 350 = $787.5
Therefore, using percentages we know that the savings bond will be worth $787.5 on Greg's 30th birthday.
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How to restore stuff
We can see here that in order to restore stuff, here are some steps to take:
Research the item: Learn as much as you can about the item you want to restore, including its age, materials, and any history or sentimental value.Assess the damage: Determine the extent of the damage and what needs to be done to restore the item.Gather materials: Collect all the necessary materials, such as paint, glue, and any tools you may need.What is restoration?Restoration is the process of returning an object or structure to its original condition or a close approximation of it. This can include cleaning, repairing, and/or preserving items such as furniture, antiques, artwork, historic buildings, and more.
The goal of restoration is to preserve the integrity of the item and maintain its historical or sentimental value. This process can include various techniques such as carpentry, metalworking, painting, and conservation.
To still restore a stuff,
Clean the item: Use a gentle cleaner to remove any dirt or grime from the item.Repair any damage: Use glue or other adhesives to fix any broken part.Learn more about restoration on https://brainly.com/question/2843805
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How do you convert a base 2 number to base-3?
The most common way to convert a base-2 number to base-3 number is to convert a base-2 number to decimal or base-10 number first then convert base-10 number to base-3 number. You actually can directly convert it to base-3 number, but it is more complicated to do.
How to convert it base-2 number to decimal and decimal to base-3 number?There is two ways to convert base-2 number to decimal or base-10 number, using positional notation methods and doubling methods. Positional notation methods are done as follow:
First, list every digit of base-2 number in a row. Ex : 101101. The list will be 1 - 0 - 1 - 1 - 0 - 1Second, multiply each digit in a row start from the right from zero then continue with +1 for the next-left of the number. Lets continue the calculation from step 1 as follow:1 - 0 - 1 - 1 - 0 - 1
2⁵ 2⁴ 2³ 2² 2¹ 2⁰
Last, summarize all the result in step 2. Let use the previous example, the calculation will be : 2⁵ + 2⁴ + 2³ + 2² + 2¹ + 2⁰ = 45₁₀After we get base 10, then convert base-10 number to base-3 number like this:
Divide the decimal by 3 until we cant divide the number with 3 anymore.The remainder of the division will be put as a base-number 3. To write the result, start writing from the last remainder to the first reminder. Example: The result of 72₁₀ will be 2200₃. See the attached picture.Learn more about base number here
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Earth approximately 33x 107 miles from the sun. Saturn is approximately 8.87 x 108 miles from the sun. About how much farther is S
from the sun than Earth is?-
OA 794x107 miles
OB 724x10 miles
0 43×10 miles
OD 4.3x10 miles
Reset
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at a football game, a vender sold a combined totalf of 248 sodas and hot dogs. the number of sodas sold was three times the number of hot dogs sold. find the number of sodas and hot dogs sold.
Answer:
Number of soda = 186
Number of hot dog= 62
Step-by-step explanation:
Let us take number of sodas as x and number of hot dogs as y
Then
x + y = 248 [Equation 1]
and
3y = x
Hence,
3y -x = 0 [Equation 2]
By adding [Equation 1 & 2]
(+x -x) 3y + y = 248 + 0
4y = 248
4 4
y = 62
Substitute y= 62 in [Equation 1] to get
x + y = 248
x + 62 = 248
x = 248 - 62
x = 186
Is the triangle with sides 25 cm 5 cm and 24 cm a right triangle?
The triangle with sides 25cm, 5cm and 24cm is not a right triangle.
Now, According to the question:
Let us assume that :
ABC is a right triangle,
A = 25cm
B = 5 cm
C = 24 cm
We have to find if the given sides of a triangle form a right triangle.
By using Pythagoras theorem for a right triangle,
[tex]A^2 = B^2+C^2[/tex]
[tex](25)^2 = (5)^2 + (24)^2[/tex]
LHS:[tex](5)^2 + (24)^2[/tex]
= 25 + 576
= 601
RHS:[tex](25)^2[/tex]
= 625
LHS ≠ RHS
Since, the Pythagorean theorem does not apply, the given sides do not form a right triangle.
Therefore, the triangle with sides 25cm, 5cm and 24cm is not a right triangle.
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The sides of a triangle are as follows. The second side of a triangle is twice the length of the first side. The third side of the triangle is half of the second side. If the perimeter of the triangle is 36 units, what is the measure of all the sides? Write and solve an equation.
How do you write a function from a table of values?
To write a function from a table of values, you can use the data in the table to determine the pattern or relationship between the input (x) and output (y) values. Once you have identified this pattern or relationship, you can use mathematical notation to express it as a function in the form of y = f(x).
Give an example of the function from a table of values.For example, if you have a table of values that shows a linear relationship between x and y, you can use the slope-intercept form of a linear equation (y = mx + b) to write the function. You can use the values in the table to find the slope (m) and the y-intercept (b) and then plug them into the equation to get the function.
You may also use the interpolation method to estimate a function from a table of values with a non-linear relation.
It's helpful to plot the data points on a graph to help identify the pattern or relationship, and to check that the function you've written correctly represents the data in the table.
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Complete question is: How do you write a function from a table of values?
Andrew is paid 4$ per hour for the first 30 hours he works each week. he makes 5$ per hour for each hour he works over 30 hours per week. in other words, total wages= fixed wages for 30 hours + additional wages at 5$ per hour.
Part A
Write a function that gives Andrews total wages when he works more than 30 hours. use the variables w for wages and h for hours.
Answer: For the first 30 hours, Andrew will earn 4 (30) = $120. For each additional hour beyond 30 that Andrew works, he will earn 5 (h - 30). Therefore, the function that gives Andrew's total wages when he works more than 30 hours is
Step-by-step explanation: For the first 30 hours, Andrew will earn 4(30) = $120. For each additional hour beyond 30 that Andrew works, he will earn 5(h - 30). Therefore, the function that gives Andrew's total wages when he works more than 30 hours is:
w = 120 + 5(h - 30).
So, if he works 35 hours, he will earn:
120 + 5(35 - 30) = 120 + 5(5) = 120 + 25 = $145.
If he works 42 hours, he will earn:
120 + 5(42 - 30) = 120 + 5(12) = 120 + 60 = $180.
I hope this helps!
Question
Which statement describes the relationships between x and y in these two equations?
y = 10x
y = x + 10
In y = 10x the value of y is twice the value of x, and in y = x + 10 the value of y is 10 more than the value of x.
What is an Equations?
Equations are mathematical statements with two algebraic expressions on either side of an equals (=) sign. It illustrates the equality between the expressions written on the left and right sides. To determine the value of a variable representing an unknown quantity, equations can be solved. A statement is not an equation if there is no "equal to" symbol in it. It will be regarded as an expression.
y = 10x, we can say that the algebraic equation represents "the value of y is twice the value of x.
Also, for the equation y = x + 10, we can say "the value of y is two more than the value of x.
Hence, In y = 10x the value of y is twice the value of x, and in y = x + 10 the value of y is 10 more than the value of x.
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