The critical point(s) of the function f(x) = x^3 + x - 3 + 2 are determined to find the x-coordinate(s) of the local minimum or local maximum.
To find the critical point(s) of the given function, we need to first find the derivative of the function and then solve for the value(s) of x that make the derivative equal to zero.
Given function: f(x) = x^3 + x - 3 + 2
Find the derivative of the function f(x) with respect to x.
f'(x) = 3x^2 + 1
Set the derivative f'(x) equal to zero and solve for x.
3x^2 + 1 = 0
Subtract 1 from both sides of the equation.
3x^2 = -1
Divide both sides of the equation by 3.
x^2 = -1/3
Take the square root of both sides of the equation.
x = ±√(-1/3)
Since the square root of a negative number is not a real number, the function f(x) does not have any real critical points. Therefore, the critical point(s) for the function f(x) = x^3 + x - 3 + 2 is DNE (Does Not Exist) in terms of real numbers.
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a restaurant meal cost $90 and there was a 6% meals tax on the price of the meal hey a)how much was the mail tax b) what was the total price of the meal with a meal tax
A restaurant meal cost $90 and there was a 6% meals tax on the price of the meal. The meal tax was $5.40 and the total price of the meal with the meal tax was $95.40.
Find the meal tax, you need to calculate 6% of the $90 meal cost.
Convert the percentage to a decimal by dividing by 100, so 6% = 0.06.
Multiply the meal cost by the decimal. In this case, $90 × 0.06 = $5.40.
So, the meal tax was $5.40.
Find the total price of the meal with the meal tax, you need to add the meal tax to the original cost of the meal.
Add the meal tax to the original cost, so $90 + $5.40 = $95.40.
The total price of the meal with the meal tax was $95.40.
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4/625 x 625/9 cross cancellation
Answer:
Step-by-step explanation:
4/625 x 625/9 = 4 x 1 / 5 x 5 x 5 x 1 = 4/625. The cross cancellation did not change the result.
A 20ft ladder is set up that it reaches up 16ft if Christian pulls it 2 feet farther from its base how far up the side of the house is the ladder
The ladder reaches up 20ft the side of the house.
If a 20ft ladder reaches 16ft up the side, what would be the new distance of the ladder's base from the house if it is moved 2ft farther from its initial position?The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.
This theorem can be used to solve problems involving right triangles, such as finding the length of the sides or the height of an object.
In this problem, we are given the length of the ladder and the height up the side of the house that it reaches.
We can use the Pythagorean theorem to find the distance from the base of the ladder to the side of the house.
We can then use this distance and the height up the side of the house that the ladder reaches to find the length of the ladder using the Pythagorean theorem again.
Let's call the distance from the base of the ladder to the side of the house "x". We can then use the Pythagorean theorem to find the height that the ladder reaches up the side of the house.
According to the Pythagorean theorem, the length of the ladder (which is the hypotenuse of the right triangle formed by the ladder, the ground, and the side of the house) is equal to the square root of the sum of the squares of the other two sides.
So, if we let "h" be the height up the side of the house that the ladder reaches, we have:
ladder length = √(x^2 + h^2)
We know that the ladder is 20ft long and reaches up 16ft, so we can set up the equation:
20 = √(x^2 + 16^2)
Squaring both sides of the equation, we get:
400 = x^2 + 256
Subtracting 256 from both sides, we get:
144 = x^2
Taking the square root of both sides, we get:
x = 12
So the ladder is leaning against the house 12ft away from the base, and we can use the Pythagorean theorem to find the height up the side of the house that the ladder reaches:
ladder length = √(12^2 + 16^2) = √(144 + 256) = √400 = 20
Therefore, the ladder reaches up 20ft the side of the house.
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Determine the measure of arc cad thanks grade 9-10-11 it is either 240 or 260
The measure of arc CAD is either 240 or 260.
How to do measure of arc?Without additional information, it is not possible to determine the measure of arc CAD with certainty. The measure of an arc depends on the central angle that subtends it.
If the central angle is known, the measure of the arc can be calculated using the formula: measure of arc = (central angle / 360) x circumference of the circle. However, without knowing the central angle, we cannot determine the measure of arc CAD.
Therefore, we need to be provided with additional information such as the measure of another angle that is related to the central angle, or the length of a chord that subtends the arc in order to determine the central angle and the measure of arc CAD.
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Will any ramp with one angle of 4. 8 degrees have a slope ratio of 1 : 12?
Yes, any ramp with an angle of 4.8 degrees will have a slope ratio of 1:12.
The slope ratio is the ratio of the vertical rise to the horizontal run of the ramp, and it is equivalent to the tangent of the angle of inclination of the ramp.
The tangent of 4.8 degrees is approximately 0.0084, which means that for every 1 unit of vertical rise, there is 0.0084 units of horizontal run. To convert this to a ratio, we can multiply both sides by 100 to get:
1 unit of rise : 100 x 0.0084 = 0.84 units of run
Simplifying this ratio by dividing both sides by 0.84, we get:
1 unit of rise : 1.19 units of run
which is equivalent to a slope ratio of 1:12 (since 12 = 1/0.084). Therefore, any ramp with an angle of 4.8 degrees will have a slope ratio of 1:12.
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Ryan buys some jumpers to sell on a stall.
He spends £130 buying 40 jumpers.
He sells 80% of the jumpers for £12 each.
He then puts the rest of the jumpers on a Buy one get one half price offer.
He manages to sell half the remaining jumpers using this offer.
How much profit does Ryan make?
Answer: £326
Step-by-step explanation:
Step 1: Calculate the cost per jumper
To find out how much Ryan spent on each jumper, we divide the total cost by the number of jumpers.
[tex]\frac{130}{40} = 3.25[/tex]
This gives us a cost of £3.25 per jumper.
Step 2: Calculate the revenue from selling 80% of the jumpers
Ryan sells 80% of the 40 jumpers, so:
[tex]\text{0.8 x 40 = 32}[/tex]
So he sold 32 Jumpers.
He sells each jumper for £12:
[tex]\text{32 x 12 = 384}[/tex]
So his revenue from selling these jumpers is £384
Step 3: Calculate the revenue from selling the remaining jumpers on the Buy one get one half price offer
Ryan has 8 jumpers left after selling 80% of them. He puts these on a Buy one get one half price offer, which means that for every jumper sold at full price, he sells another one at half price.
This means that he sells 4 jumpers at full price (£12 each) and 4 jumpers at half price (£6 each).
His revenue from selling these jumpers is:
[tex]\text{(4 x 12) + (4 x 6) = 72}[/tex]
Step 4: Calculate the total revenue
Ryan's total revenue is the sum of the revenue from selling 80% of the jumpers and the revenue from selling the remaining jumpers on the Buy one get one half price offer.
This is:
[tex]\text{384 + 72 = 456}[/tex]
So Ryan's total revenue is £456
Step 5: Calculate the total cost
Ryan's total cost is the amount he spent on buying the jumpers, which is £130.
Step 6: Calculate the profit
Ryan's profit is the difference between his total revenue and his total cost:
[tex]\text{456 - 130 = 326}[/tex]
Therefore, Ryan makes a profit of £326.
HELP! BRAINLIST! THIS IS DUE IT IS END OF UNIT ASSESSMENT
The surface area of the cone is approximately 793.10 cm².
What is cone?
A cone is a three-dimensional geometric shape that tapers smoothly from a flat base (usually circular) to a point called the apex or vertex.
What is area of cone?
The surface area of a cone is given by the formula:
Surface Area = πr² + πrℓ
where r is the radius of the circular base and ℓ is the slant height of the cone.
According to given information:To find the surface area of a cone, we need to find the area of its base and the area of its lateral surface and then add them together.
The formula for the lateral surface area of a cone is given by:
L = πrℓ
where r is the radius of the base and ℓ is the slant height of the cone.
The formula for the area of the base of a cone is given by:
B = πr²
where r is the radius of the base.
Given the slant height ℓ = 19 and the radius r = 9, we can find the lateral surface area of the cone as follows:
L = πrℓ
= π(9)(19)
≈ 538.63 cm²
Next, we can find the area of the base of the cone as follows:
B = πr²
= π(9)²
≈ 254.47 cm²
Therefore, the surface area of the cone is:
A = B + L
≈ 793.10 cm²
So, the surface area of the cone is approximately 793.10 cm².
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Roger logs the number of miles he runs each week. The mean number of miles Roger ran in October was 30. 2 miles and the mean number of miles Roger ran in November was 25. 6. The mean absolute deviation for both months is 2. What is the difference between the means expressed as a multiple of the mean absolute deviation?
The difference between the means expressed as a multiple of the mean absolute deviation is 2.3.
How to find the difference between the means expressed as a multiple of the mean absolute deviation?To find the difference between the means expressed as a multiple of the mean absolute deviation, we need to calculate the absolute difference between the two means and divide it by the mean absolute deviation.
The absolute difference between the means is:
|30.2 - 25.6| = 4.6
To express this difference as a multiple of the mean absolute deviation, we divide it by the mean absolute deviation:
4.6 / 2 = 2.3
Therefore, the difference between the means expressed as a multiple of the mean absolute deviation is 2.3.
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Sarah wants to attend a private college with a yearly tuition of $31,000. Room and board costs are estimated to be $12,000 per year, and the cost of books and supplies is estimated to be $2,000. Assuming she receives no financial aid, how much will it cost her to get a four-year degree from this college?
Sarah wants to attend a private college with a yearly tuition of $31,000. Room and board costs are estimated to be $12,000 per year, and the cost of books and supplies is estimated to be $2,000. To calculate the total cost of her four-year degree, follow these steps:
1. Add the yearly costs together: $31,000 (tuition) + $12,000 (room and board) + $2,000 (books and supplies) = $45,000 per year.
2. Multiply the yearly cost by the number of years in the degree program: $45,000 * 4 = $180,000.
Assuming she receives no financial aid, it will cost Sarah $180,000 to get a four-year degree from this private college.
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Find the perimeter of the polygon with the vertices G(2, 4), H(2,-3), J(-2,-3), and K(-2, 4).
The perimeter is ___ units.
Check the picture below.
One of the flights was 350 miles and its residual was -
105. 0. What was the fare for this flight?
Based on data taken from airline fares and distances
flown, it is determined that the equation of the least-
squares regression line is ý = 102. 50 +0. 65x, where
ý is the predicted fare and x is the distance, in miles.
O $102. 50
O $435. 00
O $225. 00
O $330. 00
The fare for this flight would be: $225.
How we get the fare for the flight?To determine the fare for the flight that was 350 miles with a residual of -105, we need to use the least-squares regression equation:
ý = 102.50 + 0.65x
where ý is the predicted fare and x is the distance in miles.
We know that the distance for this flight is 350 miles, so we can substitute x = 350 into the equation:
ý = 102.50 + 0.65(350)
ý = 102.50 + 227.50
ý = 330
Therefore, the predicted fare for this flight is $330.
The residual of -105 means that the actual fare for this flight was $105 less than the predicted fare based on the regression line. Therefore, the actual fare for this flight would be:
$330 - $105 = $225
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Solve the separable differential equation for u. du dt e2u+9t Use the initial condition u(0) = 4. = U =
The solution to the differential equation with the given initial condition is:
[tex]u = -1/2 * ln(-2/9 * e^{(9t)} + 4/9 * e^{(-8)} + 2/9)[/tex]
How to solve the separable differential equation?To solve equation, we can separate the variables and write:
[tex]1/e^{(2u)} du = e^{(9t)} dt[/tex]
Integrating both sides, we get:
[tex]\int 1/e^{(2u)} du = \int e^{(9t)} dt[/tex]
Integrating the left side requires the substitution v = 2u, dv/du = 2, and du = dv/2, which gives:
[tex]\int 1/e^{(2u)} du = \int 1/2 * 1/e^v dv = -1/2 * e^{(-2u)}[/tex]
Integrating the right side gives:
[tex]\int e^{(9t)} dt = 1/9 * e^{(9t)}[/tex]
Substituting these integrals back into the original equation, we get:
[tex]-1/2 * e^{(-2u)} = 1/9 * e^{(9t)} + C[/tex]
where C is the constant of integration.
We can solve for the constant of integration using the initial condition u(0) = 4:
[tex]-1/2 * e^{(-24)} = 1/9 * e^{(90)} + C[/tex]
[tex]-1/2 * e^{(-8)} = 1/9 + C[/tex]
[tex]C = -1/2 * e^{(-8)} - 1/9[/tex]
Therefore, the solution to the differential equation [tex]du/dt = e^{(2u+9t)}[/tex] with initial condition u(0) = 4 is:
[tex]-1/2 * e^{(-2u)} = 1/9 * e^{(9t)} - 1/2 * e^{(-8)} - 1/9[/tex]
Solving for u, we get:
[tex]e^{(-2u)} = -2/9 * e^{(9t)} + 4/9 * e^{(-8)} + 2/9[/tex]
Taking the natural logarithm of both sides, we get:
[tex]-2u = ln(-2/9 * e^{(9t)} + 4/9 * e^{(-8)} + 2/9)[/tex]
Dividing by -2, we get:
[tex]u = -1/2 * ln(-2/9 * e^{(9t)} + 4/9 * e^{(-8)} + 2/9)[/tex]
Therefore, the solution to the differential equation with the given initial condition is:
[tex]u = -1/2 * ln(-2/9 * e^{(9t)} + 4/9 * e^{(-8)} + 2/9)[/tex]
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Three times a year a camera shop has a sale on packages of batteries. In the second month of the year the packages are 3 for $4.49. In April they are 5 for $7.39 and in the last month of the year, they are 4 for $5.88. List the months in order from the smallest price per package to the largest price per package.
Answer:
The order from smallest to largest price per package is: December, April, February.
Step-by-step explanation:
For the sale in February:
- Price per package = $4.49 ÷ 3 = $1.50 per package
For the sale in April:
- Price per package = $7.39 ÷ 5 = $1.48 per package
For the sale in December:
- Price per package = $5.88 ÷ 4 = $1.47 per package
We told Gavin not to run but he did anyway he took 18 steps from second base got caught and took 7 steps back then 3 steps forward 5 steps back and 11 steps forward and 4 steps back and was tagged out halfway between second and third base how many steps is it from second base to third pls help
it is 16 steps from second base to third base .we can get this answer by
solving the logic given in the question .we need to add up the number of steps
what is add up ?
"Add up" means to calculate the total of two or more numbers or quantities by combining them together. It involves the mathematical operation of addition, which is the process of finding the sum of two or more numbers. For example, if you add up the numbers 3, 5, and 7, t
In the given question,
To find out how many steps it is from second base to third base, we need to add up the number of steps Gavin took in each direction.
Starting at second base, he took 18 steps forward to get caught, and then took 7 steps back. This leaves him 11 steps forward from second base.
Next, he took 3 more steps forward, for a total of 14 steps forward from second base. But then he took 5 steps back, leaving him 9 steps forward from second base.
Then he took 11 more steps forward, for a total of 20 steps forward from second base. But then he took 4 steps back, leaving him 16 steps forward from second base.
Finally, he was tagged out halfway between second and third base. Since he was 16 steps forward from second base, and halfway between second and third base, we can assume that third base is 16 steps away from second base.
Therefore, it is 16 steps from second base to third base.
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Help with problem in photo! Find the perimeter!
The perimeter of the shape is 53.7 units
What is perimeter ?Perimeter is a math concept that measures the total length around the outside of a shape.
A theorem of circle geometry states that the tangent from a point on a circle are equal.
Therefore the base sides is calculated as
9.9 + 3.2
= 13.1
since the perimeter is the addition of all the sides then;
P = 13.1 + 21.9 + 18.7
P = 53.7
therefore the perimeter of the triangle is 53.7
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a)cos 165 in terms of sine and cosine of acute angle
Cos 165 in terms of sine and cosine of acute angle would give cos(165) = -(1 + √3) / (2√2).
How to find the cosine ?To find the cosine of 165 degrees in terms of sine and cosine of an acute angle, we can use the cosine angle addition formula:
cos(A + B) = cos(A)cos(B) - sin(A)sin(B)
Since 120 degrees is in the second quadrant, the cosine is negative, and the sine is positive:
cos(120) = -cos(60) and sin(120) = sin(60)
cos(165) = -cos(60)cos(45) - sin(60)sin(45)
Now we can plug in the values of the trigonometric functions:
cos(165) = - (1/2) x (1/√2) - (√3/2) x (1/√2)
cos(165) = -(1 + √3) / (2√2)
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I need help hurry!!!
Answer: 8
Step-by-step explanation:
okay so do 17 x 17 - 15 x 15
then to that result do :
squared root.
I need this by the end of the day may someone help me only have 13 points left
There are different ways a person can make up a story about a word problem. The square root of 81 - 7 is 2. Hence the story is given below.
What is the story of the word problem?The hypothetical story goes like this: Mia was trying to figure out the length of the missing side of a square garden bed. She knew that the total area of the garden bed was 81 square feet. She also knew that she had already planted in a section of the garden bed that was 7 feet wide.
So, what will be the length of the missing side of the garden bed if Mia wants to make sure it is completely filled with soil. In order to solve this problem, Mia used the equation: the square root of 81-7=2. She plugged in the values she knew and solved for the missing side length. Therefore, The solution will be:= ✓81 - 7= 9 - 7= 2
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A story for the word problem is that what will be the length of the missing side of a square garden when the total area is 81 feet² and the width was 7 feet wide?
How to explain the square rootFrom the information, we are seeking a story problem that has the equation had the square root of 81 - 7 = 2.
This will be written as story for the word problem is that what will be the length of the missing side of a square garden when the total area is 81 feet ² and the width was 7 feet wide?
The length will be calculated thus :
= √ 81 - 7
= 9 - 7
= 2
The length of the missing side is 2 feet.
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I seriously need help with this please anyone.
1. Complete the Pythagorean triple. (24,143, ___)
2. Given the Pythagorean triple (5,12,13) find x and y
3. Given x=10 and y=6 find associated Pythagorean triple
4. Is the following a possible Pythagorean triple? (17,23,35)
Answer:
no it is not possible
Step-by-step explanation:
Question 3 Next ſsin"" e cos"" Evaluate the indefinite integral xdu
But there seems to be some missing information in your question. Please provide more context or details so that I can assist you accurately.
Hi! I'd be happy to help you evaluate the indefinite integral. Based on the provided terms and information, it seems like you want to evaluate the following integral:
∫x * sin(e * cos(x)) dx
To solve this integral, we can use integration by parts, which is defined as:
∫u dv = u * v - ∫v du
Let's choose u = x and dv = sin(e * cos(x)) dx. Then, we need to find du and v:
du = dx
v = ∫sin(e * cos(x)) dx
Unfortunately, the integral for v does not have a simple closed-form expression. However, you can use numerical methods or software (like Wolfram Alpha) to approximate it. Once you have an approximation for v, you can plug it back into the integration by parts formula to obtain an approximation of the original integral:
∫x * sin(e * cos(x)) dx ≈ x * v - ∫v dx
Keep in mind that this is an indefinite integral, so don't forget to add the constant of integration, C, to your final answer.
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Mr linden drives from his home to his office every day. if he drives at an average speed of 70 km/h for 45 min, what is the distance of the journey from his home to his office?
If he drives at an average speed of 70 km/h for 45 min, the distance of the journey from Mr. Linden's home to his office is 52.5 km.
To find the distance of Mr. Linden's journey from his home to his office, we can use the formula:
Distance = Speed x Time
Since Mr. Linden drives at an average speed of 70 km/h for 45 minutes, we first need to convert the time to hours:
45 minutes = 0.75 hours
Now, we can plug in the values we have into the formula:
Distance = 70 km/h x 0.75 hours
Distance = 52.5 km
Therefore, the distance of the journey from Mr. Linden's home to his office is 52.5 km.
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David has 3
1
2
cups of blueberries. He uses
1
4
of a cup of blueberries to make a breakfast smoothie. He uses
1
2
of the remaining blueberries to make blueberry pancakes. How many cups of blueberries does he use for the pancakes?
Write your answer as a whole number, fraction, or mixed number. Simplify any fractions
The fraction, David used 13/8 cups of blueberries for the pancakes.
Let's solve it step-by-step using the given information.
1. David has 3 1/2 cups of blueberries.
2. He uses 1/4 cup for a breakfast smoothie.
3. He uses 1/2 of the remaining blueberries for pancakes.
Step 1: Calculate the remaining blueberries after making the smoothie.
3 1/2 - 1/4 = (7/2) - (1/4)
To subtract the fractions, they need a common denominator, which in this case is 4.
(7/2) * (2/2) - (1/4) = (14/4) - (1/4) = 13/4 cups
Step 2: Calculate the amount of blueberries used for the pancakes.
David uses 1/2 of the remaining blueberries for the pancakes, so:
(13/4) * (1/2) = 13/8 cups
David uses 13/8 cups of blueberries for the pancakes.
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15 Points! 15 Points 15 Points!
A student is graduating from college in 12 months but will need a loan in the amount of $10,720 for the last two semesters. The student may receive either an unsubsidized Stafford Loan or a PLUS Loan. The terms of each loan are:
Unsubsidized Stafford Loan: annual interest rate of 5. 95%, compounded monthly, and a payment grace period of six months from time of graduation
PLUS loan: annual interest rate of 6. 55%, compounded monthly, with a balance of $11,443. 63 at graduation
Which loan will have a lower balance, and by how much, at the time of repayment?
The Stafford loan will have a lower balance by $485. 06 at the time of repayment.
The PLUS loan will have a lower balance by $485. 06 at the time of repayment.
The Stafford loan will have a lower balance by $274. 54 at the time of repayment.
The PLUS loan will have a lower balance by $274. 54 at the time of repayment
The Stafford loan will have a lower balance by $272.54 at the time of repayment.
For the Stafford Loan, the principal is $10,720 and the interest rate is 5.95% compounded monthly, so the monthly interest rate is 0.0595/12 = 0.00495833.
After 12 months, the balance of the loan will be:
$10,720(1 + 0.00495833)¹² = $11,204.60
After the time of six-month grace period, the balance will be:
$11,204.60(1 + 0.00495833)⁶ = $11,689.66
For the PLUS Loan, the principal is $11,443.63 and the interest rate is 6.55% compounded monthly, so the monthly interest rate is 0.0655/12 = 0.00545833.
After 12 months, the balance of the loan will be:
$11,443.63(1 + 0.00545833)¹² = $11,962.20
Therefore, the Stafford Loan will have a lower balance at the time of repayment by:
$11,962.20 - $11,689.66 = $272.54
Hence, the Stafford loan will have a lower balance by $272.54 at the time of repayment.
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f(x)=x^2+6x+8
Rewrite the function into vertex form
y=(x+3)^2-1
have a good day :)
Answer: F(x) = (x + 3)^2 - 1
Step-by-step explanation:
The graph of a linear function is shown on the grid.
What is the rate of change of y with respect tox for this
function?
A. 7/9
B. 3/4
C. -7/9
D. -3/4
Answer: D)-3/4
Step-by-step explanation: Rate of change of y with respect to x implies the following formula...(y2-y1)/(x2-x1)...which is also the gradient of the line, you can substitute the value in accordance with the points already ahown in the grid to get, (7-1)/(-4-4)=-3/4
Question 1 (Essay Worth 30 points) 2. (10.07 HC) Consider the Maclaurin series g(x)=sin x = x - 3! + x х" х9 7! 9! + x2n+1 ... + Σ (-1). 2n+1 5! n=0 Part A: Find the coefficient of the 4th degree term in the Taylor polynomial for f(x) = sin(4x) centered at x = (10 points) Part B: Use a 4th degree Taylor polynomial for sin(x) centered at x = to estimate g(0.8) out to five decimal places. Explain why your answer is so close to 1. (10 points) x2n+1 263 Part C: The series { (-1)" has a partial sum S. when x = 1. What is an interval, |S - S5l = R5| for which the actual sum exists? 2n +1 315 Provide an exact answer and justify your conclusion. (10 points) n=0
Part A: The coefficient of the 4th degree term in the Taylor polynomial for f(x) = sin(4x) centered at x = 0 is -1/3! = -1/6.
Part B: Using a 4th degree Taylor polynomial for sin(x) centered at x = 0, we can write g(x) = sin(0.8) ≈ P4(0.8), where P4(0.8) is the 4th degree Taylor polynomial for sin(x) evaluated at x = 0.8.
Evaluating P4(0.8) using the formula for the Taylor series coefficients of sin(x), we get P4(0.8) = 0.8 - 0.008 + 0.00004 - 0.0000014 ≈ 0.78333. This estimate is very close to 1 because sin(0.8) is close to 1, and the Taylor series for sin(x) converges very rapidly for values of x close to 0.
Part C: The series { (-1)n / (2n + 1) } has a partial sum S when x = 1. To find an interval |S - S5| = R5| for which the actual sum exists, we can use the alternating series test. The alternating series test states that if the terms of a series alternate in sign, decrease in absolute value, and approach zero, then the series converges.
Since the terms of the series { (-1)n / (2n + 1) } alternate in sign and decrease in absolute value, we know that the series converges. To find an interval |S - S5| = R5|, we can use the remainder formula for alternating series, which states that |Rn| ≤ a_n+1, where a_n+1 is the first neglected term in the series.
Since the terms of the series decrease in absolute value, we know that a_n+1 ≤ |a_n|. Therefore, we have |R5| ≤ |a6| = 1/7!, which means that the actual sum of the series exists in the interval S - 1/7! ≤ S5 ≤ S + 1/7!. Therefore, an interval for which the actual sum exists is [S - 1/7!, S + 1/7!].
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The number of hours julie practices her violin each week, y, is 3 hrs more than the numbers of hours she studies, x. write an equation to show the relationship of the two activities.
The equation is y = x + 3 which shows the relationship of the two activities.
The equation to show the relationship between the number of hours Julie practices her violin each week (y) and the number of hours she studies (x) is:
y = x + 3
This means that the number of hours Julie practices her violin each week is equal to the number of hours she studies, plus three additional hours.
A linear equation is an equation that represents a straight line on a graph. It can be written in the form:
y = mx + b
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help me please Which choice below is NOT a possible feature of a conjecture?
Group of answer choices
A) It’s a declarative statement
B) It’s a falsehood
C) It’s the truth.
D) It’s a question
b. use the overhead rate in (a) to determine the amount of total and per-unit overhead allocated to each of the three products, rounded to the nearest dollar.
The amount of total and per-unit overhead allocated to each of the three products using overhead rate is equal to,
Total Per Unit Factory Overhead , Cost Factory Overhead Cost
Flutes $530 $1,060,000
Clarinets $795 $1,192,500
Oboes $397.5 $695,625
Total $1,722.5 $2,948,125
Budgeted factory overhead cost = $2,948,125
The single plantwide overhead rate
= Dividing the budgeted factory overhead cost by the total budgeted direct labor hours.
For this,
Flutes= 2,000×2
= 4,000 hours
Clarinets= 1,500×3
= 4,500 hours
Oboes= 1,750×1.5
= 2,625 hours
Total direct labor hours = 11,125
Substitute the value we have,
⇒ Single plantwide overhead rate = $2,948,125 / (2,000 x 2.0 + 1,500 x 3.0 + 1,750 x 1.5)
= $2,948,125 / 11,125
= $265 per direct labor hour
To allocate overhead to each product
=Multiply the overhead rate by the budgeted direct labor hours per unit for each product.
Substitute the value we have,
Flutes,
$265 x 2.0 = $530 total overhead cost, $265 per unit
Clarinets,
$265 x 3.0 = $795 total overhead cost, $265 per unit
Oboes,
$265 x 1.5 = $397.5 total overhead cost, $265 per unit
And
Total factory overhead cost allocated = Estimated manufacturing overhead rate× Actual amount of allocation base
For,
Flutes
= 4,000× 265
= $1,060,000
Clarinets
= 4,500×265
= $1,192,500
Oboes
= 2,625×265
= $695,625
This implies,
The total and per-unit overhead allocated to each product, rounded to the nearest dollar is,
Total Per Unit Factory Overhead , Cost Factory Overhead Cost
Flutes $530 $1,060,000
Clarinets $795 $1,192,500
Oboes $397.5 $695,625
Total $1,722.5 $2,948,125
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The above question is incomplete, the complete question is:
Bach Instruments Inc. makes three musical instruments: flutes, clarinets, and oboes. The budgeted factory overhead cost is $2,948,125. Overhead is allocated to the three products on the basis of direct labor hours. The products have the following budgeted production volume and direct labor hours per unit:
Budgeted Production Volume Direct Labor Hours Per Unit
Flutes 2,000 units 2.0
Clarinets 1,500 3.0
Oboes 1,750 1.5
a. Determine the single plantwide overhead rate.
$ per direct labor hour
b. Use the overhead rate in (a) to determine the amount of total and per-unit overhead allocated to each of the three products, rounded to the nearest dollar.
Total Per Unit
Factory Overhead Cost Factory Overhead Cost
Flutes $ $
Clarinets
Oboes
Total $
A mechanic had412 gallons of motor oil at the start of the day. At the end of the day, only 5 pints remained
The mechanic used 412 - 411.375 = 0.625 gallons of motor oil during the day.
A mechanic had 412 gallons of motor oil at the start of the day and ended up with only 5 pints of oil remaining.To solve this problem, we need to convert both measurements to the same unit.
1 gallon = 8 pints (since there are 8 pints in a gallon)
So the mechanic started with:
412 gallons * 8 pints/gallon = 3,296 pints
And ended with:
5 pints
To find how much motor oil the mechanic used during the day, we can subtract the ending amount from the starting amount:
3,296 pints - 5 pints = 3,291 pints
To convert this back to gallons, we divide by 8:
3,291 pints / 8 pints/gallon = 411.375 gallons (rounded to three decimal places)
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