a boat traveled 210 miles downstream and back. the trip downstream took 10 hrs. the trip back took 70 hours.
Answers
The speed of the boat in still water is 12 miles per hour, and the speed of the current is 9 miles per hour.
To solve this problem, we can use the concept of relative speed and the formula: Distance = Speed x Time.
Let's denote the speed of the boat in still water as 's' (in miles per hour) and the speed of the current as 'c' (in miles per hour).
When the boat is traveling downstream (with the current), its effective speed is increased by the speed of the current. Therefore, the speed downstream is s + c.
Similarly, when the boat is traveling upstream (against the current), its effective speed is decreased by the speed of the current. Therefore, the speed upstream is s - c.
Given:
Distance downstream = 210 miles
Time downstream = 10 hours
Using the formula: Distance = Speed x Time, we can write the equation for the downstream journey as:
210 = (s + c) x 10
Simplifying the equation, we have:
21 = s + c
Similarly, for the upstream journey:
Distance upstream = 210 miles
Time upstream = 70 hours
The equation for the upstream journey becomes:
210 = (s - c) x 70
Simplifying:
3 = s - c
Now we have a system of equations:
21 = s + c
3 = s - c
We can solve this system of equations to find the values of 's' and 'c'. Adding the two equations together, we get:
24 = 2s
s = 12
Substituting the value of 's' back into either equation, we find:
3 = 12 - c
c = 9
Therefore, the speed of the boat in still water is 12 miles per hour, and the speed of the current is 9 miles per hour.
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a boat traveled 210 miles downstream and back. the trip downstream took 10 hrs. the trip back took 70 hours. Use the concept of relative speed to solve this problem.
Related Questions
Diane works at a gardening store, and today she is helping assemble gas trimmers to be sold. An employee from an earlier shift already assembled 7 trimmers, and Diane can assemble 4 trimmers per hour.
Write an equation that shows how the total number of trimmers assembled, y, depends on the number of hours Diane spends assembling them, x.
y = _______
Answers
Answer:4x+7
Step-by-step explanation:
The linear function for the number of trimmers assembled is:
y = 7 + 4x.
--------------------------------
A linear function has the following format:
\(y = ax + b\)
In which:
a is the rate of change.b is the fixed amount.--------------------------------
In an earlier shift, 7 trimmers had already been produced, thus 7 is the fixed amount, that is, \(b = 7\).Diane assembles 4 trimmers per hour, thus the rate of change is 4, that is, \(a = 4\)The amount of trimmers y produced after x hours is given by:\(y(x) = 4x + 7\)
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pls help if you can asap!!!!
Answers
Answer: x= 6
Step-by-step explanation:
Since the shape is a parallelogram, the angles will either be equal to each other or add up to 180.
You can see they do not look the same so they add up to equal 180
12x + 3 +105 = 180
12x + 108 = 180
12x = 72
x = 6
Suppose that the spun racquet lands with the label facing up 48 times out of 100. Explain, as if to a friend who has not studied statistics, why this result does not constitute strong evidence against believing that the spinning process is fair.
Answers
The result of 48 label-up spins out of 100 might be surprising, it is not strong evidence against believing that the spinning process is fair.
Imagine you have a racquet and you want to test if it's fair, meaning that it has an equal chance of landing with the label facing up or down when you spin it. You decide to spin the racquet 100 times and count how many times it lands with the label facing up. Surprisingly, you find that it landed with the label facing up 48 times out of the 100 spins.
Now, you might think that this result suggests that the spinning process is not fair, since it landed with the label facing up less than half of the time. However, this is not necessarily the case. In fact, this result alone is not enough to conclude that the spinning process is unfair or biased.
To understand why, we need to consider the concept of probability. Even if a process is completely fair, it is still possible to observe outcomes that are unlikely or even surprising. For example, if you flip a fair coin 10 times, it's possible (although unlikely) to get heads 9 or 10 times in a row.
Similarly, even if the spinning process is completely fair, it's possible (although unlikely) to observe 48 or fewer label-up spins out of 100. In fact, if the spinning process is fair, the probability of observing 48 or fewer label-up spins out of 100 is about 12%, which is not a very small probability.
Therefore, while the result of 48 label-up spins out of 100 might be surprising, it is not strong evidence against believing that the spinning process is fair. To make a stronger case for or against fairness, we would need to gather more data and perform statistical tests to evaluate the evidence.
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simplify Cos(a+b) +Cos(a+b)
Answers
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=2cos()cos()
(12x+2) what is the answer
Answers
Answer:
26
Step-by-step explanation:
Answer: If you are wanting the expression factored the answer would be 2(6x+1)
Estimate the instantaneous rate of change of h(t)=3t2−4 at the point: t=−3 In other words, choose x-values that are getting closer and closer to -3 and compute the slope of the secant lines at each value. Then, use the pattern you see to estimate the slope of the tangent line. Your answer should be accurate to at least 2 decimal places.
Answers
The estimated instantaneous rate of change of h(t) = 3t^2 - 4 at t = -3 is approximately 22.97. To estimate the instantaneous rate of change of the function h(t) = 3t^2 - 4 at the point t = -3, we can calculate the slope of the secant lines formed by choosing x-values that are getting closer to -3.
Let's choose x-values that are approaching -3: -2.9, -2.99, -2.999, and so on. We will calculate the corresponding function values and find the slopes of the secant lines formed by these points.
For t = -2.9:
h(-2.9) = 3(-2.9)^2 - 4 = 23.81 - 4 = 19.81
For t = -2.99:
h(-2.99) = 3(-2.99)^2 - 4 = 26.7301 - 4 = 22.7301
For t = -2.999:
h(-2.999) = 3(-2.999)^2 - 4 = 26.973001 - 4 = 22.973001
We can observe that as the x-values get closer to -3, the function values are approaching 22.97.
Using the pattern we see in the slopes of the secant lines, we can estimate the slope of the tangent line at t = -3 to be approximately 22.97.
Therefore, the estimated instantaneous rate of change of h(t) = 3t^2 - 4 at t = -3 is approximately 22.97.
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how many integer values of x are there so that x, 5, and 8 could be the lengths of the sides of a triangle?
Answers
The integer value of x is 6.
What is a side of a triangle?
The three vertices of a triangle connect the straight lines that make up its sides. In other terms, we can state that a triangle's sides are line segments that converge at the triangle's vertices.
Here, we have
Given,
the lengths of the sides of a triangle are x, 5, and 8.
x² + 5² < 8²
x² + 25 < 64
x² < 39, now perfect squares less than 39 are 36, 25, 16, 9, 4, 1.
x² + 5² = 8²
x² + 25 = 64
x² = 39, No integer values.
x² + 5² > 8²
x² + 25 > 64
x² + > 39
Here the possible integer values are infinite.
Hence, the integer value of x is 6.
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The normal to the curve x2 + 2xy - 3y2 = 0 at (1, 1) (a) does not meet the curve again (b) meets the curve again in the second quadrant (c) meets the curve again in the third quadrant (d) meets the curve again in the fourth quadrantRead more on Sarthaks.com - https://www.sarthaks.com/185106/the-normal-to-the-curve-x-2-2xy-3y-2-0-at-1-1
Answers
The normal to the curve x^2 + 2xy - 3y^2 = 0 at (1, 1) meets the curve again in the third quadrant.
Thus, the correct option is :
(c) meets the curve again in the third quadrant
To find the normal to the curve x^2 + 2xy - 3y^2 = 0 at (1, 1), we'll first find the gradient of the curve at the point (1, 1):
∂/∂x (x^2 + 2xy - 3y^2) = 2x + 2y
∂/∂y (x^2 + 2xy - 3y^2) = 2x - 6y
So, at (1, 1), the gradient is:
∇f(1, 1) = (4, -4)
The normal to the curve at (1, 1) is then perpendicular to this gradient vector.
The equation of the normal line passing through (1, 1) is then:
(y - 1) = -1/1(x - 1)
y = -x + 2
Substituting y = -x + 2 into the equation of the curve x^2 + 2xy - 3y^2 = 0, we get:
x^2 + 2x(-x + 2) - 3(-x + 2)^2 = 0
x^2 - 4x - 3(x^2 - 4x + 4) = 0
-2x^2 + 16x - 12 = 0
x^2 - 8x + 6 = 0
Using the quadratic formula, we find that the solutions for x are:
x = 4 ± √10
Therefore, the normal to the curve x^2 + 2xy - 3y^2 = 0 at (1, 1) meets the curve again in the third quadrant, and the answer is (c).
The correct question should be :
Choose the correct option about the curve x^2 + 2xy - 3y^2 = 0 at (1, 1) :
(a) does not meet the curve again
(b) meets the curve again in the second quadrant
(c) meets the curve again in the third quadrant
(d) meets the curve again in the fourth quadrant
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Say you are considering two loans. Loan F has a nominal interest rate of 5. 66%, compounded monthly. Loan G has a rate of 6. 02%, compounded semiannually. Which loan will give the lower effective interest rate, and how much lower will it be? a. Loan G’s effective rate will be 0. 091 percentage points lower than Loan F’s. B. Loan G’s effective rate will be 0. 058 percentage points lower than Loan F’s. C. Loan F’s effective rate will be 0. 302 percentage points lower than Loan G’s. D. Loan F’s effective rate will be 0. 149 percentage points lower than Loan G’s.
Answers
Answer:
loan F = 5.66%
loan G =6.02
then loan F gives lower interest rate
Loan F's effective rate will be 0.302 percentage points lower than Loan G's.
Given that,
Loan F has a nominal interest rate of 5.66%, compounded monthly.
Loan G has a rate of 6.02%, compounded semiannually.
We have to determine,
Which loan will give the lower effective interest rate, and how much lower will it be?
According to the question,
The lower effective rate is determined by the following formula.
\(P = \left(1+\dfrac{r}{n}\right)^n - 1\)
Where; r is the interest rate,
And n is the number of compounding periods per year.
Loan F has a nominal interest rate of 5.66%, compounded monthly.
\(\rm P = \left(1+\dfrac{0.0566}{12}\right)^{12} - 1\\\\P = \left(1+\0.0047\right)^{12} - 1\\\\P = \left(1.0047\right)^{12} - 1\\\\P = 1.0.581-1\\\\P = 0.0581\)
And Loan G has a rate of 6.02%, compounded semiannually.
\(\rm P = \left(1+\dfrac{0.0602}{2}\right)^{2} - 1\\\\P = \left(1+\0.0301\right)^{2} - 1\\\\P = \left(1.0301\right)^{12} - 1\\\\P = 1.0611-1\\\\P = 0.0611\)
The difference between the amount of Loan F and Loan G is,
= 0.0611 - 0.0581 = 0.003
Converting to percentage gives : 0.003 × 100 = 0.3%
Hence, Loan F's effective rate will be 0.302 percentage points lower than Loan G's.
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Will a large-sample confidence interval be valid if the population from which the sample is taken is not normally distributed? explain
Answers
A normal distribution is a type of continuous probability distribution for a real-valued random variable in statistics.
Yes, the large-sample confidence interval will be valid.
What is meant by normal distribution?A normal distribution is a type of continuous probability distribution for a real-valued random variable in statistics.
The normal distribution, also known as the Gaussian distribution, is a symmetric probability distribution about the mean, indicating that data near the mean occur more frequently than data far from the mean.
The confidence interval will be valid regardless of the shape of the population distribution as long as the sample is large enough to satisfy the central limit theorem.
What does a large sample confidence interval for a population mean?A sample is considered large when n ≥ 30.
By 'valid', it means that the confidence interval procedure has a 95% chance of producing an interval that contains the population parameter.
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MsDaily can grade 54 essays in 6 hours. Which of the following rates represent the number of essays per hour ms. Daley can grade?
A-19 of an essay
B-one essay can be graded in 9 hours
C-it takes 9 hours per essay to grade
D- 9 essays can be graded per hour
Answers
Step-by-step explanation:
Rate = 54/6
= 9 essays per hour
Answer:
D- 9 essays can be graded per hour
Step-by-step explanation:
54 / 6= 9
By how much is sum of a power 4-6a²b²+ b power 4 and -2a power 4 + 5a² b²+3b power 4 greater than-a power 4-a square b square -4b power 4?
Answers
Answer:
I dont quite understand the question
You are interested in playing a game where youhave to flip three fair coins. To win, all three coinsmust show the same face (all heads or all tails), andyou will win four times your original wager.Otherwise, you lose your original bet. If you pay $1each time you play this game, and you play 20times, what is your expected net gain or loss.
Answers
First, let's calculate the probability of winning the game.
We win the game if we get three heads or three tails, so the probability is:
\(\begin{gathered} P(3\text{ heads})=\frac{1}{2}\cdot\frac{1}{2}\cdot\frac{1}{2}=\frac{1}{8}\\ \\ P(3\text{ tails})=\frac{1}{2}\cdot\frac{1}{2}\cdot\frac{1}{2}=\frac{1}{8}\\ \\ P(win)=\frac{1}{8}+\frac{1}{8}=\frac{2}{8}=\frac{1}{4} \end{gathered}\)If the probability of winning is 1/4, the probability of losing is 3/4.
If the wager is $1, winning will return $4 plus the original bet, so a net earning of $4.
Losing will return nothing, so the net "earning" is -$1.
Calculating the expected value of one game, we have:
\(\begin{gathered} E(x)=\sum x\cdot p(x)\\ \\ E(x)=\frac{1}{4}\cdot4+\frac{3}{4}\cdot(-1)\\ \\ E(x)=\frac{4}{4}-\frac{3}{4}\\ \\ E(x)=\frac{1}{4} \end{gathered}\)Playing 20 times will result in an earning of 20 * 1/4, that is, a gain of $5.
Correct option: fourth one.
x = 6y – 14
-X + 9y = 17
Answers
Answer:
(x, y)=(-8,1) this is substantial method
A center lane with solid and broken yellow lines that is used by vehicles making left turns in both directions is called a:
A) Two-way Left-Turn lane.
B) Median strip with driving allowed.
C) Shared passing lane.
D) None of these answers.
Answers
The center lane with solid and broken yellow lines used by vehicles turning left in both directions is called a Two-way Left-Turn lane. The correct option A. This lane is marked as two solid yellow lines on either side and broken yellow lines in the middle.
What is a two-way left-turn lane?A two-way left-turn lane is a center lane with solid and broken yellow lines used by vehicles making left turns in both directions. It is also known as a median lane, a center left-turn lane, and a center two-way left-turn lane.
This lane is marked as two solid yellow lines on either side and broken yellow lines in the middle.Only left-turning traffic should use the lane. It's illegal to drive in this lane for more than 300 feet, pass other cars in the lane, or turn left from other lanes when a two-way left-turn lane is present. It is used in order to lessen the amount of crashes and lower traffic congestion in both directions, hence it helps in making the traffic flow smoothly.
A center lane with solid and broken yellow lines used by vehicles turning left in both directions is known as a Two-way Left-Turn lane.
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Make a spiral root for:
The best answer will be marked brainliest
Answers
To make a spiral root, you can start by drawing a circle to represent the center of the root.
Next, draw a curved line extending from the circle, gradually curving outward as you move away from the center. This will form the first section of the spiral root.
Continue drawing curved lines in a spiral pattern around the center circle, gradually increasing in size as you move outward. The spiral shape will give the root a unique and interesting look. You can also add smaller roots branching off the main spiral to make it look more realistic.
1. Draw a small circle in the center of your paper.
2. Begin drawing a spiral around the circle, gradually getting larger as you move away from the center.
3. Continue drawing the spiral until you reach your desired size.
A spiral root is a pattern where a line or curve starts from a central point and gradually moves away from it, forming a spiral shape. It is often used in art and design, as well as in mathematics to represent various functions and shapes.
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What percentage of total expenses is spent on food, according to the budget table below?
Answers
\( \: \huge \tt{ \fbox{\pink{Answer}}} \\ \: \: \\ \rightarrow {\bf{21.281\% \: \: or \: \: 21.28\%}} \)
EXPLAINATION : Total Expenses = $4558 Expenses on Food = $970
\( \\ \\ \sf \: Food \: Expenses \: in \: Total \: Expenses(\%) \\ \\ \sf = \frac{Food \: expense}{Total \: expenses} \times 100 \\ \\ = \frac{\cancel {970} \: \: {}^{0.2128} }{ \cancel{4558}} \times 100 \)
Hence, Out of total expenses about
21.28% are spending on food.
The percentage of total expenses is spent on food is 21.28%.
What is percentage?Percentage is defined as a given part or amount in every hundred. It is a fraction with 100 as the denominator and is represented by the symbol "%".
From the given table, total expenses =$4558 and the money spent on food = $970.
Here, percentage = The money spent on food/Total expenses ×100
= 970/4558 ×100
= 0.2128×100
= 21.28%
Therefore, the percentage of total expenses is spent on food is 21.28%.
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at time zero, there are 10.0 grams of w - 187. if the half - life is 23.9 hours, how much will be present at the end of one day? two days? seven days?
Answers
There are 10.0g of w – 187 at time zero. If the half-life is 23.9 hours, then the amount of quantity for: 1 day = 4.98 g, 2 day = 2.48 g, on 7th day = 0.0765 g.
A drug's half-life is the duration it takes for the amount of its active ingredient to halve in your body. A radioactive isotope's half-life is the length of time it takes for one half of the isotope to decay. A particular radioactive isotope's half-life is constant; it is unaffected by environmental factors and is unrelated to the starting concentration of that isotope.
time 24.0 hr / 23.9 hr/half-life = 1.0042 half-lives
One day half-life is:
= (1/2)^1.0042
= 0.4985465
= 4.98 g
For Two days:
= (1/2)^2.0084
= 0.2485486
= 2.48 g
For Seven days:
= (1/2)^7.0294
= 0.0076549
= 0.0765 g
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The polar bear is becoming extinct in the North pole. There are currently 60,000 polar bears, but each year the population is cut in half. How many polar bears will be left in 6 years ?
Answers
Answer:
The will be 937 bears left in 6 years.
Step-by-step explanation:
If the polar bear population is cut in half every year, then after one year there will be 60,000/2 = 30,000 polar bears left. After two years, there will be 30,000/2 = 15,000 polar bears left, and so on.
Solve 7=6+b .
b= _____
Answers
b=1
To solve -6 on both sides of the equal sign to isolate the variable B
Sandra is 1.8 m tall. She stood 0.9 m from the base of the mirror and could see the top of
the cliff in the mirror. The base of the mirror is 5.4 m from the base of the cliff. What is
the height of the cliff?
Answers
The cliff rises 10.8 metres in height.
To determine the height of the cliff, we can use similar triangles and apply the concept of proportions.
Let's denote the height of the cliff as "h."
According to the given information, Sandra is 1.8 m tall and stands 0.9 m from the base of the mirror. The distance between the base of the mirror and the base of the cliff is 5.4 m.
We can form a proportion based on the similar triangles formed by Sandra, the mirror, and the cliff:
(Height of Sandra) / (Distance from Sandra to Mirror) = (Height of Cliff) / (Distance from Mirror to Cliff)
Plugging in the values we know:
1.8 m / 0.9 m = h / 5.4 m
Simplifying the equation:
2 = h / 5.4
To solve for h, we can multiply both sides of the equation by 5.4:
2 * 5.4 = h
10.8 = h
Therefore, the height of the cliff is 10.8 meters.
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In the House of Commons, citizens elect their members. Of the 800 members, 530 are from England, 120 are from Wales, 100 are from Scotland and 50 are from Northern Ireland. What is the percentage of members from Wales?
Answers
Answer:
15%
I like your demon slayer profile picture
Answer:
The answer is 15%.
Step-by-step explanation:
If 100 is 10% it only makes since that 15% is the right answer.
Hope This Helps!
a quadrilateral with no piar of parallel sides
Answers
The quadrilateral with no pair of parallel sides is trapezium
Given data ,
A = a quadrilateral with no pair of parallel sides
This type of quadrilateral is called a trapezium. In some countries, a trapezium is defined as having exactly one pair of parallel sides, while in other countries, a trapezium is defined as having at least one pair of parallel sides.
In any case, a quadrilateral with no pair of parallel sides is not considered a trapezium. Instead, it is known as a general quadrilateral.
There are three types of trapezoids , and those are given below:
a) Isosceles Trapezoid
b) Scalene Trapezoid
c) Right Trapezoid
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Clara's office had already recycled 1 kilogram this year before starting the new recycling plan, and the new plan will have the office recycling 6 kilograms of paper each week. Write an equation that shows the relationship between the weeks w and the paper recycled p. Write your answer as an equation with p first, followed by an equals sign.
Answers
Answer:
p = 6w + 1
Step-by-step explanation:
The 6w represents that six kilograms are recycled for every week the variable w represents. For example if the w were 2 they would have recycled twelve kilograms of paper
The plus 1 was included because before they started to recycle six kilograms weekly they had already recycled one.
Solve for x
0.5x = 20
1. x = 40
2. x = 10
3. x = 2.5
Answers
Answer:
It's the first answer. 40
Step-by-step explanation:
divide both sides by 0.5
Answer:
1. x=40
Step-by-step explanation:
x=20÷0.5
x=40
The exchange rate at the post office is £1=€1. 17
how many euros is £280
Answers
The exchange rate at the post office is £1 = €1.17. Therefore, to find how many euros is £280, we have to multiply £280 by the exchange rate, which is €1.17.
Let's do this below:\[£280 \times €1.17 = €327.60\]Therefore, the amount of euros that £280 is equivalent to, using the exchange rate at the post office of £1=€1.17, is €327.60. Therefore, you can conclude that £280 is equivalent to €327.60 using this exchange rate.It is important to keep in mind that exchange rates fluctuate constantly, so this exchange rate may not be the same at all times. It is best to check the current exchange rate before making any currency conversions.
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help me..........................
no need to answer number 13
Answers
In order to find the average of a group of numbers you first add all of the numbers together:
20+15+55+10+20= 120
Then you divide the answer by the amount of numbers in the group:
120/5= 24
-10/3 improper fraction as a mixed number
Answers
You see how many times you can put the bottom number into the top number that is your whole number then the top of the fraction is how much is left and the bottom you keep the denominator
Because it’s a improper faction
A dilation is a or a figure with respect to a fixed point
Answers
A dilation is a transformation in which a figure is enlarged or reduced with respect to a fixed point.
In a dilation, the figure is either enlarged or reduced, meaning that it either grows bigger or smaller in size. The fixed point is known as the center of dilation, and all points on the figure are moved away from or toward this point by a scale factor. The scale factor determines how much the figure is enlarged or reduced. If the scale factor is greater than 1, the figure is enlarged. If the scale factor is less than 1, the figure is reduced.
Here is an example of a dilation:
Step 1: Draw a figure, such as a triangle, and choose a fixed point as the center of dilation.
Step 2: Determine the scale factor for the dilation.
Step 3: For each point on the figure, draw a line through the point and the center of dilation.
Step 4: Locate the new points on these lines that are the correct distance from the center of dilation, based on the scale factor.
Step 5: Connect the new points to form the dilated figure.
In conclusion, a dilation is a transformation that enlarges or reduces a figure with respect to a fixed point, using a scale factor.
Note: The question is incomplete. The complete question probably is: A dilation is a __________ in which a figure is ________ or ________ with respect to a fixed point.
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Hurry I need help!
Solve F(x) for the given domain.
F(x) = x^2 + 3x -2
F(a) =
Answers
Answer:
a^2+3a+2
Step-by-step explanation:
Answer:
i think it might be ↓
Step-by-step explanation:
F(x) = 1/3(x³) + 3/2(x²) - 2x + C