find the volume of the solid obtained by rotating the region bounded by the given curves about the specified axis. y = 0 , y = cos ( 6 x ) , x = π /12 , x = 0 about the axis y = − 8
The volume of the solid obtained by rotating the region bounded by the curves y = 0, y = cos(6x), x = π/12, x = 0 about the axis y = -8 is 10.635 cubic units.
To find the volume of the solid obtained by rotating the region bounded by the curves around the axis y = -8, we will use the method of cylindrical shells.
The curves y = 0 and y = cos(6x) intersect at x = arccos(0)/6 = π/12. So we will integrate from x = 0 to x = π/12.
Now let's consider an element of width dx at a distance x from the y-axis. This element will generate a cylindrical shell of thickness dx, radius (y+8), and height ds, where ds is the arc length of the curve at x. The arc length can be found using the formula ds = √(1 + (dy/dx)²) dx. Since y = cos(6x), we have dy/dx = -6sin(6x)
So, ds = √(1 + (dy/dx)²) dx
= √(1 + 36sin²(6x)) dx
The volume of the shell is given by
dV = 2π(y+8) ds dx
= 2π(y+8) √(1 + 36sin²(6x)) dx
Integrating from x = 0 to x = π/12, we get the total volume as
V = ∫(0 to π/12) 2π(y+8) √(1 + 36sin²(6x)) dx
= 2π ∫(0 to π/12) (cos(6x)+8) √(1 + 36sin²(6x)) dx
This integral is not easy to evaluate analytically, but we can use numerical integration to get an approximate value. Using a computer algebra system or numerical integration software, we get:
V ≈ 10.635
Therefore, the volume of the solid obtained by rotating the region bounded by the curves y = 0, y = cos(6x), x = π/12, x = 0 about the axis y = -8 is approximately 10.635 cubic units.
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what is the quotion of 5/6 divided by 5/24
Step-by-step explanation:
remember, dividing one fraction by a second is the same as multiplying the first one with the inverse fraction of the second.
5/6 ÷ 5/24 = 5/6 × 24/5 = 24×5 / 6×5 = 24/6 = 4
Find the volume of a right circular cone that has a height of 19.4 cm and a base with a diameter of 9.9 cm. Round your answer to the nearest tenth of a cubic centimeter.
Answer:
V = 497.8 cm^3
Step-by-step explanation:
Thats Righttt
The volume of the cone is 1592.6 cm³
What is volume?Volume is defined as the space occupied within the boundaries of an object in three-dimensional space. It is also known as the capacity of the object.
The right circular cone's vertex is immediately above the base's centre. The line connecting the vertex with the centre point of the base is perpendicular to the cone's radius. A cone, on the other hand, can have its vertex anywhere.
Given that, a right circular cone with the height of 19.4 cm and a base with a diameter of 9.9 cm. we need to find the volume,
Volume of cone = 1/3 × π × radius² × height
= 1/3 × 3.14 × (9.9/2)² × 19.4
= 1592.6 cm³
Hence, the volume of the cone is 1592.6 cm³
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how many 1/3 cubes would it take to fill a rectangular prism that is 2 1/5 m long, 5 m tall, and 3/4 m wide
We need to calculate the total of the rectangular prism and divide it with the volume of single 1/3 cubes to get the number of cubes. It takes almost 25 cubes to fill the rectangular prism of given dimension.
The rectangular prism has 2.5 m length, 5 m tall and 0.75 m wide.
The total volume of the rectangular prism will be 2.5 m × 5 m × 0.75 m = 8.25 m³.
The volume of single cube will be (1/3) m³ = 0.33 m³
Now to find the number of cubes to fill the rectangular prism, we can divide the volume of the prism with the volume of single cube.
8.25 m³ / 0.33 m³ = 25 cubes.
It takes almost 25 cubes to fill the rectangular prism of dimension 2.5 m length, 5 m tall and 0.75 m wide.
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Use the Distributive Property to write an equivalent expression for the expression (a + b)(2 + y).
Answer:
2a+ay+2b+by
We multiple the first number by the two numbers in the next parentheses
Answer:
\(2a+2b+ay+ab\)
Step-by-step explanation:
\((a+b)(2+y)\\(2a+ay+2b+by)\\(2a + 2b+ay+ab)\)
What is the solution of 5/6 x 4/9.
The answer is 10/27
please see the attached picture for full solution
hope it will helps
Good luck on your assignment
Answer:
10/27
Step-by-step explanation:
5/6 x 4/9=5/3 x 2/9=10/27
need help pls help
:D
Answer:
x = 3y + 1
Step-by-step explanation:
0-(-1) = 1
1-0 = 1
2-1 = 1
1-(-2) = 3
4-1 = 3
7-4 = 3
As x increases by 1, y increases by 3. At x = 0, y is already 1. Thus:
x = 3y + 1
Answer:
Slope-intercept Form: \(y = 3x + 1\)
Standard Form: \(9x -3y = -3\)
Point-slope Form: \(y -7 = 3(x - 2)\)
Step-by-step explanation:
What is the equation of the line?
Answer:
the second one
Step-by-step explanation:
the independent number is the y intercept (where it touches the y-axis which would make the y-intercept 2) and the slope is 1/2 if you use rise/run. so it seems as if the equation is written in y=mx+b form. so the answer is y=1/2x+2
this is section 3.1 problem 14: for y=f(x)=− 2 x , x=2, and δx=0.2 : δy= , and f'(x)δx . round to three decimal places unless the exact answer has less decimal places.
The derivative of f(x) is f'(x) = -2, so we can substitute these values into the formula to get δy = -2 * 0.2 = -0.4.
How to calculate the change in the output variable y?This problem involves using the concept of the derivative to calculate the change in the output variable y, given a small change in the input variable x.
Specifically, we are given the function y = f(x) = -2x, the value of x at which we want to evaluate the change, x = 2, and the size of the change in x, δx = 0.2.
To find the corresponding change in y, δy, we can use the formula δy = f'(x) * δx, where f'(x) is the derivative of f(x) evaluated at x.
In this case, the derivative of f(x) is f'(x) = -2, so we can substitute these values into the formula to get δy = -2 * 0.2 = -0.4.
This tells us that a small increase of 0.2 in x will result in a decrease of 0.4 in y, since the derivative of the function is negative.
This problem illustrates the concept of local linearization, which is the approximation of a nonlinear function by a linear function in a small region around a point.
The derivative of the function at a point gives us the slope of the tangent line to the function at that point, and this slope can be used to approximate the function in a small region around the point.
This approximation can be useful for estimating changes in the output variable given small changes in the input variable.
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Which sign goes in the circle to make the number sentence true?
4/5+5/8 ○ 1
A) >
B) <
C) Greater than or equal to
D) Less than or equal to
The sign that goes in the circle to make the sentence true is >• 4/5+5/8= >1
ExplanationLet us compare 4/5 and 5/8.
To compare the numbers, we have to get the lowest common multiple (LCM). We can derive the LCM by multiplying the denominators which are 5 and 8. 5×8 = 40
LCM = 40.
Converting 4/5 and 5/8 to fractions with a denominator of 40:
4/5 = 32/40
5/8 = 25/40
= 32/40 + 25/40
= 57/40
= 1.42.
4/5+5/8 = >1
1.42>1
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What do you call the process of charging a conductor by bringing it near another charged object and
grounding it?
O conduction
O friction
O induction
O neutralization
Answer:
Induction
Step-by-step explanation:
Induction is "the creation of a voltage difference across a conductive material (such as a coil of wire) by exposing it to a changing magnetic field."
Iḿ stuck on this question
Answer:
4
Step-by-step explanation:
99/9 is 11 so to get what the missing number is divide 44 by 11 to get 4
a rectangular hole is to be cut in a wall for a vent. if the perimeter of the hole is 48 in. and the length of the diagonal is a minimum, what are the dimensions of the hole?
The hole will be of a radius of 7.63 inches when its perimeter is 48 inches.
The hole is in the form of a circle.
The perimeter of the circle = perimeter of the hole = 48 inches.
Let r be the radius of the vent,
The perimeter of the circle is known as the Circumference.
Circumference of the circle is given by \(2\pi r\)
So,
\(2\pi r = 48\\\\2*\frac{22}{7} *r =48\\\\r =\frac{48*7}{22*2} =7.63\)
The hole will be of a radius of 7.63 inches.
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Two firms producing identical products engage in price competition. Cost of firm 1 is $20 per unit produced and cost of firm 2 is $15 per unit produced. There are no fixed costs. Firms produce only after they learn the quantity demanded. Each firm can choose any real number in the interval [15,25] as its price.
For tie-breaking we will assume that if both firms set the same price, all consumers purchase from firm 2.
The payoff/profit function of firm 1 is:
(p1 - 20)(100 - p1) if p1 is less than or equal to p2,
0 if p1 is greater than p2
The payoff/profit function of firm 2 is:
(p2 - 15)(100 - p2) if p2 is less than p1,
0 if p2 is greater than or equal to p1
Given all of this information, solve the following parts of the problem:
a) is p1 = 20, p2 = 19.50 a Nash Equilibrium?
b) is there a Nash Equilibrium in which Firm 2 makes a positive profit?
c) How many strategies does player 1 have?
d) is p1 = 15, p2 = 15 a Nash Equilibrium?
e) is p1 = 21, p2 = 21 a Nash Equilibrium?
a) No, p1 = 20, p2 = 19.50 is not a Nash Equilibrium.
b) Yes, there is a Nash Equilibrium in which Firm 2 makes a positive profit.
c) Player 1 has infinitely many strategies.
d) Yes, p1 = 15, p2 = 15 is a Nash Equilibrium.
e) No, p1 = 21, p2 = 21 is not a Nash Equilibrium.
What is Nash Equilibrium?Nash Equilibrium is a state of a strategic game where no player has an incentive to deviate from his or her chosen strategy after considering the strategies of other players. A game has more than one Nash equilibrium if players are unable to agree on a cooperative strategy to play.
Finding Nash Equilibrium
a) Is p1 = 20, p2 = 19.50 a Nash Equilibrium?No. Firm 1 has an incentive to decrease the price to 19.49, thus breaking the tie in its favour. So p1=20, p2=19.5 is not a Nash equilibrium.b) Is there a Nash Equilibrium in which Firm 2 makes a positive profit?Yes. There are several equilibria in which Firm 2 makes a positive profit. One such equilibrium is when both firms charge the same price of 15, at which both firms earn a profit of 375.c) How many strategies does player 1 have?Player 1 has infinitely many strategies to choose from as they can choose any real number in the interval [15,25] as their price.d) Is p1 = 15, p2 = 15 a Nash Equilibrium?Yes. This is a Nash Equilibrium because neither firm has an incentive to change their strategy as they are earning non-zero profits. Both firms earn a profit of 375.e) Is p1 = 21, p2 = 21 Nash Equilibrium?No. If Firm 1 changes its price to 20.99, its profit increases from 405 to 407.99. Therefore, p1=21 and p2=21 is not a Nash Equilibrium.Learn more about Nash equilibrium at
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Tina pays $45.50 for 10 boxes of wheat crackers. What is the unit price? *
Unit price = total price / quantity
Unit price = 45.50 / 10
Unit price = $4.55
Answer:
$4.55 because I look it up
For an arithmetic sequence a,= 7+3(n-1), what is the 31st term?a.) 97b.) 100c.) 91d.) 94
For an arithmetic sequence a,= 7+3(n-1)
when n is 31
For an arithmetic sequence a,= 7+3(31-1)
An arithmetic sequence a,= 7+3(30)
An arithmetic sequence a,= 7+90
An arithmetic sequence a= 97
THE CORRESCT
The velocity in a fluid flow field is given by u=2x+y^2u=2x+y2 and v=3x^2yv=3x2y where uu is the x-component of velocity, and vv is the y-component of velocity. What is the x-component of fluid acceleration in terms of x and y?
The x-component of fluid acceleration in terms of x and y is 2.
To find the x-component of fluid acceleration (ax), we need to differentiate the x-component of velocity (u) with respect to time.
However, the given equations provide the expressions for u in terms of x and y, not time. Therefore, we need to differentiate u with respect to x and y instead.
Given: u = 2x + y^2
To find the x-component of fluid acceleration (ax), we differentiate u with respect to x while treating y as a constant:
ax = ∂u/∂x = ∂(2x + y^2)/∂x = 2
The x-component of fluid acceleration, ax, is simply 2.
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suppose we want there to be exactly three 8s in the phone number (starting the number with 0 is ok). how many different phone numbers can be created under these conditions?
To find the number of different phone numbers that can be created with exactly three 8s, we need to consider the possible positions of the 8s within the number.
Let's break it down step by step:
1. Determine the total number of positions in the phone number:
- Phone numbers typically have 10 digits (0-9).
- Since we can start the number with 0, we have 11 possible positions (including the first digit).
2. Choose the positions for the three 8s:
- We need to select 3 positions out of the 11 available positions.
- This can be calculated using combinations. The number of combinations of selecting 3 positions out of 11 is denoted as "11 choose 3" or C(11,3).
- The formula for combinations is: C(n, r) = n! / (r! * (n-r)!), where n is the total number of positions and r is the number of positions we need to choose.
- Substituting the values, C(11,3) = 11! / (3! * (11-3)!)
3. Calculate the number of phone numbers:
- Once we have the number of combinations, we need to calculate the number of phone numbers that can be created.
- For each of the selected positions for the 8s, we have 10 choices (0-9) for the remaining digits.
- So, the total number of phone numbers that can be created is the product of the number of combinations and the number of choices for each position: C(11,3) * 10^8
Let's calculate the number of different phone numbers:
C(11,3) = 11! / (3! * 8!) = (11 * 10 * 9) / (3 * 2 * 1) = 165
Number of phone numbers = C(11,3) * 10^8 = 165 * 10^8 = 1,650,000,000
Therefore, under the given conditions, there are 1,650,000,000 different phone numbers that can be created with exactly three 8s.
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A small amount of the trace element selenium, 50–200 micrograms (μg) per day, is considered essential to good health. Suppose that random samples of
n1 = n2 = 40 adults
were selected from two regions of Canada and that a day's intake of selenium, from both liquids and solids, was recorded for each person. The mean and standard deviation of the selenium daily intakes for the 40 adults from region 1 were
x1 = 167.8
and
s1 = 24.5 μg,
respectively. The corresponding statistics for the 40 adults from region 2 were
x2 = 140.9
and
s2 = 17.3 μg.
Find a 95% confidence interval for the difference
(μ1 − μ2)
in the mean selenium intakes for the two regions. (Round your answers to three decimal places.)
μg to μg
Interpret this interval.
In repeated sampling, 5% of all intervals constructed in this manner will enclose the difference in population means.There is a 95% chance that the difference between individual sample means will fall within the interval. 95% of all differences will fall within the interval.In repeated sampling, 95% of all intervals constructed in this manner will enclose the difference in population means.There is a 5% chance that the difference between individual sample means will fall within the interval.
We have come to find that confidence interval is (16.802, 37.998) μg
What is Micrograms?Micrograms: This is a unit for measuring the weight of an object. It is equal to one millionth of a gram.
To find a 95% confidence interval for the difference in mean selenium intakes between the two regions, we can use the following formula:
Confidence interval = (x1 - x2) ± t * SE
where:
x1 and x2 are the sample means for region 1 and region 2, respectively.
t is the critical value from the t-distribution for a 95% confidence level.
SE is the standard error of the difference, calculated as follows:
\(\rm SE = \sqrt{((s_1^2 / n_1) + (s_2^2 / n2))\)
Let's calculate the confidence interval using the given values:
x₁ = 167.8
s₁ = 24.5 μg
n₁ = 40
x₂ = 140.9
s₂ = 17.3 μg
n₂ = 40
SE = √((24.5² / 40) + (17.3² / 40))
SE ≈ 4.982
Now, we need to determine the critical value from the t-distribution. Since both sample sizes are 40, we can assume that the degrees of freedom are approximately 40 - 1 = 39. Consulting a t-table or using a statistical software, the critical value for a 95% confidence level with 39 degrees of freedom is approximately 2.024.
Substituting the values into the confidence interval formula:
Confidence interval = (167.8 - 140.9) ± 2.024 * 4.982
Confidence interval = 26.9 ± 10.098
Rounded to three decimal places:
Confidence interval ≈ (16.802, 37.998) μg
Interpretation:
We are 95% confident that the true difference in mean selenium intakes between the two regions falls within the interval of 16.802 μg to 37.998 μg. This means that, on average, region 1 has a higher selenium intake than region 2 by at least 16.802 μg and up to 37.998 μg.
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A mathematics teacher wanted to see the correlation between test scores and homework. The homework grade (x) and test grade (y) are given in the accompanying table. Write the linear regression equation that represents this set of data, rounding all coefficients to the nearest hundredth. Using this equation, find the projected test grade, to the nearest integer, for a student with a homework grade of 68.
Answer:
add to the x and y hyujfti
If the 1t peron ave 1/4 of total , 2nd peron ave 2/3 of total and the 3rd peron ave 1/10 which fraction i left to pay for the birthday party
Although part of your question is missing, you might be referring to this full question: If the 1st person saves 1/4 of total, 2nd person saves 2/3 of total, and 3rd person saves 1/10, which fraction left to pay for the birthday party?
The fraction left to pay for the birthday party is 17/30.
The calculation is as follows:
1 * 1/4 = 1/4 … (1)
1/4 * 2/3 = 2/12 … (2)
2/12 * 1/10 = 2/120 … (3)
Fraction left to pay:
= 1 - (1/4 + 2/12 + 2/120)
= 1 - (30/120 + 20/120 + 2/120)
= 1 - (52/120)
= 1 - 13/30
= 30/30 - 13/30
= 17/30
Thus, the fraction left to pay for the birthday party is 17/30.
What is fraction?A fraction is a part of a whole. In arithmetic, the number is expressed as a quotient, where the numerator is divided by the denominator. In a simple fraction, both are integers. A complex fraction has a fraction in the numerator or denominator. In a proper fraction, the numerator is less than the denominator.
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Sam's Cat Hotel operates 52 weeks per year, 5 days per week, and uses a continuous review inventory system. It purchases kitty litter for $10.75 per bag. The following information is available about these bags. Refer to the standard normal table for z-values. > Demand = 100 bags/week > Order cost = $57/order > Annual holding cost = 30 percent of cost > Desired cycle-service level = 92 percent Lead time = 1 week(s) (5 working days) Standard deviation of weekly demand = 16 bags Current on-hand inventory is 310 bags, with no open orders or backorders.a. What is the EOQ? What would the average time between orders (in weeks)?
b. What should R be?
c. An inventory withdraw of 10 bags was just made. Is it time to reorder?
D. The store currently uses a lot size of 500 bags (i.e., Q=500). What is the annual holding cost of this policy? Annual ordering cost? Without calculating the EOQ, how can you conclude lot size is too large?
e. What would be the annual cost saved by shifting from the 500-bag lot size to the EOQ?
The required answer is the annual cost saved by shifting from the 500-bag lot size to the EOQ is $1,059.92.
Explanation:-
a. Economic order quantity (EOQ) is defined as the optimal quantity of inventory to be ordered each time to reduce the total annual inventory costs.
It is calculated as follows: EOQ = sqrt(2DS/H)
Where, D = Annual demand = 100 x 52 = 5200S = Order cost = $57 per order H = Annual holding cost = 0.30 x 10.75 = $3.23 per bag per year .Therefore, EOQ = sqrt(2 x 5200 x 57 / 3.23) = 234 bags. The average time between orders (TBO) can be calculated using the formula: TBO = EOQ / D = 234 / 100 = 2.34 weeks ≈ 2 weeks (rounded to nearest whole number).
Hence, the EOQ is 234 bags and the average time between orders is 2 weeks (approx).b. R is the reorder point, which is the inventory level at which an order should be placed to avoid a stockout.
It can be calculated using the formula:R = dL + zσL
Where,d = Demand per day = 100 / 5 = 20L = Lead time = 1 week (5 working days) = 5 day
z = z-value for 92% cycle-service level = 1.75 (from standard normal table)σL = Standard deviation of lead time demand = σ / sqrt(L) = 16 / sqrt(5) = 7.14 (approx)
Therefore,R = 20 x 5 + 1.75 x 7.14 = 119.2 ≈ 120 bags
Hence, the reorder point R should be 120 bags.c. An inventory withdraw of 10 bags was just made. Is it time to reorder?The current inventory level is 310 bags, which is greater than the reorder point of 120 bags. Since there are no open orders or backorders, it is not time to reorder.d. The store currently uses a lot size of 500 bags (i.e., Q = 500).What is the annual holding cost of this policy.
Annual ordering cost. Without calculating the EOQ, how can you conclude the lot size is too large?Annual ordering cost = (D / Q) x S = (5200 / 500) x 57 = $592.80 per year.
Annual holding cost = Q / 2 x H = 500 / 2 x 0.30 x 10.75 = $806.25 per year. Total annual inventory cost = Annual ordering cost + Annual holding cost= $592.80 + $806.25 = $1,399.05Without calculating the EOQ, we can conclude that the lot size is too large if the annual holding cost exceeds the annual ordering cost.
In this case, the annual holding cost of $806.25 is greater than the annual ordering cost of $592.80, indicating that the lot size of 500 bags is too large.e.
The annual cost saved by shifting from the 500-bag lot size to the EOQ can be calculated as follows:Total cost at Q = 500 bags = $1,399.05Total cost at Q = EOQ = Annual ordering cost + Annual holding cost= (D / EOQ) x S + EOQ / 2 x H= (5200 / 234) x 57 + 234 / 2 x 0.30 x 10.75= $245.45 + $93.68= $339.13
Annual cost saved = Total cost at Q = 500 bags - Total cost at Q = EOQ= $1,399.05 - $339.13= $1,059.92
Hence, the annual cost saved by shifting from the 500-bag lot size to the EOQ is $1,059.92.
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Katrina drinks 0.5 gallons of water per day which expression shows how to find the number of cups of water she drinks in a week there are 16 cups in I
Answer:
56 cups of water
Step-by-step explanation:
Katrina drinks 0.5 gallons of water per day
We have 7 days in a week, hence, the number of gallons of water she drinks per week is calculated as:
1 day = 0.5 gallons
7 days = x
Cross Multiply
1 day × x = 7 days × 0.5 gallons
x = 7 days × 0.5 gallons/1 day
x = 3.5 gallons
Note that 16 cups = 1 gallon
The number of cups of water she drinks per week is
1 gallon = 16 cups
3.5 gallons = x
Cross Multiply
1 gallons × x = 3.5 gallons × 16 cups
x = 3.5 gallons × 16 cups/1 gallons
x = 56 cups
Therefore, Katrina drinks 56 cups of water in a week
Please graph this equation y=4|x-1|+3
The graph of equation y=4|x-1|+3 is as shown below.
In this question, we need to graph the equation y=4|x-1|+3
We know that the parent function of given equation is z = |x|
A parent function is translated right by 1 unit then it is dilated vertically by 4 units and the resulting image is translated up by 3 units.
The graph of equation y=4|x-1|+3 is as shown below.
The vertex of equation y=4|x-1|+3 is at (1, 3)
Therefore, the graph of equation y=4|x-1|+3 is as shown below.
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Alvin and his friends set out to sea on their annual fishing trip. There is a proportional relationship between the time (in hours) Alvin and his friends spend sailing, x, and their distance from shore (in miles), y.
After sailing for 2 hours, Alvin and his friends are 10 miles from shore. Write the equation for the relationship between x and y.
y =
Now, use your equation to find their distance from shore after sailing for 3 hours.
Answer:From the given information, we know that after sailing for 2 hours, Alvin and his friends are 10 miles from shore. This can be written as y = 10 when x = 2.
Since there is a proportional relationship between x and y, we can write an equation using this information: y = kx, where k is the proportionality constant.
Substituting the known values, we get: 10 = k * 2
Solving for k, we get: k = 10/2 = 5
So, the equation relating x and y is: y = 5x
To find their distance from shore after sailing for 3 hours, we can plug in x = 3 into the equation:
y = 5x
y = 5 * 3
y = 15
So, after sailing for 3 hours, Alvin and his friends are 15 miles from shore.
Step-by-step explanation:
Please help Will give BRAINLIEST !!! :)
Answer:
D no. is for sure another I also don't know. So sorry.......
PLZ HELP ASAP I WILL GIVE BRAINLIEST
The means and mean absolute deviations of Sidney’s and Phil’s grades are shown in the table below the question.
Which expression represents the ratio of the difference of the two means to Sidney’s mean absolute deviation?
A. 82/3.28
B. 4/3.28
C. 4/0.68
D. 82/0.68
Answer:
B.
Step-by-step explanation:
Answer:
B.
StartFraction 4 over 3.28 EndFraction
Step-by-step explanation:
If the value of y varies directly with x, which function represents the relationship between x and y when y= 16/5 and x = 20?
Not sure if this is the answer but this is what I got
Answer: y= 4/25 x
Multiply the vector in the graph by a scale factor of Negative one-half.
o The resulting vector will be
o shorter than
o the original vector.
0The resulting vector will be in Quadrant
The resulting vector will be shorter than the original vector.
How to determine the property of the vectorFrom the question, we have the following parameters that can be used in our computation:
Multiplying the vector by a scale factor of Negative one-half.
This means that
Scale = -1/2
When a vector is multiplied by a scale whose absolute value is less than 1
The new vector will be shorter
using the above as a guide, we have the following:
The resulting vector will be shorter than the original vector.
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Find the solution point(s) for the system of equations given by y = 2x^2 + 5x – 10 and 4x – y = –11
Answer:
the solution points for the system of equations are (3, 25) and (-7/2, -7).
Step-by-step explanation:
We can solve this system of equations using substitution or elimination. Here, we will use the substitution method:
Substitute y = 2x^2 + 5x - 10 into the second equation:
4x - (2x^2 + 5x - 10) = -11
Simplifying the left side of the equation:
4x - 2x^2 - 5x + 10 = -11
Rearranging the terms:
2x^2 - x + 21 = 0
Using the quadratic formula:
x = (-(-1) ± sqrt((-1)^2 - 4(2)(21))) / 2(2)
x = (1 ± sqrt(169)) / 4
x = (1 ± 13) / 4
Simplifying:
x = 3 or x = -7/2
Now, substitute each value of x back into one of the original equations to find the corresponding value(s) of y:
For x = 3:
y = 2(3)^2 + 5(3) - 10 = 25
So one solution point is (3, 25).
For x = -7/2:
y = 4(-7/2) + 11 = -7
So the other solution point is (-7/2, -7).
Therefore, the solution points for the system of equations are (3, 25) and (-7/2, -7).