1 ptAn object moves in the xy-plane so that its position at any time t is given by the parametric equations x(t) = t3 – 3t2 + 2 and y(t) = √(t2 + 16). What is the rate of change of y with respect to x when t = 3?1/901/153/55/2
Answers
At t = 3, the rate οf change οf y with respect tο x is:
dy/dx = (dy/dt) / (dx/dt) = (3/5) / 9 = 1/15
What is differentiatiοn?The prοcess οf differentiatiοn cοmpares the rate οf change οf the functiοn tο the rate οf change οf the independent variable. The οutcοme οf differentiating a functiοn is referred tο as the functiοn's derivative. It prοvides each pοint's slοpe οn the functiοn's graph.
Tο find the rate οf change οf y with respect tο x, we need tο find dy/dx at t = 3. We can use the chain rule tο express dy/dx in terms οf derivatives with respect tο t:
dy/dx = (dy/dt) / (dx/dt)
We can find dx/dt and dy/dt as follows:
dx/dt = 3t² - 6t
dy/dt = (1/2)(t² + 16\()^{(-1/2)\) * 2t
Substituting t = 3, we get:
dx/dt = 3(3)² - 6(3) = 9
dy/dt = (1/2)((3)² + 16\()^{(-1/2)\) x 2(3) = 3/5
Therefore, at t = 3, the rate of change of y with respect to x is:
dy/dx = (dy/dt) / (dx/dt) = (3/5) / 9 = 1/15
So the answer is 1/15.
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Related Questions
x/3 + 3 = 4.Find the value of x
Answers
Answer:
3
Step-by-step explanation:
x/3 + 3 = 4
x/3 = 4 - 3
x/3 = 1
x = 3
Answer: x = 3
Step-by-step explanation:
Given
x/3 + 3 = 4
Subtract 3 on both sides
x/3 + 3 - 3 = 4 - 3
x/3 = 1
Multiply 3 on both sides
x/3 × 3 = 1 × 3
\(\boxed{x=3}\)
Hope this helps!! :)
Please let me know if you have any questions
solve these equations
and don't troll or I will report you
Answers
Answer:
1) x= 268
2) y= 282
3) x= 15
4) x= 133
5= -13
6= -4
Step-by-step explanation:
Is 4/3=8/6 equivalent
Answers
Answer:
Yes
Trust me it is right!Good Luck:)NEED EXPLINATION PLEASE COMMENT BELLOW
Answer:
yes 4/3 is equivalent to 8/6
Step-by-step explanation:
8/6 divided both the numerator and the denominator by 2 you get 4/3.thus 8/6 is equivalent to 4/3
The number of CDs per hour that Snappy Hardware can manufacture at its plant is given by P=064 where x is the number of workers at the plant and y is the monthly budget in dollars. Assuming that P is constant.compute dy/d when w100 and y 120,000, Coninuing with the previous problem,give an interpretation in 3 parts of the value you computed in terms of CDs produced by Snoppy Hardware.
Answers
The value of dy/d in this case represents the rate of change in the monthly budget required to maintain a constant production level of CDs.
When w100 and y 120,000, dy/d can be computed by taking the partial derivative of the given equation with respect to y: dy/d = -0.64/x. Plugging in the given values, we get dy/d = -0.0064.
1. If the monthly budget is increased by $1, Snappy Hardware can manufacture 0.0064 fewer CDs per hour while maintaining the same number of workers.
2. If the number of workers is increased by 1, Snappy Hardware can manufacture an additional 0.0064 CDs per hour while maintaining the same monthly budget.
3. If Snappy Hardware wants to maintain a constant production level of CDs, they need to decrease their monthly budget by $156,250 for every 10,000 CDs they want to produce per hour.
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I need this equation solved
Answers
Answer:
28
Step-by-step explanation:
similar triangles are proportional
and add all the sides of the bigger triangle
1. A typical city of 100,000 people has 1,400 miles of city streets. The surface area of
that city is 72 square miles. What is the surface area of your city now with 50,000
people? How many miles of city streets are in your city now?
Answers
The surface area of the city with 50,000 people is 36 square miles, and there are 700 miles of city streets in the new city.
Assuming that the city's surface area remains constant with a decrease in population from 100,000 to 50,000 people, we can use proportionality to calculate the new surface area and the number of city streets.
If 100,000 people have a surface area of 72 square miles, then we can set up the following proportion:
100,000 / 50,000 = 72 / x
Solving for x, we get:
x = (50,000 * 72) / 100,000
x = 36
Therefore, the new surface area of the city with 50,000 people is 36 square miles.
To calculate the number of miles of city streets in the new city, we can use the same proportion:
100,000 / 50,000 = 1,400 / y
Solving for y, we get:
y = (50,000 * 1,400) / 100,000
y = 700
Therefore, the new city with 50,000 people has 700 miles of city streets.
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According to a recent survey, the probability that the driver in a fatal vehicle accident is female (event F) is 0.2805. The probability that the driver is 24 years old or less (event A) is 0.1759. The probability that the driver is female and is 24 years old or less is 0.0424. Answer parts (a) through (d) below.
(a) Find the probability of FUA. P (FUA)Round to four decimal places as needed.)
(b) Find the probability of F'UA. P(FUA) (Round to four decimal places as needed.)
(c) Find the probability of FnA'
Answers
Question d:
(D) Find the probability of F'nA'
Answer:
0.4140
0.7619
0.2381
0.9576
Step-by-step explanation:
Given that :
Female in fatal accident P(F) = 0.2805
Driver is 24 years or less P(A) = 0.1759
Driver is female and 24 years or less P(FnA) = 0.0424
A.) Find the probability of FUA.
P(FUA) = P(F) + P(A) - P(FnA)
= 0.2805 + 0.1759 - 0.0424
= 0.4140
(b) Find the probability of F'UA.
P(F'UA) = 1 - P(F) + P(FnA)
= 1 - 0.2805 + 0.0424
= 0.7619
C.) P(FnA') = 1 - P(F'UA)
= 1 - 0.7619
= 0.2381
(d) Find the probability of F'nA'
P(F'nA') = (FnA)' = 1 - (FnA)
= 1 - 0.0424
= 0.9576
Solve the system of equations algebraically. Verify your answer using the graph.
y = 4x – 5
y = –3
What is the solution to the system of equations?
((StartFraction one-fourth EndFraction, negative 3), –3)
((StartFraction one-half EndFraction, negative 3), –3)
(–3, (negative 3, StartFraction 2 over 3 EndFraction))Solve the system of equations algebraically. Verify your answer using the graph.
y = 4x – 5
y = –3
What is the solution to the system of equations?
((StartFraction one-fourth EndFraction, negative 3), –3)
((StartFraction one-half EndFraction, negative 3), –3)
(–3, (negative 3, StartFraction 2 over 3 EndFraction))
Answers
Answer:
Step-by-step explanation:
To solve the system of equations algebraically, we need to substitute the second equation into the first equation and solve for x:
y = 4x – 5 (equation 1)
y = -3 (equation 2)
Substitute equation 2 into equation 1:
-3 = 4x – 5
Add 5 to both sides:
2 = 4x
Divide both sides by 4:
x = 1/2
Now, we can substitute this value of x back into either equation to find y:
y = 4(1/2) – 5 = -3
Therefore, the solution to the system of equations is (1/2, -3).
To verify this solution using the graph, we can plot the two equations on the same set of axes:
y = 4x – 5 (red line)
y = -3 (blue line)
The two lines intersect at the point (1/2, -3), confirming our solution.
Therefore, the answer is (B) (1/2, -3).
What is the yield to maturity of a ten-year, $1000 bond with a 5.2% coupon rate and semi-annual coupons if this bond is currently trading for a price of $884?
5.02%
6.23%
6.82%
12.46%
G
5.20%
Answers
The yield to maturity of a ten-year, $1000 bond with a 5.2% coupon rate and semi-annual coupons, if the =bond is currently trading for a price of $884, is 6.23%. Thus, option a and option b is correct
Yield to maturity (YTM) is the anticipated overall return on a bond if it is held until maturity, considering all interest payments. To calculate YTM, you need to know the bond's price, coupon rate, face value, and the number of years until maturity.
The formula for calculating YTM is as follows:
YTM = (C + (F-P)/n) / ((F+P)/2) x 100
Where:
C = Interest payment
F = Face value
P = Market price
n = Number of coupon payments
Given that the bond has a coupon rate of 5.2%, a face value of $1000, a maturity of ten years, semi-annual coupon payments, and is currently trading at a price of $884, we can calculate the yield to maturity.
First, let's calculate the semi-annual coupon payment:
Semi-annual coupon rate = 5.2% / 2 = 2.6%
Face value = $1000
Market price = $884
Number of years remaining until maturity = 10 years
Number of semi-annual coupon payments = 2 x 10 = 20
Semi-annual coupon payment = Semi-annual coupon rate x Face value
Semi-annual coupon payment = 2.6% x $1000 = $26
Now, we can calculate the yield to maturity using the formula:
YTM = (C + (F-P)/n) / ((F+P)/2) x 100
YTM = (2 x $26 + ($1000-$884)/20) / (($1000+$884)/2) x 100
YTM = 6.23%
Therefore, If a ten-year, $1000 bond with a 5.2% coupon rate and semi-annual coupons is now selling at $884, the yield to maturity is 6.23%.
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Where is the blue dot located on the number line
Answers
===================================================
Explanation:
Use the midpoint formula to find the midpoint of -10 and -4
A = -10 = left endpoint
B = -4 = right endpoint
C = midpoint of A and B
C = (A+B)/2
C = (-10+(-4))/2
C = -14/2
C = -7
The value -7 is exactly midway between -10 and -4, so that's the missing tickmark between those values. Consequently, it also means each gap is 3 units wide (i.e., distance from -10 to -7 is 3 units).
Start at -10 and subtract 3 to move to the left by that amount. Do this three times to follow this pattern:
move from -10 to -13move from -13 to -16move from -16 to -19The blue dot is located at -19
Help please!! Thanks a lot I’m advance
Answers
if y = x^2 - 2 what is the value of y when x=3
Answers
Answer: y = 7
Step-by-step explanation: 3^2 is 9 and 9 - 2 is 7.
type in symbols to make 2,3,7, and 12 equal 55
Answers
Answer: 3(7+12) - 2
Step-by-step explanation:
x=a-√b
x = a + √b
what are the values of a and b?
Answers
Answer:
\(a=x\\\\b = 0\)
Step by step explanation:
\(x = a - \sqrt b~~~~~~~~~~...(i)\\\\x = a + \sqrt b ~~~~~~~~~~...(ii)\\\\\text{From eq (i) and eq (ii),}\\\\~~~~a - \sqrt b = a+ \sqrt b\\\\\implies \sqrt b + \sqrt b = a-a \\\\\implies 2 \sqrt b = 0\\\\\implies \sqrt b = 0\\\\\implies b = 0\\\\\text{Substitute b = 0 in eq (i):}\\\\~~~~~~x = a- \sqrt {0}\\\\\implies x = a -0\\\\\implies x = a\\\\\implies a = x\\\)
HELP PLZ TEXT MESSAGE: The cost of a text message increases from $0.10 per messages to $0.25 per message. What is the percent increase in the cost of sending a text message?
Answers
0.2x+40=50
0.2x = 10
5(0.2x) = 5(10)
x = 50
Therefore, 50 text messages would have to be sent or received in order for the plans to cost the same each month.
3/8
×
2/9
please help so hard!!!!!!!
Answers
Answer:
\(\frac{1}{12}\)
Step-by-step explanation:
\(\frac{3}{8}\)×\(\frac{2}{9}\)
You can cut off 3 and 9 because they have 3s there
You can also cut off 2 and 8 since they have 2s there.
\(\frac{1}{4}\)×\(\frac{1}{3}\)
\(=\frac{1}{12}\)
a pizza parlor can make 100 pizzas in an evening. they make 40 pepperoni pizzas and 60 extra cheese pizzas. they are producing each pizza at the lowest possible cost. 100 people order pizza, but 50 people would like a pepperoni pizza and 50 would like an extra cheese pizza. this pizza parlor is what?
Answers
The pizza parlor is technically efficient, but its not allocatively or economically efficient because technically efficient if all supply is used, allocate is if desired demand is met.
What is meant by technically efficient?Technical efficiency is related to how productive a company can be given this same fewest inputs, as well as resources, required to complete a task.
An input would be any quantifiable resource required to produce an output, or product. Labor, materials, and equipment are all examples of inputs. Outputting cakes, for example, necessitates at least the mentioned inputs: bakers, ingredients, and ovens.What is meant by economically efficient?The concept of economic efficiency is related but distinct. Technical efficiency seeks to minimize inputs, whereas economic efficiency seeks to minimize costs, that might or might not necessitate fewer inputs.
In other words, the company wants to cut costs as much as possible even while meeting production targets. For instance, the bakery would perhaps purchase cheaper materials to lower costs without lower productivity.To know more about technical efficiency and economic efficiency, here
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The complete question is;
A pizza parlor can make 100 pizzas in an evening. They make 40 pepperoni pizzas and 60 extra cheese pizzas. 100 people order pizza, but 50 people would like a pepperoni pizza and 50 would like an extra cheese pizza. This pizza parlor is what?
Technically efficient
allocatively efficient
economically efficient
Alisha hiked a trail that was 9/10 mile and Joseph hiked a trail that was 5/10 mile. How much farther did Alisha hike than Joseph?
Answers
Answer:
4/10 or 2/5 of a mile more.
Step-by-step explanation:
Since the denominators are the same, all you have to do is subtract the numerators.
9-5=10.
Therefore, Alisha hiked 2/5 of a mile further than Joseph.
ANSWE NOW SYHSDDBsbshdhdhd
Answers
A prism mainly consists of:
two basesflat surfacesequal (uniform) cross-section(s).1. A cone can't be a prism, its sides can't curve.
2. A prism has two bases, but the pyramid only has one.
3. Is a prism, meets the requirements to be a prism. (Triangular Prism)
4. Is a prism, meets the requirements to be a prism. (Rectangular Prism)
5. A square does not meet any of the requirements to be a prism.
Note: A Square Prism (Cube) can be an answer, however, this square is flat.
Answers:
3) Triangular Prism.
4) Rectangular Prism.
Ten less than the product of a number and 45.
Answers
Answer:
45*x-10
Step-by-step explanation:
10 less than a number would give you
x - 10
and the product of a number means your multiplying and your multiplying 45 so you would get
45*x
add them together and you get
45*x-10
7. Write equations that show how these cost variables depend on the
number n of customers for the two-day tours.
a. bike rental B
b. lunch and snacks L
c. hotel rooms H
d. rental of the tour support van V
Answers
A football team is selling raffle tickets for $5.00 each. Isaac purchased 10tickets. The team sold a total of 300 tickets. What is the probability thatIssac will win the raffle?
Answers
The probability is:
\(P=\frac{IsaacTickets}{TotalTickets}\)\(P=\frac{10}{300}=\frac{1}{30}=0.03333=3.33\%\)The probability that Isaac will win the raffle is 3.33%
Plsss help me i will mark you brainliest
Answers
Answer:
it will be 7
Step-by-step explanation:
A room is 3.4 m wide and 2.6 m long. What is the perimeter of the room
Answers
Answer:
The perimeter of the room is 12m
can somebody please double-check these for me.
just in case if the pictures blurry, I will provide the answers that I put below
my answers:
1. I got 27
2. I got 18.154
3. I got 44
4. I got 41.5
please correct me on any mistakes that I may have made
Answers
1. is a central angle, therefore, the arc will have the same measurement as the angle. Set the equation:
Arc = Central Angle
2x - 7 = 47
Isolate the variable, x. Note the equal sign, what you do to one side, you do to the other. Do the opposite of PEMDAS.
First, add 7 to both sides of the equation:
2x - 7 (+7) = 47 (+7)
2x = 47 + 7
2x = 54
Next, divide 2 from both sides of the equation:
(2x)/2 = (54)/2
x = 54/2 = 27
27 is your answer.
2. is a inscribed angle, meaning that the angle measurement will be half of the arc. Set the equation:
212 = 2(13x - 24)
Isolate the variable, x. Note the equal sign, what you do to one side, you do to the other. Do the opposite of PEMDAS.
First, divide 2 from both sides of the equation:
(212)/2 = (2(13x - 24))/2
106 = 13x - 24
Next, add 24 to both sides of the equation:
106 (+24) = 13x - 24 (+24)
106 + 24 = 13x
130 = 13x
Finally, divide 13 from both sides of the equation:
(130)/13 = (13x)/13
x = 130/13
x = 10
10 is your answer.
3. is a central angle. The arc and the angle will, therefore, have the same measurement:
137 = 3x + 5
First, subtract 5 from both sides of the equation:
137 (-5) = 3x + 5 (-5)
137 - 5 = 3x
132 = 3x
Next, divide 3 from both sides of the equation to isolate the variable, x:
(132)/3 = (3x)/3
x = 132/3 = 44
44 is your answer.
4. is a inscribed angle. The arc will be twice the measurement of the angle.
86 = 2(2x + 3)
First, isolate the variable x by dividing 2 from both sides of the equation.
(86)/2 = (2(2x + 3)/2
43 = 2x + 3
Next, subtract 3 from both sides of the equation:
43 (-3) = 2x + 3 (-3)
40 = 2x
Finally, divide 2 from both sides of the equation:
(40)/2 = (2x)/2
x = 40/2 = 20
20 is your answer.
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a) A shopkeeper sold a mobile set for Rs 9,600 and made a loss of 5%. For what price should he sell it to gain 10 percent
Answers
Answer:
Rs 11115.5
Step-by-step explanation:
Selling price =Rs 9600
%loss = cost price - selling price. ×100
cost price.
5 = cost price - Rs 9600 ×100
cost price
Let Cp = cost price
5Cp = 100Cp - Rs 960000
5Cp - 100Cp = - Rs 960000
-95Cp = -Rs 960000
Cp = 960000/95
Cp = Rs 10105
%profit = Sp - Cp ×100
Cp
10 = Sp - 10105 ×100
10105
(10105×10)/100 = Sp - 10105
1010.5 = Sp -10105
Sp = 1010.5 +10105
Sp = Rs 11115.5
Answer:
Rs 10600
Step-by-step explanation:
we can use cross multiplication
95 = 9600
105 = x
95x = 1008000
x=1008000/95
x = 10610.5
to 3sf = 10600
sell it for Rs 10600
a runner competed in a 5 mile run. how many yards did she run (1 mile =1760 yards)
Answers
Answer:8,800
Step-by-step explanation:
1760 times 5 = 8,800
I thought the answer was 110 but the answer was so wrong so I’m doing something wrong. Can someone please help me?
Answers
Answer:
b= 50
Step-by-step explanation:
the entire angle equals 80 degrees and a portion of it equals 30. therefore the portion that equals b = 50 because 30+50=80 hope this helps.
How many zeros are at the end of 459 · 885? Explain how you can answer this question without actually computing the number. (Hint: 10 = 2 · 5.) When this number is written in ordinary decimal form, each 0 at its end comes from a factor of , or one factor of 2 and one factor of . Since there are factors of 2 and factors of 5, there are exactly factors of 10 in the number. This implies that the number ends with zeroes.
Answers
Answer:
Step-by-step explanation:
If the multiplication of two numbers has the zero at the end, one of them will have a factor of 2 and the other number will have the factor of 5.
Example: Multiplication of 25 and 8.
Factors of 25 = 5 × 5 [5 is a factor of 25]
Factors of 8 = 2 × 2 × 2 [2 is a factor of 8]
Multiplication of 8 × 25 = 200 [Zero at the end]
Two numbers are 459 and 885.
Factors of 459 = 3 × 3 × 3 × 17
Factors of 885 = 3 × 5 × 59
[Since, 2 is not a factor in both the numbers multiplication of the numbers will not have 0 at the end]
459 × 885 = 406215
a translation maps the point (5,7) onto the point (2,9) and the point A onto the point (-3 ,-5) . find the cooridinates of A.
Answers
(2 , -10) is the co- Oridinates of A.
What exactly does coordinate geometry mean?
The discipline of coordinate geometry is the study of geometry using coordinate points. It is possible to use coordinate geometry to determine distances between points, divide lines into m:n segments, locate a line's midpoint, determine the area of a triangle in the Cartesian plane, and perform other operations.
x coordinate is reduced by -5; y coordinate is increased by -5
so transformation is (x,y) -> (x +5, y-5)
applying the same transformation to B(-3,-5)
B' = (-3 +5 , -5 - 5) = (2 , -10)
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The complete question is -
A translation maps the point (5,7) onto the point (2,9) and the point A onto the point (-3 ,-5) . find the co - oridinates of A.