Answers
The values of x and y at t=3 are -4.95 and 0.423 respectively.
The value of dx/dt and dy/dt are 0.71 and -2.97 respectively.
The value of the tangent slope at t=3 is 4.21.
The speed at t=3 is 3.05 units/sec.
Given the equation of x as the function of t is
x= 5 cos t
similarly, the equation of y as the function of t is
y= 3 sin t
At t=3 the value of x will be
x (at t=3) = 5 cos 3= 5(-0.989)= -4.95
At t=3 the value of y will be
y (at t=3) = 3 sin 3= 3(0.141)= 0.423
The derivative of the function of x with respect to t will be
dx/dt= d(5 cos t)/dt= 5d(cos t)/dt= -5 sin t
at t=3 the value of dx/dt will be
dx/dt (at t=3) = -5 sin 3= -5(0.141)= 0.71
The derivative of the function of y with respect to t will be
dy/dt= d(3 sin t)/dt= 3d(sin t)/dt= 3 cos t
at t=3 the value of dy/dt will be
dy/dt (at t=3) = 3 cos t= 3(-0.989)= -2.97
The tangent slope is dy/dx which can be calculated by
dy/dx= (dy/dt)(dt/dx)= (dy/dt)/(dx/dt)= 3 cos t/ -5 sin t= (-3/5) cot t
at t=3 the value of tangent slope will be
dy/dx (at t=3) = (-3/5) cot 3= 4.21
The speed at t=3 will be
speed v= [tex]\sqrt{v_{x} ^{2} + v_{y} ^{2} }[/tex]
= √(dx/dt)²+(dy/dt)²
at t=3
= √(0.71)²+(-2.97)²
= √9.325
= 3.05 unit/sec
Therefore the values of x and y at t=3 are -4.95 and 0.423 respectively.
The value of dx/dt and dy/dt are 0.71 and -2.97 respectively.
The value of the tangent slope at t=3 is 4.21.
The speed at t=3 is 3.05 units/sec.
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Related Questions
Which statements about the system are true? Select two options.
y=-x-4
3y - x = -7
O The system has one solution.
O The system consists of parallel lines.
O Both lines have the same slope.
Both lines have the same y-intercept.
The equations represent the same line.
Answers
The system of equation has one solution
How to determine the true statements?The equations are given as:
y = -x - 4
3y -x = -7
Rewrite the first equation as:
y + x = -4
Add y + x = -4 to the second equation to eliminate x
4y = -11
Divide by 4
y = -11/4
Substitute y = -11/4 in y + x = -4
-11/4 + x = -4
Make x the subject
x = -4 + 11/4
Evaluate
x = -5/4
The above means that the system of equation has one solution
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Option A and B. The system has one solution and the system consists of parallel lines.
Slope of the linesThe slope of the lines is calculated as follows;
y = -x - 4
slope = - 1
3y - x = -7
3y = x - 7
y = x/3 - 7/3
slope = 1/3
Solution of the equationsy = -x - 4 ----(1)
3y - x = -7 ----(2)
solve (1) and (2)
3(-x - 4) - x = -7
-3x -12 - x = -7
-4x = 5
x = -5/4
y = -5/4 - 4
y = -5.25
Thus, the system has one solution and the system consists of parallel lines.
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can i charge my hp laptop more than 1000 times
Answers
Answer: Yes.
Step-by-step explanation: However, charging your battery to high voltages except for the first time can significantly decrease your battery's lifespan. According to some studies charging a battery to only 85% to 90% can improve its discharge cycle from 300 to even an extra 1000 recharges.
find the value of the hypotenuse for each of the following right triangles.
Answers
Answer:
I have done the 1st 2 sums in proper systematic manner. The remaining sums I'll be writing only the main formula and substitution. I hope you will write the missing sentences .
Step-by-step explanation:
Hope you will understand the sums..Also I would appreciate it if you could marke my answer as BRAINLIEST and THANK ME.｡◕‿◕｡
Answer:
Step-by-step explanation:
1. hypotenuse = 89
2. hypotenuse = 85
3. hypotenuse = 97
4. hypotenuse = 153
5. hypotenuse = 34
6. hypotenuse = 113
7. hypotenuse = 916
8. hypotenuse = 170
9. hypotenuse = 394
10. hypotenuse = 61
An asset has a cost of $50,000, with a residual value of $10,000. It has a life of 5 years and was purchased on January 1. Under double-declining-balance, what’s the asset’s fourth full year of depreciation expense?
Answers
The asset’s fourth full year of depreciation expense will be $6,666.67.
What is double-declining-balance?An enhanced technique for recording loss over the lifetime of a product by adjusting the item's starting sales price by a discount factor.
An asset has a cost of $50,000, with a residual value of $10,000.
It has a life of 5 years and was purchased on January 1.
Then the asset’s fourth full year of depreciation expense will be
Annual depreciation = (cost – salvage value)/ useful life
Annual depreciation = (50000 – 10000) / 5 = $8,000
Year 1 Depreciation (for 10 months, from March to December) = $8,000 × 10/12 = $6,666.67.
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Help please I will do anything
Answers
Answer:
? = 12
Step-by-step explanation:
[tex]\frac{7}{12} +\frac{10}{12} =\frac{7+10}{12} =\frac{17}{12}[/tex]
[tex]\frac{17}{12} =\frac{12}{12} +\frac{5}{12} =1+\frac{5}{12} =1\frac{5}{12}[/tex]
Hope this helps
Please help quickly!!
Answers
Answer:
D
Step-by-step explanation:
My supersonic jet burns 4 gallons of jet fuel in 3 seconds. How many gallons of jet fuel do I need to fly for an hour?
Answers
The number of gallons of Jet fuel that is needed to fly for an hour is; 14400 gallons
How to solve simple Algebra?We are given;
Number of gallons burned = 4 gallons
Time to burn 4 gallons = 3 seconds
Now, for 1 hour there are 3600 seconds and so;
Number of gallons that is burnt in 3600 seconds = 3600 * 4
Number of gallons that is burnt in 3600 seconds = 14400 gallons
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Please I need help on Fundametal Trigonometric Identities?
Answers
Fundamental Trigonometric Identities are listed below:
[tex]sin^{2}[/tex]Θ + [tex]cos^{2}[/tex]Θ = 1[tex]sec^{2}[/tex]Θ - [tex]tan^{2}[/tex]Θ = 1[tex]cosec^{2}[/tex]Θ - [tex]cot^{2}[/tex]Θ = 1sinΘ = 1 / cosec Θ cos Θ = 1 / sec Θ tan Θ = 1 / cot Θ tan Θ = sinΘ / cosΘ cotΘ = cosΘ / sinΘMeaning of Fundamental Trigonometric IdentitiesFundamental Trigonometric Identities can be defined as the basic identities or variables that can be used to proffer solutions to any problem relating to angles and trigonometry.
In conclusion, A few Fundamental Trigonometric Identities are listed above.
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Find two positive numbers such that their sum is 60 and their product is a maximum. Select one: O a. 30 and 30 O b. 25 and 35 O c. 1 and 59 O d. 20 and 40
Answers
Answer:
B: 25 and 35
Step-by-step explanation:
25 product 35 875
B. 25 x 35 = 875
C. 1 x 59 = 59
D. 20 x 40 = 800
The biggest product is for 30 and 30
If you call one number x the other will be 60 - x
Product = x(60 - x) = 60x - x^2
This is a parabola with roots at 0 and 60
The maximum product is halfway between 0 and 60 ie when x = 30
Question 10: Each tablet in a bottle of 30 costs the pharmacy $4.60. The pharmacy has additional costs including supplies and shipping of $1.40 per pill. If a 12% profit is desired, how much would the pharmacy charge for entire bottle?
Answers
The pharmacy must charge for $201.6 for the entire bottle.
Profit is the financial gain to the seller after selling some commodity
Revenue is the total sale of the seller after selling some commodity
Expenses is the expenditure to the seller before selling the commodity
Profit = Revenue - Expenses
Cost of the tablet = $4.60
Total cost of the bottle=$4.60x30
=$138
Additional cost=$1.40 x 30
= $42
Total expenses=$180
Profit %=125
Revenue= $180 x (1+12/100)
=$180 x (112/100)
=$201.6
Therefore, The pharmacy must charge for $201.6 for the entire bottle for a profit of 12%
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Solve for x:
5(1 – x) = 20
x = __
Answers
[tex]5(1-x)=20\\5-5x=20\\5x=-15\\x=-3[/tex]
Hii!
__________________________________________________________
[tex]\stackrel\star{\rightsquigarrow\circ\boldsymbol{\underbrace{Answer}}}\circ\leftharpoonup[/tex]
The value of x is -3! ^^
[tex]\stackrel\star{\rightsquigarrow\circ\boldsymbol{\underbrace{Explanation}}}\circ\leftharpoonup[/tex]
[tex]\bullet[/tex] First multiply 5 times 1 and -x
[tex]\twoheadrightarrow\sf 5(1-x)=20[/tex]
[tex]\twoheadrightarrow\sf 5-5x=20[/tex]
[tex]\bullet[/tex] Now subtract 5 from both sides
[tex]\twoheadrightarrow\sf -5x=15[/tex]
[tex]\bullet[/tex] Now divide both sides by -5
[tex]\twoheadrightarrow\sf x=-3[/tex]
--
Hope that this helped! Best wishes.
--
SHL T Teleperformance
each interaction matters
Choose the correct option.
You arrived at your office at 9:35 AM. You left your office at 6:05 PM. How many hours did
spend in the office?
Answers
Answer:
8 hours 30 minutes
Step-by-step explanation:
6:05 pm - 9:35 am =
= 18:05 - 9:35
= 17:65 - 9:35
= 8:30
Answer:
Citcitdutditdutdtuditditdtiditf this is what is adjective 6hftuiouhvcutxyrzyt
Step-by-step explanation:
huuugggguytzurzt8st8s8ts9td96097g79t8dtrudutfitf8tfitftid8tdtdtudutd
What is the domain of the function
f(x) = [tex]\sqrt{1/3 x + 2}[/tex]
Answers
The domain of the function is:
D: {x ∈ R | x ≥ -6}
How to get the domain of the function?
Here we have:
[tex]f(x) = \sqrt{(1/3)*x + 2}[/tex]
Remember that the argument of a square root can be only numbers equal to or larger than zero, so the domain of that function is such that:
[tex](1/3)*x + 2 \geq 0[/tex]
Now we can solve that for x.
[tex](1/3)*x + 2 \geq 0\\(1/3)*x \geq -2\\\\x \geq -2*(3/1)\\\\x \geq -6[/tex]
So the domain of the function is:
D: {x ∈ R | x ≥ -6}
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Answer:
The domain of the function is:
D: {x ∈ R | x ≥ -6}
look at the picture
thank you
Answers
The correct answer to this question is the first option
Which of the following statements must be true about this diagram? Check
all that apply.
A. mz2+ mz3 = mz4
B. mz1+ m2 2 = m/3
C. m23 is greater than m<2
D. m24 is greater than mz1
E. mz1+mz2 = mz4
F. mz4 is greater than m<2
Answers
Answer:
D, E, F is the answer.
Step-by-step explanation:
From the diagram:-
m∠ 4 is greater than m∠ 1m∠ 4 is greater than m∠ 2m∠ 1 + m∠ 2 = m∠ 4Therefore, D, E, F.
-------------------------------
Which of these is the algebraic expression for the verbal expression "twelve times the difference of a number and four?"
12 ⋅ x − 4
x − 4 ⋅ 12
4(x − 12)
12(x − 4)
Answers
Answer:
[tex]12(x - 4)[/tex]
Step-by-step explanation:
The question says, "twelve times the difference of a number and four"
Let's start with the first number, which is twelve = 12. Moving on, we have times = ×, then the difference which is minus(-). A number is unknown, any aphabet can be used to represent the number, so, we represent with 'x', and then four = 4.
Arranging them, we have:
[tex]12 \times x - 4[/tex]
in algebraic equations, times is always represented by bracket. Therefore, our final answer is:
[tex]12(x - 4)[/tex]
I hope this helps.
On May 6, Jim Ryan borrowed $14,000 from Lane Bank at 712% interest. Jim plans to repay the loan on March 11. Assume the loan is on ordinary interest. How much will Jim repay on March 11?
Answers
The amount to be repaid by Jim Ryan is $14,891.78.
Given that, Principal (P) =$14,000, the rate of interest (R) =7[tex]\frac{1}{2}[/tex]% and T=310 days.
What is ordinary interest?Ordinary interest is calculated on the basis of a 360-day year or a 30-day month; exact interest is calculated on a 365-day year.
Now, the interest=14,000×7.5 %×[tex]\frac{310}{365}[/tex].
=$891.78
The amount to be repaid=14,000+891.78=$14,891.78
Therefore, the amount to be repaid by Jim Ryan is $14,891.78.
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Which expression is equivalent to...
Answers
Answer:
first option
Step-by-step explanation:
[tex]\frac{(2g^5)^3}{(4h^2)^3}\\= \frac{8g^1^5}{64h^6} \\= \frac{g^1^5}{8h^6}[/tex]
Step-by-Step Solution:
= (2g^5)^3 / (4h^2)^3
= 8g^15 / 64h^6
=> g^15 / 8h^6
Which of the following is equivalent to the radical expression below when
x>=2?
(√x-2)(√x+9)
Answers
The equivalent expression of [tex](\sqrt x - 2)(\sqrt x + 9)[/tex] is [tex]x + 7\sqrt x - 18[/tex]
How to determine the equivalent equation?The expression is given as:
[tex](\sqrt x - 2)(\sqrt x + 9)[/tex]
Expand the expression
[tex]x - 2\sqrt x + 9\sqrt x - 18[/tex]
Evaluate the like terms
[tex]x + 7\sqrt x - 18[/tex]
Hence, the equivalent expression of [tex](\sqrt x - 2)(\sqrt x + 9)[/tex] is [tex]x + 7\sqrt x - 18[/tex]
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What data collection
used in face-to-face
or written questionnaires?
method is
interview
O A. survey
O B. observation
O C. experiment
O D. publication
Answers
Answer:
survey (A)
A questionnaire (or someone asking questions) is considered to be a survey. It is "surveying" someone's opinion on data.
hope this helps!!
An arithmetic sequence is shown in the graph.
What is the equation for the nth term of the arithmetic sequence?
an = –3 + 5(n – 1)
an = –3 + 5(n + 1)
an = –3 – 5n
an = –3 + 5n
Answers
Answer:
an= -3+5(n-1)
Step-by-step explanation:
Try writing out the terms and finding a pattern. In this case, inserting any plotted x-value into the sequence -3+5(n-1) produces the correct y-value.
Answer:
A.) an = -3 + 5(n - 1)
Explanation:
Given: (1, -3), (2, 2), (3, 7), (4, 12), (5, 17)
Arithmetic Series: a + (n - 1)d
['a' is first term, 'n' determines term position, 'd' is common difference]
Determine the following:
a = -3d = second term - first term = 2 - (-3) = 5Putting into equation:
-3 + (n - 1)5-3 + 5(n - 1)Pls answer quickly, make sure to answer all parts
Find the area of the region bounded by the line y =3x -6 and line y=-2x+8 and
a) the x-axis. b) the y-axis. c) the line y=6. d) the line x=5.
Answers
The area of the region bounded by the line y =3x -6 and line y=-2x+8 is 12/5 units
How to find the area?y = 3x - 6
y = -2x + 8
Set these two equations equal to each other.
3x - 6 = -2x + 8
Add 2x to both sides of the equation.
5x - 6 = 8
Add 6 to both sides of the equation.
5x = 14
Divide both sides of the equation by 5.
x = 14/5
Find the y-value where these points intersect by plugging this x-value back into either equation.
y = 3(14/5) - 6
Multiply and simplify.
y = 42/5 - 6
Multiply 6 by (5/5) to get common denominators.
y = 42/5 - 30/5
Subtract and simplify.
y = 12/5
These two lines intersect at the point 12/5. This is the height of the triangle formed by these two lines and the x-axis.
Now let's find the roots of these equations (where they touch the x-axis) so we can determine the base of the triangle.
Set both equations equal to 0.
(I) 0 = 3x - 6
Add 6 both sides of the equation.
6 = 3x
Divide both sides of the equation by 3.
x = 2
Set the second equation equal to 0.
(II) 0 = -2x + 8
2x = 8
x = 4
The base of the triangle is from (2,0) to (4,0), making it a length of 2 units.
The height of the triangle is 12/5 units.
A = 1/2bh
Substitute 2 for b and 14/5 for h.
A = (1/2) · (2) · (12/5)
A = 12/5
The area of the region bounded by the lines y = 3x - 6 and y = -2x + 8 between the x-axis is 12/5 units.
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What does the ratio 6 to 8 represent in the situation?
Answers
Answer:
its 80
Step-by-step explanation:
the ratio is 80 hope this helps!
Normal annual capacity for star company is 36,000 machine hours, with fixed factory overhead budgeted as Rs. 16,920 and an estimated variable factory overhead rate of Rs. 2.10 per hour, During October actual production required 2,700 machine hours, with a total factory overhead of Rs. 7,400. Required: Compute: 1) The applied factory overhead 2) The over-or underapplied factory overhead amount for October,
Answers
The applied factory overhead is $6,939 and the over-or underapplied factory overhead amount for October is $461.
Applied and under applied factory overhead1. Applied factory overhead:
Predetermine overhead rate=Fixed overhead/Machine hours
Predetermine overhead rate=16,920/36,000
Predetermine overhead rate=0.47
Applied overhead=Machine hours×Rate
Variable=2700×2.10 per hour= $5,670
Fixed=2700×0.47 per hour=$1,269
Total overhead applied=$6,939
($5,670+$1,269)
2. Under applied overhead
Total overhead applied $6,939
Less Total factory overhead $7,400
Under applied overhead -$461
($6,939-$7,400)
Therefore the applied factory overhead is $6,939 and the over-or underapplied factory overhead amount for October is $461.
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What is the solution to the following equation?
-3+x= -8
A. x = -5
B. x=5
C. x = 11
D. x=-11
Answers
Add 3 to each side, -8 + 3 = -5
Answer:
[tex]\mathsf {A. x = -5}[/tex]
Step-by-step explanation:
[tex]\implies \mathsf {-3 + x = -8}[/tex]
[tex]\implies \mathsf {x = -8 + 3}[/tex]
[tex]\implies \mathsf {x = -5}[/tex]
Rectangle 1 has length x and width y. Rectangle 2 is made by multiplying each dimension of Rectangle 1 by a factor of k, where k > 0.
Write a paragraph proof to show that the perimeter of Rectangle 2 is k times the perimeter of Rectangle 1.
Write a paragraph proof to show that the area of Rectangle 2 is times the area of Rectangle 1.
Answers
Answer:
Perimeter of rectangle2 = k × perimeter of rectangle 1
area of rectangle 2 = k² × area of rectangle 1
Step-by-step explanation:
• rectangle 1 :
Length x
Width y
perimeter1 = 2×(x + y)
area1 = x × y
……………………
•• rectangle 2 :
Length kx
Width ky
Perimeter2 = 2×(Kx + ky)
area2 = kx × ky
……………………………………………
therefore,
Perimeter of rectangle 2
= 2×(Kx + ky)
= 2×k×(x + y)
= k×2×(x + y)
= k × perimeter of rectangle 1
On the other hand,
area of rectangle 2
= Kx × ky
= k×k×(x × y)
= k²×(x × y)
= k² × area of rectangle 1
HELP DUE SOON A farmer has decided to divide his land area in half in order to plant soy and corn. Calculate the area of the entire area so he knows how much soil is needed.
A parallelogram with a height of 6 yards and side length 9 yards. The height forms a triangle with the slanted side of the rhombus with a base of 2.5 yards. Rhombus is split into a soy half and a corn half.
Each bag of soil covers 20 square yards. How many bags should the farmer purchase?
Answers
The farmer should purchase 2 bags of soil for his farm.
What is Area of parallelogram?A parallelogram is a two-dimensional figure with four sides. It is a special case of the quadrilateral, where opposite sides are equal and parallel. The area of a parallelogram is the space enclosed within its four sides. Area is equal to the product of length and height of the parallelogram.
The shape of the farm, according to the picture is a parallelogram. Therefore, the total area can be calculated as follows:
Area = base X height
where
b = base
h = height
base = 6.5 + 2.5 = 9.0 yards
height = 6 yards
Area = 6 × 9 = 54 square yards.
40 square yards requires 1 bag of soil .
54 square yards will require ?
Bags required = 54 / 40 = 1.35 bag
Thus, the farmer will require 2 bags of soil for his farm.
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Study each of the growing geometrical patterns. Then do the following for each pattern. (I) Give a verbal description of how the pattern is growing. (ii)Set up a table of values.(III) Write down a numerical description for each pattern (you must relate the number of the frame to the number of figures in the frame). (IV) For each pattern, write down a formula that can be used to calculate the number of building blocks in any term. (v) Write down the value of the 10th frame. Use your formula to determine how many building blocks there are in the 100th frame of each growing pattern. M M Δ Δ Δ 2 (6) (6) (8) [40]
Answers
A description of how the pattern is growing is that the pattern is growing by the addition of two blocks every time.
How to illustrate the pattern?A numerical description of the pattern is:
1 - 2 blocks.
2 - 4 blocks.
3 - 6 blocks
4 - 8 blocks.
The formula that can be used to calculate the number if building blocks in any term will be 2n. For example, the number of blocks for the 5th term will be:
= 2n = 2 × 5 = 10
The value for the 10th frame will be:
= 2n
= 2 × 10 = 20
The value for the 100th frame will be:
= 2n
= 2 × 100 = 200
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ξ = {x:x is an integer, 2 ≤ x ≤ 14}
� = {x:x is a prime number}
� = {x:x is a multiple of 3}
Given that C ⊂ A, n(C)=3 and B ∩ C = ∅, list the members of a possible set C
Answers
The members of a possible set C are {6, 9, 12}
Set theoryThe universal set is the set that contains all other sets. Given the following sets
ξ = {x:x is an integer, 2 ≤ x ≤ 14}
B = {x:x is a prime number}
A = {x:x is a multiple of 3}
The sets B and A are:
B = {2, 3, 5, 7, 11}
A = {3, 6, 9, 12}
If C is a subset of A with a cardinality of 3, hence the required set will be {6, 9, 12}. Note that 3 is excluded since B n C must be an empty set.
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In a certain town, the ratio of the number of children to the number of adults is 3 to 7. What percent of the town’s population are adults?
Answers
Answer:
70%
Step-by-step explanation:
If 3 child and 7 adult is in the town, then there are total 10 people. 7 ÷ 10 is equal to 0.7, which is 70%.
