For the following parameterized curve, find the unit tangent vector T(t) at the given value of t. r(t) = < 8 t,10,3 sine 2 t >, for 0
Answers
Answer:
The tangent vector for \(t = 0\) is:
\(\vec T (t) = \left \langle \frac{8}{10}, 0, \frac{6}{10} \right\rangle\)
Step-by-step explanation:
The function to be used is \(\vec r(t) = \langle 8\cdot t, 10, 3\cdot \sin (2\cdot t)\rangle\)
The unit tangent vector is the gradient of \(\vec r (t)\) divided by its norm, that is:
\(\vec T (t) = \frac{\vec \nabla r (t)}{\|\vec \nabla r (t)\|}\)
Where \(\vec \nabla\) is the gradient operator, whose definition is:
\(\vec \nabla f (x_{1}, x_{2},...,x_{n}) = \left\langle \frac{\partial f}{\partial x_{1}}, \frac{\partial f}{\partial x_{2}},...,\frac{\partial f}{\partial x_{n}} \right\rangle\)
The components of the gradient function of \(\vec r(t)\) are, respectively:
\(\frac{\partial r}{\partial x_{1}} = 8\), \(\frac{\partial r}{\partial x_{2}} = 0\) and \(\frac{\partial r}{\partial x_{3}} = 6 \cdot \cos (2\cdot t)\)
For \(t = 0\):
\(\frac{\partial r}{\partial x_{1}} = 8\), \(\frac{\partial r}{\partial x_{2}} = 0\) and \(\frac{\partial r}{\partial x_{3}} = 6\)
The norm of the gradient function of \(\vec r (t)\) is:
\(\| \vec \nabla r(t) \| = \sqrt{8^{2}+0^{2}+ [6\cdot \cos (2\cdot t)]^{2}}\)
\(\| \vec \nabla r(t) \| = \sqrt{64 + 36\cdot \cos^{2} (2\cdot t)}\)
For \(t = 0\):
\(\| \vec r(t) \| = 10\)
The tangent vector for \(t = 0\) is:
\(\vec T (t) = \left \langle \frac{8}{10}, 0, \frac{6}{10} \right\rangle\)
Related Questions
a proportion question
Answers
Answer:
because x,y,z are in continuous proportion
=> x/y = y/z
<=> xz = y² =>
\(\frac{xz}{y} =y\\\\=>\frac{x^{3}z^{3} }{y^{3} }=y^{3}\)(1)
with (1), we have:
\(x^{2}y^{2}z^{2}(\frac{1}{x^{3} }+\frac{1}{y^{3} }+\frac{1}{z^{3} })\\\\= (xyz)^{2}(\frac{1}{x^{3} } +\frac{y^{3} }{x^{3}z^{3} }+\frac{1}{z^{3} })\\\\=(xyz)^{2} (\frac{x^{3}+y^{3}+z^{3} }{x^{3}z^{3}} )\\\\=y^{2}.\frac{x^{3}+y^{3}+z^{3} }{xz} \\\\= xz.\frac{x^{3}+y^{3}+z^{3} }{xz} \\\\=x^{3}+y^{3}+z^{3}\)
Step-by-step explanation:
How to find the square root in long division method for 5.4289
Answers
(explanation attached)
the ceo of a cable company claims that the mean wait time for callers at the company's customer service center is no more than 7 minutes. a random sample of 36 customers who called the company's customer service center produces the following data:
Answers
To test the CEO's claim about the mean wait time we need to conduct a hypothesis test.
The null hypothesis is that the mean wait time is no more than 7 minutes, which we can represent as H0: μ ≤ 7. The alternative hypothesis is that the mean wait time is greater than 7 minutes, which we can represent as Ha: μ > 7. We can use a one-tailed t-test for this situation, with a significance level of alpha = 0.05.
To perform the t-test, we need to calculate the sample mean, sample standard deviation, and the t-statistic. The sample mean is the sum of the wait times divided by the sample size, which is 36 in this case. The sample standard deviation is a measure of the dispersion of the data. The t-statistic is calculated using the sample mean, sample standard deviation, and the hypothesized mean wait time of 7 minutes.
Once we have calculated the t-statistic, we can compare it to the critical value from the t-distribution table to determine the p-value. If the p-value is less than alpha, we can reject the null hypothesis and conclude that the mean wait time is indeed greater than 7 minutes. If the p-value is greater than alpha, we cannot reject the null hypothesis and must conclude that the mean wait time is no more than 7 minutes.
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f(x) = 2x³ + 3x² - 7x + 2
g(x) = 2x - 5
Find (f + g)(x).
that’s the correct answer
Answers
The sum of the functions is option B. (f + g)(x) = 2x³ + 3x² - 5x - 3.
What is a Function?A function is defined as a relation from a set to another set such that the elements in the first set maps to one and only one element in the second set.
Or in other words, no elements in the first set has more than one image in the second set.
Given the two functions,
f(x) = 2x³ + 3x² - 7x + 2 and g(x) = 2x - 5.
We have to find (f + g) (x).
Sum of the functions is,
(f + g)(x) = f(x) + g(x)
= (2x³ + 3x² - 7x + 2) + (2x - 5)
= 2x³ + 3x² - 7x + 2x + 2 - 5
= 2x³ + 3x² - 5x - 3
Hence the sum of the given function is 2x³ + 3x² - 5x - 3.
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Point A is a representation of which number on the number line?
A number line has points blank, A, negative 2, B, 0, C, 2, blank, D.
–4
–3
1
4
Answers
Answer:
B
Step-by-step explanation:
Answer
-3
Step-by-step explanation:
on edge 2020
PLZ HELP ME FAST
The table shows the ratio of caramel corn to hot pepper corn in a bag. What is the constant of proportionality? (4 points)
Hot Pepper Corn Caramel Corn
5 8
10 16
15 24
Answer Options
a-3
b-8
c-1.6
d-0.625
Answers
Answer:
A-3 because 5+8=3, 10+3 doubled=16, and so on so on
Step-by-step explanation:
Answer:
It is c, 1.6
Step-by-step explanation:
To find the constant of proportionality, you divided y by x. 8 divided by 5 is 1.6. 16 divided by 10 is 1.6 24 divided by 15 is 1.6.
So therefore it is c, 1.6 :)
Which of the following statements is true?
(A) The greatest prime factor of 18 is 9.
(B) The greatest prime factor of 21 is 3.
(C) The greatest prime factor of 4 is 2.
(D) The greatest prime factor of 34 is 11.
atidew stel vonbris mebeoAno
Answers
The answer is option c. The greatest prime factor of 4 is 2.
Whoever answers correctly gets brainlist.
Answers
Answer:
1.- 4/5 + 5/12= 1 and 13/60
2.- 5/6 + 6/12= 1 and 1/3
3.- 1/3 + 2/6= 2/3
4.- 7/8 + 8/10= 1 and 27/40
Please help I am doing test ! A woman borrows $4,000 at 9% compounded monthly, which is to be amortized over 3 years in equal monthly payments. for tax purposes, she needs to know the amount of interest paid during each year of the loan. find the interest paid during the first year, the second year, and the third year of the loan. [hint: find the unpaid balance after 12 payments and after 24 payments.
Answers
Answer:
Monthly Loan Payment
Loan Amount (P) = $6,000
Monthly Interest Rate (n) = 0.75% per month [9.00% / 12 Months]
Number of months (n) = 36 Months [3 Years x 12 months]
Monthly Loan Payment = [P x {r (1+r)n} ] / [( 1+r)n – 1]
= [$6,000 x {0.0075 x (1 + 0.0075)36}] / [(1 + 0.0075)36 – 1]
= [$6,000 x {0.0075 x 1.308645}] / [1.308645 – 1]
= [$6,000 x 0.009815] / 0.308645
= $58.89 / 0.308645
= $190.80
Monthly Loan Amortization Schedule
“Therefore, the total interest paid during the first year will be $465.99”
HOPE this example helps
Aimee's garbage disposal has 7/8 horse power. Vincent's garbage disposal has 3/5 horse power. How much more power does aimee's garbage disposal have?
Answers
Answer:
Aimee's garbage disposal has 11/40 more power than Vincent's garbage disposal.
Step-by-step explanation:
Aimee's garbage disposal horse power = 7/8
Vincent's garbage disposal horse power = 3/5
All we need is to subtract Vincent's power from Aimee's power.
i.e.
\(\frac{7}{8}-\frac{3}{5}\)
Thus,
\(\frac{7}{8}-\frac{3}{5}\:=\frac{35}{40}-\frac{24}{40}\)
\(\mathrm{Apply\:the\:fraction\:rule}:\quad \frac{a}{c}-\frac{b}{c}=\frac{a-b}{c}\)
\(=\frac{35-24}{40}\)
\(=\frac{11}{40}\)
Thus, Aimee's garbage disposal has 11/40 more power than Vincent's garbage disposal.
A certain prescription drug diminishes in the system at a rate of 25% per hour. If a person was administered 1450mg of the drug, how much will remain in 4 hours? How many hours will it take for the amount of the drug in their system to be less than 5mg?
Answers
9514 1404 393
Answer:
459 mgabout 20 hoursStep-by-step explanation:
The decay factor is 1 -25% = 0.75 per hour, so the exponential equation can be written ...
r(t) = 1450·0.75^t . . . . . milligrams remaining after t hours
__
a) After 4 hours, the amount remaining is ...
r(4) = 1450·0.75^4 ≈ 458.79 . . . mg
About 459 mg will remain after 4 hours.
__
b) To find the time it takes before the amount remaining is less than 5 mg, we need to solve ...
r(t) < 5
1450·0.75^t < 5 . . . . use the function definition
0.75^t < 5/1450 . . . . divide by 1450
t·log(0.75) < log(1/290) . . . . . take logarithms (reduce fraction)
t > log(1/290)/log(0.75) . . . . . divide by the (negative) coefficient of t
t > 19.708
It will take about 20 hours for the amount of the drug remaining to be less than 5 mg.
Given right triangle ABC, where side "c" is the hypotenuse, angle B measures 42 degrees, and side c measures 18 m, find the length of side b.
Answers
The length of side b of the given right angle triangle using law of sines is; b = 12.044 m
How to use the law of sines?The law of sines states that when we divide side "a" by the sine of angle A, it is equal to side "b" divided by the sine of angle B, and also equal to side "c" divided by the sine of angle C
Thus;
a/sin A = b/sin B = c/sinC
The parameters are;
B = 42°
c = 18m
Since c is the hypotenuse, it is the side that will be opposite the right angle and so;
C = 90°
Thus, using sine rule;
c/sinC = b/sin B
18/sin 90 = b/sin 42
b = (18 * sin 42)/1
b = 12.044 m
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True or False: If there are "m" ways of doing one thing, and "n" ways of doing another thing, the multiplication formula states that there are (m) × (n) ways of doing both.
Answers
Given statment "If there are "m" ways of doing one thing, and "n" ways of doing another thing, the multiplication formula states that there are (m) × (n) ways of doing both." is true. Because, When two or more independent events occur at the same time, the multiplication rule formula can be used to compute the probability of all of them happening.
Multiplication formula:
The multiplication formula in probability is used to determine the number of possible outcomes when two events are combined.
The multiplication rule formula can be used to determine the likelihood that multiple independent occurrences will take place at the same time.
The multiplication rule formula for probability is:
P(A and B) = P(A) x P(B|A).
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write two equations in one variable that have the same number of solutions as this equation solve 49x + 9 equals 49x + 83
Answers
To solve this equation you need to clear the variable x, as follow:
\(\begin{gathered} 49x-49x=83-9 \\ 0=74 \end{gathered}\)As 0 is not equal to 74. The equation has no solution.To write two equations with no solutions you write equations that when you clear the variable the solution make no mathematical sense:
\(\begin{gathered} y-45=y+9 \\ y-y=9+45 \\ 0=54 \end{gathered}\)\(\begin{gathered} -5z=25-5z \\ -5z+5z=25 \\ 0=25 \end{gathered}\)1. The area of a square is directly proportional to the square of the length of its side. The area of a square is 144 square units, for a side of length 12 units. What is the area of a square having a side of length 20 units? please step by step only
Answers
Answer:
400 unit
Step-by-step explanation:
Answer:
400
Step-by-step explanation:
area us length times width
A piece of wire is 72cm long. Is used to form 2 identical squares. What is the length of each each side of squares?
Answers
Answer:
the length of each side of the square are 6 cm
Because each square has 4 sides
So (4*9)+(4*9)=72
So the answer is 9
The price of a car is £21500 before it is reduced by 11%.
How much does it cost after the reduction?
Answers
Answer:
19135
Step-by-step explanation:
did the math in a calculator
Answer:
£19135
Step-by-step explanation:
Calculated
55 liters = ______ microliters
Answers
When we transform the big quantity to the small one, we always have to multiply something. So micro refers x 10 to the power of 6
55 x 10^6 = 55,000,000 microliters.
There are 4 windows in the living room. Each window has 1 set of blinds and 2 panels of curtains. The blinds cost $20 each. Each curtain panel cost $28. How much do the window treatments cost?
Answers
4x20= 80
80+224=304
$304 total
Answer:
$304
Step-by-step explanation:
4 Windows (each window has 1 blind and 2 panels of curtains)
1 blind = $20 * 4 = $80
1 panels curtains = $28 * 2 = $56 * 4 = $224
$80 + $224 = $304
Use the information to answer the question.
Miranda is making a vegetable salad. She adds 2 cups of cucumbers, 4 cups of carrots, and some cherry tomatoes. Then, Miranda puts all of the
salad into 5 bowls. She puts cups into each bowl.
How many cups of cherry tomatoes did Miranda put in the vegetable salad? Enter the answer in the box.
cups
Answers
Answer:
Step-by-step explanation:
The equation is poorly written and I cannot unfortunately solve it.
Multiple 24 by 8.95 I need to show the work. I don’t know the steps
Answers
Answer: 214.8
Step-by-step explanation:
First move the decimal to the right, in this case 8.95 = 895., then multiply the 24 by 895. to get 21480., you then move the decimal to the left and you get 214.80 or 214.8.
simplify √([2m5z6]/[ xy])
Answers
The simplified form of √([2m5z6]/[xy]) is (√2m√5z√6) / (√x√y).
To simplify the expression √([2m5z6]/[xy]), we can break it down step by step:
Simplify the numerator:
√(2m5z6) = √(2) * √(m) * √(5) * √(z) * √(6)
= √2m√5z√6
Simplify the denominator:
√(xy) = √(x) * √(y)
Combine the numerator and denominator:
√([2m5z6]/[xy]) = (√2m√5z√6) / (√x√y)
Thus, the simplified form of √([2m5z6]/[xy]) is (√2m√5z√6) / (√x√y).
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can you check to see if my work is correct?
Answers
The Solution.
\(P=-\frac{1}{250}T^2+2.8T-394\)To obtain the maximum value of T, we differentiate with respect to x and equate to zero.
\(\begin{gathered} \frac{dP}{dT}=2(-\frac{1}{250}T)+2.8\text{ =0} \\ \\ -\frac{1}{125}T+2.8=0 \\ \\ -\frac{T}{125}=-2.8 \\ \text{Cross multiplying, we get} \\ T=125\times2.8=350^oF \end{gathered}\)To get the maximum value of P, we shall substitute 350 for T in the given function.
\(\begin{gathered} P=-\frac{1}{250}(350^2)+2.8(350)-394 \\ \\ P=-490+980-394 \\ P=96\text{ percent} \end{gathered}\)The correct answer is T = 350 degrees Fahrenheit , and P = 96 percent.
Can someone please help me
Answers
Answer:
The 2nd one
Step-by-step explanation:
let me know if this is helpful :)
I would have answered sooner i just have not been on brainly in a while and you were the first person to be helped by ME!!
Solve, expressing your answer in an exact form involving a natural logarithm and showing your steps: 3*e^1/2t+4=27
Answers
Answer:
3 e^t/2 + 4 = 27
e^t/2 = 23 / 3
Taking natural log of both sides
t/2 = ln 23/3 = ln 7.667 = 2.037
t = 4.074
Check:
3 e^4.074/2 + 4 = 27
27 = 27
Malcolm has $50 gift card to a local car wash and order is the ultimate car wash each visit is $8.95
Answers
The amount cheaper is the car washes Malcolm orders than the car washes Martha's order is $13.
The correct answer choice is option B.
How much cheaper is the car washes Malcolm orders than the car washes Martha's order?Malcolm's gift card = $50.
Cost Malcolm's car wash per visit = $7
Martha's gift card = $180
Cost Martha's car wash per visit = Difference between gift card balance of first and second visit
= $180 - $160
= $20
How cheap is the car washes Malcolm orders than the car washes Martha's order = $20 - $7
= $13
Therefore, Malcolm's car wash is cheaper than Martha's car wash by $13
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find the perimeter of a triangle whose each sides is 10cm.
Answers
Answer:
perimeter= 10+10+10
= 30 cm
mark me brainliestt :))
Answer:
here is your ans .
I have explain your ans Above
Without writing the equation x^2 + y^2 + 24x – 26y+ 277 = 0 in the standard form, state whether the graph of this equation is a
parabola, circle, ellipse, or hyperbola.
a. parabola
c. hyperbola
b. ellipse
d. circle
Answers
Answer:
circle
Step-by-step explanation:
You can see there is a x^2 and y^2 and 24 x and 26 y meaning if you do complete the square you can write it as a circle in standard form
A motorcycle can travel 500 miles on 25 gallons of gasoline. How far can it travel on 32 gallons of gasoline.
Answers
For us to be able to determine how far will 32 gallons of gasoline will go, we will be using ratios and proportions.
We get,
Let x = the distance it can travel at 32 gallons
\(\text{ 500 miles : 25 gallons = x : 32 gallons}\)\(\text{ 500 miles : 25 gallons = x : 32 gallons }\rightarrow\text{ }\frac{\text{ 500 miles}}{\text{ 25 (gallons)}}\text{ = }\frac{\text{ x}}{\text{ 32 (gallons)}}\)\(\text{ (500 miles)}(32)\text{ = (}x)(25)\)\(\text{ 16000 miles = 25x}\)\(\text{ }\frac{\text{16000 miles}}{25}\text{ = }\frac{\text{25x}}{25}\)\(\text{ x = }640\text{ miles}\)Therefore, 32 gallons of gasoline can make the motorcycle travel 640 miles.
What is the central angle(pic included)
Answers
Answer:
72
Step-by-step explanation:
circumference = 20
arc = 4
4/20 =1/5
a circle = 360°
1/5 * 360 = 72