Mathematics High School

Find the derivative, r ′(t), of the vector function. r(t) = i +
2j + e^(3t) k

Answers

Answer 1

The derivative of the vector function r(t) = i + 2j + e^(3t)k is r'(t) = 3e^(3t)k.

To find the derivative r'(t) of the vector function r(t) = i + 2j + e^(3t)k, we differentiate each component of the vector function with respect to t.

r'(t) = d/dt (i) + d/dt (2j) + d/dt (e^(3t)k)

The derivative of a constant with respect to t is zero, so the first two terms will be zero.

r'(t) = 0 + 0 + d/dt (e^(3t)k)

To differentiate e^(3t) with respect to t, we use the chain rule. The derivative of e^(3t) is 3e^(3t) multiplied by the derivative of the exponent, which is 3.

r'(t) = 0 + 0 + 3e^(3t)k

Simplifying the expression, we have:

r'(t) = 3e^(3t)k

Therefore, the derivative of the vector function r(t) = i + 2j + e^(3t)k is r'(t) = 3e^(3t)k.

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Related Questions

Quadrilateral XENA is a parallelogram. T is the point of intersection of the diagonals. For each situation, write an equation and solve for y.

Answers

Answer:

b

Step-by-step explanation:

just took the test yyyyyyyyyyyyyyyyyyyyyyyyy

Use a formula to find the amount of wrapping paper you need to wrap a gift in the cylindrical box shown. You need to cover the​ top, bottom, and all the way around the box. Use 3.14 for pi. 9 radius 5 height

Answers

Yοu need apprοximately 1017.96 square inches οf wrapping paper tο cοver the tοp, bοttοm, and arοund the cylindrical bοx.

One needs apprοximately 1017.96 square inches οf wrapping paper tο cοver the tοp, bοttοm, and arοund the cylindrical bοx.

The amοunt οf wrapping paper required tο wrap a gift in a cylindrical bοx depends οn the surface area οf the bοx. Tο find the surface area οf a cylinder, we use the fοrmula:

Surface Area = 2πr² + 2πrh

where r is the radius οf the cylinder and h is the height οf the cylinder.

In this case, the given cylinder has a radius οf 9 and a height οf 5. Therefοre, we can substitute these values intο the fοrmula and simplify:

Surface Area = 2 * 3.14 * 9² + 2 * 3.14 * 9 * 5

Surface Area = 1017.96

Therefοre, yοu need apprοximately 1017.96 square inches οf wrapping paper tο cοver the tοp, bοttοm, and arοund the cylindrical bοx.

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97+y=167
What is this

Answers

Answer:

70

Step-by-step explanation:

167-97 = 70

Carlita will visit 14 cities in 14 days. She will have a book signing and cooking demonstration in each city, then travel overnight to the next city. The distance between each city averages 240 miles. The publisher will rent a solar powered RV camper, with a weekly rental fee plus a per-mile charge. The rental company hasn’t prepared the final estimate, but showed the publisher two recent invoices for one-week rentals. One was $1,188.15 for a 540 mile trip. The other was $1,310.55 for an 880 mile trip. Carlita will pick up the camper in the first city on the tour and leave it in the last. The other tour costs are: • Cooking demonstration production: $3,450 each • Book signing materials: $1,475 total How much should the publisher budget for total tour expenses?

Answers

Answer:

$52091.95

Step-by-step explanation:

From the given information:

Number of  cities visited = 14

Cost of each cooking demonstration = $3450

Total cost of cooking demonstration = $3450 * 14 = $48300

Book signing material = $1475

∴

Total cost of cooking demonstration and book material is:

= $48300 + $1475 = $49775 ---- (i)

Total meter traveled in visiting 14 cities = 240 * 13 = 3120 miles

However; suppose the weekly rental fee fine = $x  &

the change per mile = $y

Then

y*540 + x = 1188.15    --- (ii)

y*880 + x = 1310.55   --- (iii)

From equation (ii) and (iii)

y *340 = 122.4

y = 122.4/340

y = 0.36

From (ii)

y*540 + x = 1188.15

(0.36)540 + x = 1188.15

x = 1188.15 - (0.36)540

x = 993.75

Hence, the total cost of travelling by RV camper = $1993.75 + 3120 *(0.36)

= $2116.95

Thus, the total budget = $49975.0 + $2116.95

= $52091.95

Can someone please answer this question I don’t have much time

Can someone please answer this question I dont have much time

Answers

Answer and Step-by-step explanation:

The top right shape is the correct option.

It contains a triangle and a rectangle, in which she can use the formulas to solve for their areas.

#teamtrees #PAW (Plant And Water)

Answer: Number 2 is correct. It divides the trapezoid into a square (rectangle) and 2 triangles which is equivalent to the whole trapezoid.

How many centimeters are in 300 meters?

Answers

Answer:

30000

Step-by-step explanation:

have a great day <3

Answer:

the answer is 30000 cm

Step-by-step explanation:

by converting it

A square has vertices at (1,1), and (2, -1). Where are the two vertices located? How do you know you have created a square?

A square has vertices at (1,1), and (2, -1). Where are the two vertices located? How do you know you

Answers

If you graph the point

(1,1)

and

(2,-1)

you see this. Shown below:

Find the unknown measures. Round lengths to the nearest tenth and angle measures to the nearest degree.
AC =


BC=


∡C=
degrees

Find the unknown measures. Round lengths to the nearest tenth and angle measures to the nearest degree.

Answers

Answer:

AC= 6.3 units (nearest tenth)

BC= 2.8 units (nearest tenth)

∠C= 64°

Step-by-step explanation:

Please see attached picture for full solution.

Find the unknown measures. Round lengths to the nearest tenth and angle measures to the nearest degree.

What is the measure of angle 1 if the measure of angle 4 is 155 degreees

What is the measure of angle 1 if the measure of angle 4 is 155 degreees

Answers

Answer:

<1 = 155

Step-by-step explanation:

<1 and <4 are vertical angles and vertical angles are equal

<1 = <4 = 155

CSC2t
cot t
csct sect

Answers

Answer:

what are you saying

Step-by-step explanation:

True or False? Justify your answer. Answers without correct justification will receive no credit. (I) A square matrix with the characteristic polynomial λ 4
−4λ 3
+2λ 2
−λ+3 is invertible. Justification: True □ False (II) Matrix [ 1
3
​
3
4
​
] in Z 5
​
is digonalizable. Justification: True False (III) Two matrices A and B are similar if and only if they similar to a same diagonal matrix. Justification: True □ False (IV) There exists a matrix A with eigenvalue 5 whose algebraic multiplicity is 2 and geometric multiplicity is 3 . Justification: True □ False (V) Two diagonal matrices D 1
​
and D 2
​
are similar if and only if D 1
​
=D 2
​
. Justification:
Previous question

Answers

The statements are marked as;

I. False

II. False

III. True

IV. False

V. True

How to determine the statements

To prove the statements, we need to know the following;

The characteristic polynomial has a root = 0 in order to be an invertible matrix If and only if two matrices A and B share the same Jordan canonical form, they are comparable. The number of times an eigenvalue appears as a root of the characteristic polynomial is indicated by its algebraic multiplicity. If and only if two diagonal matrices D1 and D2 contain the same diagonal entries, they are comparable.

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Complete the point-slope equation of the line through (-1,-10) (5,2)

Answers

Answer:

Step-by-step explanation:

(2+10)/(5+1)= 12/6 =2

y + 10 = 2(x + 1)

y + 10 = 2x + 2

y = 2x - 8

help i need the answerrr

help i need the answerrr

Answers

Answer:

LN=40

Step-by-step explanation:

M is the midpoint of segment LN, meaning LM is congruent to MN. So you double the given value for MN (which is 20) and you have 40. Hope this makes sense.

Use the given conditions to determine the number of possible triangles.


first angle measure: 90∘

second angle measure: 75∘

third angle measure: 30∘

Do the given conditions create a unique triangle, more than one triangle, or no triangle?

Answers

Step-by-step explanation:

look at that nayaisamazing. GonnaCry

Simplify this expression.
–6w + (–8.3) + 1.5+ (–7w)

Answers

The simplified form of the expression -6w + (–8.3) + 1.5+ (–7w) is -13w - 6.8.

What is the simplified form of the expression?

Given the expression in the question;

-6w + (–8.3) + 1.5+ (–7w)

To simplify, first remove the parenthesis

Note that;

- × + = -- × - = ++ × + = +

-6w + × - 8.3 + 1.5 + × - 7w

-6w - 8.3 + 1.5 - 7w

Next collect and add like terms

-6w - 7w - 8.3 + 1.5

Add -6w and -7w

-13w - 8.3 + 1.5

Add -8.3 and 1.5

-13w - 6.8

Therefore, -13w - 6.8 is the simplified form.

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20 POINTS AND BRAINLIEST
A line passes through the points (k, 4) and (3, -6). The line is perpendicular to the graph of 5y + 4x = 8. What is the value of k?
A. 11
B. 2
C. -1.6
D. -9.5

Answers

Answer:

11

Step-by-step explanation:

i need help with this​

i need help with this

Answers

Answer: What you can notice is that in both equations when you combine them, the x or y terms cancel out. This is because they are opposite signs on both equations with the same numerical coeffiecent.

Step-by-step explanation: ^^^^^ Hope it helps.

Please help, 10 points :)

Please help, 10 points :)

Answers

Answer:

6.75

Step-by-step explanation:

Answer:

6.75 i think sorry if it ins't it

Step-by-step explanation:

ASAP

(only the answer pls)

ASAP(only the answer pls)

Answers

Answer:

B..........................................

There are 24 hots and 14 hamburgers write the ratio of hotdogs and hamburgers

Answers

24:14 tho I might be wrong cause idrk

Answer:

12:7

Step-by-step explanation:

24 is the number of hotdogs and for very 24 hotdogs there are 14 hamburgers:

So it can be wirriten like this: 24:14

But we can simlify it further by dividing each side by 2.

24 / 2 : 14 / 2

12:7

Help i am confused
I don't know what this is
HELP ASAP
will mark brainllest if its the best answer.

Help i am confusedI don't know what this is HELP ASAPwill mark brainllest if its the best answer.

Answers

Answer:

Below

Step-by-step explanation:

First one and third one and 4th one are true

Write the slope-intercept form of an equation of the line that passes through the given point and is perpendicular to the graph of the equation.
(−6,4), 3y=2x−3

Answers

First that the perpendicular equation and put in slope form. (Y=2/3 x-1)
Now that you have it you can get your slope for what you want. Which is 3/2
So far you have y=3/2 x+b
Take your point and put into you new equation and solve.
4=3/2(-6)+b
4=-9+b. b=13
Answer is y=3/2 x+13

help me plzzzzzzzzzzzzzzzzzzzz

help me plzzzzzzzzzzzzzzzzzzzz

Answers

Answer:

B

Step-by-step explanation:

also can i have brainly

Common causes of variation are also known as __________________________. Select one: a. usual b. ordinary c. frequent d. normal e. random

Answers

Answer:

It is also known as E: random cause

is it possible to choose (2n 1)^2 points in the disc of radius n such that the distance between any two of them is greater than 1?

Answers

Answer: its (4f 5) ^3

Step-by-step explanation:

PLEASE HELP WITH THREE AND FOUR WILL MARK BRAINLIEST!

PLEASE HELP WITH THREE AND FOUR WILL MARK BRAINLIEST!

Answers

Answer:

3. first one got no solution and the second has infinite solutions

4. that would be A

Step-by-step explanation:

PLS HELP ILL GIVE 30 POINT FOR WHOEVER HAS CORRECT ANSWER Find the total amount you will pay given an original price of $499.95 and tax rate of 4%.

Answers

Answer:

$519.948

Step-by-step explanation:

519.95.
solve by multiplying 499.95 to your percent turned decimal, 0.04. then add the original price. the easier way to do it is multiply 499.5 times 1.04. in this case, you do NOT need to add the original price again.

The coordinates of point T are ​(0,6​). The midpoint of is ​(​6,​-6). Find the coordinates of point

Answers

Step-by-step explanation:

please mark me as brainlest and follow me

The coordinates of point T are (0,6). The midpoint of is (6,-6). Find the coordinates of point

Find the derivative of f(x) = cosh^-1 (11x).

Answers

The derivative of f(x) is \(11/\sqrt{121x^{2} -1}\).

The derivative of f(x) = cosh^(-1)(11x) can be found using the chain rule. The derivative of cosh^(-1)(u), where u is a function of x, is given by 1/sqrt(u^2 - 1) times the derivative of u with respect to x. Applying this rule, we obtain the derivative of f(x) as:

f'(x) = \(1/\sqrt{(11x)^2-1 } *d11x/dx\)

Simplifying further:

f'(x) = \(1/\sqrt{121x^{2} -1}*11\)

Therefore, the derivative of f(x) is  \(11/\sqrt{121x^{2} -1}\).

To find the derivative of f(x) = cosh^(-1)(11x), we can apply the chain rule. The chain rule states that if we have a composition of functions, such as f(g(x)), the derivative of the composition is given by the derivative of the outer function evaluated at the inner function, multiplied by the derivative of the inner function.

In this case, the outer function is cosh^(-1)(u), where u = 11x. The derivative of cosh^(-1)(u) with respect to u is \(1/\sqrt{u^{2}-1}\).

To apply the chain rule, we first evaluate the derivative of the inner function, which is d(11x)/dx = 11. Then, we multiply the derivative of the outer function by the derivative of the inner function.

Simplifying the expression, we obtain the derivative of f(x) as  \(11/\sqrt{121x^{2} -1}\). This is the final result for the derivative of the given function.

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What are the values of a and b?

What are the values of a and b?

Answers

Answer:

A=44 B=68

Step-by-step explanation:

There are two congruent sides, therefore the corresponding angles are also congruent.

Answer:

a and b both are 56 degree

Step-by-step explanation:

this is due to it's isosceles triangle. So, we take (180-68):2

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