What is the first derivative of r with respect to t (i.e., differentiate r with respect to t)? r = 5/(t2)Note: Use ^ to show exponents in your answer, so for example x2 = x^2. Also, type your equation answer without additional spaces.

Answers

Answer 1

Answer:

The first derivative of [tex]r(t) = 5\cdot t^{-2}[/tex] (r(t)=5*t^{-2}) with respect to t is [tex]r'(t) = -10\cdot t^{-3}[/tex] (r'(t) = -10*t^{-3}).

Step-by-step explanation:

Let be [tex]r(t) = \frac{5}{t^{2}}[/tex], which can be rewritten as [tex]r(t) = 5\cdot t^{-2}[/tex]. The rule of differentiation for a potential function multiplied by a constant is:

[tex]\frac{d}{dt}(c \cdot t^{n}) = n\cdot c \cdot t^{n-1}[/tex], [tex]\forall \,n\neq 0[/tex]

Then,

[tex]r'(t) = (-2)\cdot 5\cdot t^{-3}[/tex]

[tex]r'(t) = -10\cdot t^{-3}[/tex] (r'(t) = -10*t^{-3})

The first derivative of [tex]r(t) = 5\cdot t^{-2}[/tex] (r(t)=5*t^{-2}) with respect to t is [tex]r'(t) = -10\cdot t^{-3}[/tex] (r'(t) = -10*t^{-3}).


Related Questions

X-21=6 what does x equal??

Answers

Answer:

The answer is 27

Hope this helps

Answer:

x=27

Step-by-step explanation:

What you need to do is isolate the x or in other words have the x be alone on one side of the equal sign. To do this you would need to add 21 to both sides because you need to cancel out -21 with the opposite which would be positve 21. After that the x should be by itself and then finally add 21 to 6 to complete solving for x.

How to work out the mean

Answers

Answer:

mean is average

1. Add all the values to find the total

2. Divide the total you have found by the amount of numbers you have added to find the total

Answer:

To work out the mean you have to add all of the numbers up then divide it by how many numbers the are

Step-by-step explanation:

Find the circumference given the area = 28.3 km². Use 3.14 for π as necessary. A. 18.9 km B. 20.8 km C. 21.4 km D. 37.8 km

Answers

Answer: choice A) 18.9 km

================================================

Work Shown:

Use the given area A = 28.3 to find the radius r

A = pi*r^2

28.3 = 3.14*r^2

3.14*r^2 = 28.3

r^2 = 28.3/3.14

r^2 = 9.01273885350319 approximately

r = sqrt(9.01273885350319)

r = 3.00212239149292

---------

Which is then used to find the circumference

C = 2*pi*r

C = 2*3.14*3.00212239149292

C = 18.8533286185756

C = 18.9

Clarence set his watch 16 seconds behind , and it falls behind 2 seconds every day . How many days behind has it been since Clarence last set his watch if the watch is 46 seconds behind

Answers

Answer:

15 days.

Step-by-step explanation:

46 - 16 = 30.

It falls 2 seconds behind each day so the number of required days

= 30 / 2 = 15.

Answer:

Step-by-step explanation:

15 days 16-40=30 the take 30/2= 15

5. Jonathan and Victoria can finish a job in 13 days. Jonathan can do the job
himself in 26 days. if Victoria wanted to do the job alone, how long would it
take her?
6. If a certain job can be finished by 18 workers in 26 days. How many workers
are needed to finish job in 12 days?
.
7. A group of 40 workers can finish digging a tunnel in 12 days. how many
workers can finish the job in 8 days?

Answers

Answer:

about 8 workers will finish the job

Consider the polynomial 6x4 + 24x3 − 72x2. What is the greatest common factor (GCF) of the terms of the polynomial?

Answers

Answer:

24x

Step-by-step explanation:

=6x×4+24x×3-72x

=24x+24×3x-72x

=24x+72x-72

=24x

What is the solution to this equation 34(x+8)=12(x−6)

Answers

Answer:

x = - 172*11

Step-by-step explanation:

Which describes the standard deviation?

Answers

Step-by-step explanation:

standard deviation is used to measure risks involved in an investment instrument. Standard deviation provides investors a mathematical basis for decisions to be made regarding their investment in financial market. Standard Deviation is a common term used in deals involving stocks, mutual funds, ETFs and others. Standard Deviation is also known as volatility. It gives a sense of how dispersed the data in a sample is from the mean.

I hope I answered correctly :)



It is a form of measurement of the average difference between sample values and the sample mean.

Shamika knows she has been listening to a music playlist for 26 minutes when she looks at the clock showing the time below. What time did Shamika begin listening to the playlist?

Answers

Answer:

t = 5:26

Step-by-step explanation:

time after 26 min = 5:52

time before 5:52 after listening for 26 min

t = 5:52 - 0:26

t = 5:26 was the time when Shanika starts listening to a music.

Answer:

t = 5:26

Step-by-step explanation:

time after 26 min = 5:52

time before 5:52 after listening for 26 min

t = 5:52 - 0:26

t = 5:26

Simplify 5/96 - 7/54

Answers

Answer:

The answer is

[tex] - \frac{67}{864} [/tex]

Step-by-step explanation:

[tex] \frac{5}{96} - \frac{7}{54} [/tex]

To solve first find the LCM of the denominators

That's

The LCM of 96 and 54 is 864

So we have

[tex] \frac{5}{96} - \frac{7}{54} = \frac{5(9) - 7(16)}{864} [/tex][tex] = \frac{45 - 112}{864} [/tex]

We have the final answer as

[tex] = - \frac{67}{112} [/tex]

Hope this helps you

If ∠P measures 27°, ∠R measures 135°, and p equals 9.5, then which length can be found using the Law of Sines?

Answers

Answer:

r = 14,8

Step-by-step explanation:

Hope you can read my writing ;-)                                                                                

The length that can be found using the Law of Sine rule is

r= 14.80 units

What is the lenght?

Generally,

Generally, the equation for sin rule is  mathematically given as

[tex]\frac{p}{sinP} = \frac{q}{sinQ} = \frac{r}{sinR}[/tex]

Where

p = 9.5 units

∠P = 27°

∠R = 135°

Therefore

[tex]\frac{9.5}{sin 27^0} = \frac{q}{sin Q} = \frac{r}{sin 135^0}[/tex]

[tex]\frac{9.5}{sin 27^0} = \frac{r}{sin 135^0}[/tex]

9.5 x 0.7071 = r x 0.4540

r = 14.80 units

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The sum of a number and its square is 42. Which equation can be used to find the two numbers for which this is
true?
x2 + x = 42
x2 + 2x = 42
x²+x+42=0
x² + 2x + 42=0

Answers

Answer:

x2 + x = 42

Step-by-step explanation:

x = nhmber

x² = its square

then:

The sum of a number and its square is 42 is:

x² + x = 42

(-4) + (-5) =
I’m confused

Answers

(-) +(-) = - always add and put the negative sign. The answer is -9
-9 is the answer for your problem

7p − p = 18 2) −5n − 4n = −9

Answers

Answer:

[tex] \boxed{ \bold{ \sf{ \boxed{ p = 3}}}} [/tex]

[tex] \boxed{ \bold{ \sf{ \boxed{n = 1}}}}[/tex]

Step-by-step explanation:

1. [tex] \sf{7p - p = 18}[/tex]

Collect like terms

⇒[tex] \sf{6p = 18}[/tex]

Divide both sides of the equation by 6

⇒[tex] \sf{ \frac{6p}{6} = \frac{18}{6} }[/tex]

Calculate

⇒[tex] \sf{p = 3}[/tex]

2. [tex] \sf{ - 5n - 4n = - 9}[/tex]

Collect like terms

⇒[tex] \sf{ - 9n = - 9}[/tex]

Divide both sides of the equation by -9

⇒[tex] \sf{ \frac{ - 9n}{ - 9} = \frac{ - 9}{ - 9} }[/tex]

Calculate

⇒[tex] \sf{n = 1}[/tex]

Hope I helped!

Best regards!!

Answer: p = 3 , n = 1
Step by step explanation
7p-p = 18
6p = 18
p = 3
Finding n
-5n-4n = (-9)
-9n = (-9)
n = -9/-9
n = 1
Hope it helped comment below!,

help me with these please​

Answers

Step-by-step explanation:

(1) y = x e^(x²)

Take derivative with respect to x:

dy/dx = x (e^(x²) 2x) + e^(x²)

dy/dx = 2x² e^(x²) + e^(x²)

dy/dx = (2x² + 1) e^(x²)

Take derivative with respect to x again:

d²y/dx² = (2x² + 1) (e^(x²) 2x) + (4x) e^(x²)

d²y/dx² = (4x³ + 2x) e^(x²) + 4x e^(x²)

d²y/dx² = (4x³ + 6x) e^(x²)

Substitute:

d²y/dx² − 2x dy/dx − 4y

= (4x³ + 6x) e^(x²) − 2x (2x² + 1) e^(x²) − 4x e^(x²)

= 4x³ + 6x − 2x (2x² + 1) − 4x

= 4x³ + 6x − 4x³ − 2x − 4x

= 0

(2) y = sin⁻¹(√x)

sin y = √x

sin²y = x

Take derivative with respect to x:

2 sin y cos y dy/dx = 1

sin(2y) dy/dx = 1

dy/dx = csc(2y)

Take derivative with respect to x again:

d²y/dx² = -csc(2y) cot(2y) 2 dy/dx

d²y/dx² = -2 csc²(2y) cot(2y)

Substitute:

2x (1 − x) d²y/dx² + (1 − 2x) dy/dx

= 2 sin²y (1 − sin²y) (-2 csc²(2y) cot(2y)) + (1 − 2 sin²y) csc(2y)

Use power reduction formula:

= (1 − cos(2y)) (1 − ½ (1 − cos(2y))) (-2 csc²(2y) cot(2y)) + (1 − (1 − cos(2y))) csc(2y)

= (1 − cos(2y)) (1 − ½ + ½ cos(2y)) (-2 csc²(2y) cot(2y)) + cos(2y) csc(2y)

= (1 − cos(2y)) (½ + ½ cos(2y)) (-2 csc²(2y) cot(2y)) + cot(2y)

= (cos(2y) − 1) (1 + cos(2y)) csc²(2y) cot(2y) + cot(2y)

= (cos²(2y) − 1) csc²(2y) cot(2y) + cot(2y)

= -sin²(2y) csc²(2y) cot(2y) + cot(2y)

= -cot(2y) + cot(2y)

= 0

8. Which of the numbers in each pair is farther to the left on the number line?
a. 305 and 17
b. 187 and 900
C. 16 and 46
d. 157,019 and 149,984

Answers

a. 305
b. 900
c. 46
d. 157,019

Jacob spent $35.40 to fill up 15 gallons of gas in his pick-up truck. How much does 6 gallons cost?

Answers

Answer:

$14.16 for 6 gallons.

Step-by-step explanation:

35.40/15 = 2.36

2.36*6 = 14.16

a process used to convert units and rates using a conversion factor and multiplication

Answers

Dimensional Analysis

Classify the numbers as rational or irrational.
6
√2.6
√2+6

Answers

Step-by-step explanation:

[tex] \sqrt 2, \: \sqrt 2. 6 \: \& \: \sqrt 2 + 6[/tex] are irrational and 6 is the only rational number.

The sequence {an) is defined by ao = 1 and
An+1=2an +1 for n = 0,1,2,.... What is the value
of a4?

Answers

Answer: 31

=======================================

Work Shown:

Use the value of a0 to find the value of a1. The idea is you double the previous value, and then add 1.

[tex]a_{n+1} = 2*(a_n) + 1\\\\a_{0+1} = 2*(a_0) + 1\\\\a_{1} = 2*(1) + 1\\\\a_{1} = 3\\\\[/tex]

Which is then used to find the value of a2. Follow the same process as before (double the previous value and then add 1).

[tex]a_{n+1} = 2*(a_n) + 1\\\\a_{1+1} = 2*(a_1) + 1\\\\a_{2} = 2*(3) + 1\\\\a_{2} = 7\\\\[/tex]

This is used to find a3

[tex]a_{n+1} = 2*(a_n) + 1\\\\a_{2+1} = 2*(a_2) + 1\\\\a_{3} = 2*(7) + 1\\\\a_{3} = 15\\\\[/tex]

Finally we can now find a4

[tex]a_{n+1} = 2*(a_n) + 1\\\\a_{3+1} = 2*(a_3) + 1\\\\a_{4} = 2*(15) + 1\\\\a_{4} = 31\\\\[/tex]

Recursive sequences like this aren't too bad if n is small, but as n gets larger, things become more tedious. For those cases, its best to try to find a closed form equation. If not, then the next best thing is using a spreadsheet to automate the process.

Two years ago ,a woman was 7 times as old as her daughter,but in 3 years time ,she would be 2 times as old as the girl,how old are they now?.​

Answers

Let present age of women and her daughter be x and y respectively.

According to the question,

Case 1 :

Two years ago,

Woman age = ( x - 2 ) years

Her daughter age = ( y - 2 ) years

Woman was 7 times old as her daughter. [ Given ]

x - 2 = 7 ( y - 2 )

=> x - 2 = 7y - 14

=> x - 2 + 14 = 7y

=> x + 12 = 7y ....( i )

Case 2 :

After Three years ,

Woman age = x + 3

Her daughter age = y + 3

she would be 4 times old as the girl. [ Given ]

x + 3 = 4 ( y + 3 )

=> x + 3 = 4y + 12

=> x = 4y + 12 - 3

=> x = 4y + 9....( ii )

Now,

★ Substituting the value of x = 4y + 9 from equation ( ii ) in equation ( i ),we get

x + 12 = 7y

=> 4y + 9 + 12 = 7y

=> 21 = 7y - 4y

=> 21 = 3y

=> 3y = 21

=> y = 21/3

=> y = 7

And,

x = 4y + 9

★ Substituting the value of y in equation ( ii ), we get

x = 4 × 7 + 9

x = 28 + 9

x = 37

Hence, the present age of women is 37 years and her daughter age is 7.

the current age of the daughter is 3 years old, and the current age of the woman is 9 years old.

Let's denote the current age of the daughter as "D" and the current age of the woman as "W".

From the given information:

1. Two years ago, the woman was 7 times as old as her daughter:

W - 2 = 7(D - 2)

2. In three years time, the woman would be 2 times as old as the girl:

W + 3 = 2(D + 3)

We now have a system of two equations with two unknowns. Let's solve this system of equations:

From equation 1, we can rewrite it as:

W = 7(D - 2) + 2

Substituting this expression for W in equation 2, we have:

7(D - 2) + 2 + 3 = 2(D + 3)

Simplifying the equation:

7D - 14 + 2 + 3 = 2D + 6

Combine like terms:

7D - 9 = 2D + 6

Subtract 2D from both sides:

7D - 2D - 9 = 6

Combine like terms:

5D - 9 = 6

Add 9 to both sides:

5D = 15

Divide both sides by 5:

D = 3

Now that we know the daughter's current age (D = 3), we can substitute it back into equation 1 to find the woman's age:

W = 7(D - 2) + 2

W = 7(3 - 2) + 2

W = 7(1) + 2

W = 7 + 2

W = 9

Therefore, the current age of the daughter is 3 years old, and the current age of the woman is 9 years old.

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Someone lmk thank youuu

Answers

Answer:

please mark my answer brainliest

Step-by-step explanation:

=8 x cube + 27

=2 X whole cube + 3 whole cube

=(2x+3)(2 X whole square + 3 whole square -2× 2 X ×3 )

=(2x+3)(4x square +9-12x)

....thats all...if require more than use splitting midterm to get more appropriate answer

Answer: (2x + 3)(4x^2 - 6x + 9)

Explanation:

form: a^3 + b^3 = (a + b)(a^2 - ab + b^2)

8x^3 + 27
= (2x + 3)[(2x)^2 - (2x)(3) + 3^2)]
= (2x + 3)(4x^2 - 6x + 9)

Evaluate −12(−2). (1 point) 14 −14 −24 24

Answers

Answer:

24.

Step-by-step explanation:

−12(−2

= -12 * -2     ( Note  - * - = +) so we have:

24 (answer).

A gas that exerts a pressure of
215 torr in a container with a volume of
51.0 mL will exert a pressure of
torr when transferred to a
container with a volume of 18.5 mL.
Assume that the number of moles and the
temperature remain constant.

Answers

Step-by-step explanation:

According to Boyle's Law :

[tex]p _1v _1 = p _2v _2[/tex]

[tex]v _2 = \frac{p _1v _1}{p _2} = \frac{215 \times 51}{18.5} = 592.7ml[/tex]

The pressure exert in a container is 592.70 torr.

To find The pressure exert in a container.

What is Molarity?

Molarity is defined as the moles of a solute per liters of a solution. Molarity is also known as the molar concentration of a solution.

Given that :

pressure([tex]P_{1}[/tex])=215 torr

volume ([tex]v_{1}[/tex])=51.0 mL

volume([tex]v_{2}[/tex])= 18.5 mL

[tex]P_{2}[/tex]=?

Number of moles and the temperature remain constant.

By the use of "Boyle's law" :

[tex]P_{1} V_{1} =P_{2} V_{2} \\\\215*51=P_{2} *18.5\\\\P_{2} =\frac{215*51}{18.5} \\\\P_{2} =592.70 torr[/tex]

So, the pressure exert in a container is 592.70 torr.

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If x * (x + 2) = 49, find x

Answers

Answer:

x = -8.07107, 6.07107

Step-by-step explanation:

Quadratic Formula: [tex]x=\frac{-b+/-\sqrt{b^2-4ac} }{2a}[/tex]

Step 1: Write out equation

x(x + 2) = 49

Step 2: Distribute

x² + 2x = 49

Step 3: Subtract 49 on both sides

x² + 2x - 49 = 0

Step 4: Quadratic Formula

a = 1

b = 2

c = -49

x = -8.07107, 6.07107

express 0.0706 to standard form​

Answers

Answer: 706 x[tex]10^{-4}[/tex]

It can also be written as 7.06 x [tex]10^{-3}[/tex]

Answer:

Step-by-step explanation:

0.0706 * 10 (0) the zero is supposed to be on top of the 10

how do you break down 213 in times

Answers

Answer:2 hundred+1 tens+3 ones

Step-by-step explanation:

if x=1 then (x-1)(x-2)= -3 -1 0 2​

Answers

The answer: 1
I used this other app to find out the answer it’s a app that helps you with mathematical problems

A triangle has vertices at (1,3),(2,-3), and (-1,-1). What is the approximate perimeter of the triangle? A. 16 B: 14 C: 15 D: 10

Answers

Answer:

B 14

explanation:

i did the math

The perimeter of the given triangle is 14 units, so the correct option is B.

How to get the perimeter of the triangle?

The perimeter of the triangle will be equal to the sum between the distances between the given points.

Remember that the distance between two points is (x₁, y₁) and (x₂, y₂) is:

[tex]d = \sqrt{(y_2 - y_1)^2 + (x_2 - x_1)^2}[/tex]

For the pair of (1,3), (2,-3): the distance is:

[tex]d = \sqrt{(2 - 1)^2 + (-3 - 3)^2} = 6.08[/tex]

For the pair (1, 3) , (-1, -1) the distance is:

[tex]d = \sqrt{(-1 - 1)^2 + (-1 - 3)^2} = 4.5[/tex]

For the pair (2, -3) and (-1, -1) the distance is:

[tex]d = \sqrt{(2 - (-1))^2 + (-3 - (-1))^2} = 3.6[/tex]

Then the total perimeter, rounded to the next whole number is:

6.08 + 4.5 + 3.6 = 14

So the correct option is B.

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reduce to simplest term 44/4

Answers

Answer:

11

Step-by-step explanation:

44/4 = 11

4/4 = 1

then:

44/4 = 11/1 = 11

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