Find the solution to the differential equation dzdt=7te7z that passes through the origin.

Answers

Answer 1

The answer is [tex]z &=-0.14\left[\ln \left(1-24.5 t^2\right)\right]\end{aligned}$$[/tex]

What do you understand by differential equation?

An ordinary derivative or a partial derivative can both be found in a differential equation. The differential equation describes the relationship between the variable that is constantly varying with respect to the change in another quantity, and the derivative represents a rate of change.

Equations with General Differential. Consider the differential equation y′=3x2, which has a derivative and is an illustration of a differential equation. The variables x and y are related because y is an unidentified function of x. The derivative of y is also on the equation's left-hand side.

Given equation:

[tex]$$\begin{aligned}&e^{-7 z} d z=7 t d t \\&:(-1 / 7) e^{-7 z}=3.5 t^2+C\end{aligned}$$[/tex]

[tex]$C=-1 / 7$[/tex]

[tex]$$(-1 / 7) e^{-7 z}=3.5 t^2-1 / 7$$[/tex]

[tex]$$e^{-7 z}=1-24.5 t^2$$[/tex]

[tex]$$\begin{aligned}-7 z &=\ln \left(1-24.5 t^2\right) \\z &=-0.14\left[\ln \left(1-24.5 t^2\right)\right]\end{aligned}$$[/tex]

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Related Questions

Is (2,-1) a solution of 2x-y=5? Explai
how your work.

Answers

Answer:

Yes, (2, -1) is a solution.

Step-by-step explanation:

Plug in 2 for x and -1 in for y and see if it is a true statement.

2x - y = 5

2(2) - (-1) = 5

4 - (-1) = 5 Subtracting a negative number is the same as adding a positive number

4 + 1 = 5

5 = 5 Since this statement is true, (2,-1) is a solution.

a certain composer wrote 10 symphonies, 4 piano concertos (music for piano and orchestra), and 35 piano sonatas (music for solo piano). a. how many ways are there to play first a symphony and and then a piano concerto? b. the manager of a radio station decides that on each successive evening (7 days a week), a symphony will be played followed by a piano concerto followed by a piano sonata. for how many nights could this be carried out before exactly the same program would have to be repeated? about how many years would this be? (round to the nearest year).

Answers

(a) According to the question, a composer wrote [tex]10[/tex] symphonies, [tex]4[/tex] piano concerts (piano and orchestra) and [tex]35[/tex] piano sonatas (solo piano):

Here, determine how many ways are there to play first a symphony and then piano concerto.

So, the probability is [tex](10P1) (4P1) = (10)(4)= 40[/tex]

Therefore, there are [tex]40[/tex] ways to play first a symphony and then piano concerto.

(b)The manager of a radio station decides that on each successive evening, a symphony will be played followed by a piano concerto followed by a sonata.

Here determine how many nights could be carried out before the same program would get repeated.

So, the probability would be [tex](35)(10)(4)=1440[/tex]

Therefore, [tex]1440[/tex] nights are carried out before the same program gets repeated.

Now, to calculate the years: [tex]\frac{1440 nights}{365days} = 3.95 years[/tex]

Therefore, it would be [tex]3.95[/tex] years.

What is probability?

Probability is the method to measure the occurred events or the occurrence of the events. It is also used to analyze the outcomes of random events. For example, to calculate the probability of a playing card which is 52 in numbers. And it is divided into four cards and each are in the count of 13.These four cards are heart, spades, diamond and club.

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Evaluate the expression when x=3 , y=−4 , and z=−6.
z−2xy=

Answers

x = 3 , y = −4 , and z = −6

z-2xy =

Substitute the value of x,y and z in the expression.

-6-2(3)(-4)

-6-2(-12)

-6+24

there are 11 books on a shelf. 9 of these books are new. the rest of them are used

Answers

Two of them are used and 9 of them are not

NEED HELP FAST, GIVING AWAY 99 POINTS.

Evaluate the numerical expression.

3/2 − (−1/4)

A -1/2
B -3/2
C 7/4
D 4/5

Answers

Answer:

The answer is C. 7/4 :)

The correct answer is C (7/4).
Have a great day!

Randy's swimming coach kept track of his average 50-meter lap times during the first 3 weeks of training. How much greater was the percent of change from Week 1 to Week 2 than from Week 2 to Week 3? Round to the nearest tenth of a percent.

Answers

The percent of the first change is greater by 2.36%.

Time in 1st week = 28.8 sec

Time in 2nd week = 27.6 sec

Time in 3rd week = 27.1 sec

∴ Change of time from week 1 to week 2 = (28.8 - 27.6) sec

= 1.2 sec

∴ Percent of change from week 1 to week 2 = [tex]\frac{time change}{1st week time} \times 100[/tex] %

= [tex]\frac{1.2}{28.8} \times 100[/tex] %

= 4.17%

∴ Change of time from week 2 to week 3 = (27.6 - 27.1) sec

= 0.5 sec

∴ Percent of change from week 2 to week 3 = [tex]\frac{Time change}{2nd week time} \times 100[/tex] %

= [tex]\frac{0.5}{27.6} \times 100[/tex] %

= 1.81%

∴ The greater change was in the first week. The amount by which it was greater is = (4.17 - 1.81) %

= 2.36%

Answer) The percent of the first change is greater by 2.36%.

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Evaluate the expression when a = 7 and c= -3.
-a+4c

Answers

Hello,

[tex] - a + 4c = - 7 + 4 \times ( - 3) = - 7 - 12 =- 19[/tex]

Answer:

-19

Step-by-step explanation:

-7 + 4(-3)

-7 - 12= -19

The recommended mass of a Soccer ball is 0.43 kilogram. The actual mass is allowed
to vary by up to 20 grams.
a. Write and solve an absolute value equation to find
the minimum and maximum acceptable soccer ball
masses.
b. A soccer ball has a mass of 423 grams. The soccer
ball loses 0.016 kilogram of mass over time. Is the
mass now acceptable? Explain.

Answers

The absolute value equation is:

|M - 430g| = 20g

And the solutions are M = 410g and M = 450g

b) No, the mass is not acceptable.

How to write the absolute value equation?

We know that the recomended mass is 0.43kg, with an accepted error of 20 grams.

Where:

0.43kg = 0.43*1000g = 430g

Then the minimum mass accepted is: 430g - 20g = 410g

The maximum mass accepted is: 430g + 20g = 450g

These are the solutions, and the absolute value equation is, if M is the mass:

|M - 430g| = 20g

b) If the ball has a mass of 423g it is in the accepted range, if now it loses 0.016kg:

0.016kg = 0.016*1000g = 16g

The new mass is:

423g - 16g = 407g

This is smaller than the minimum accepted mass, then this mass is not acceptable.

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Any genius willing to help :) , I'll give you a brainliest if you do.

Answers

Answer:

Step-by-step explanation:

(0,0)
(-3,-2)
(-5,0)
(4,0)
(2,-2)
(5,-2)

Yo help please I need this done it's about rational or irrational numbers u have to figure out if it's either rat or irr. If it's rational then figure out if it is a integers. If it's a integers then figure out if it's a whole number if it is then figure out if it's a natural number. Here's the order of it. R I W N and if it's irr then it's just I