Part A. Find the orthogonal trajectories of the family of curves. (Use C for any needed constant.)x2 + 2y2 = 17k2Part B. Find the orthogonal trajectories of the family of curves. (Use C for any needed constant.)y2 = 7kx3

Answer:

Following are the solution to the question:

Step-by-step explanation:

The objective is to find the orthogonal trajectory of the family curves:

[tex]x^2+2y^2=17k^2[/tex]

The family curves are: [tex]x^2 + 2y^2=17k^2[/tex]  

Differentiate the equation with the respect of x.

[tex]\to x^2+2y^2=17k^2 \\\\\to 2x+4y \frac{dy}{dx} =0\\\\\to \frac{dy}{dx} =- \frac{2x}{4y}\\\\\to \frac{dy}{dx} =- \frac{x}{2y}[/tex]

The negative reciprocal is:

[tex]\to \frac{dy}{dx} =-\frac{1}{-\frac{x}{2y}}\\\\\to \frac{dy}{dx} = \frac{2y}{x}[/tex]

Integration of the above equation:

[tex]\to \frac{dy}{dx} = \frac{2y}{x} \\\\\to \int \frac{dy}{2y} = \int \frac{dx}{x}\\\\\to \frac{1}{2} \log y = \log x + \log C\\\\\to \log y = 2 \log x + 2\log C \\\\\to \log y = \log x^2 +\log C^2 \\\\\to y = Ax^2 \ \ \ \ \ \ \ \ \ (A=C^2)[/tex]

Hence, the orthogonal trajectory of the family of the curves [tex]x^2 + 2y^2 =17k^2 \ \ is \ \ y=Ax^2[/tex]

Each exterior angle of the regular n-gon has a measure of 3 degrees. How many sides does the polygon have?

Best Answer gets BRAINLIEST!!!

Total Cost of Computer Repair = $1,444.50

Shipping = 2 percent of Total Cost

If Sarah wanted to include a 15 percent gratuity, based on the total cost of the computer repair, excluding shipping, how would you find her new total cost?

A and B are independent events.
PA) = 0.6
P(B) = 0.4
What is P(AB)?
O A. 0.24
B. 0.6
O c.0.4
D. Not enough information

Which step(s) would create equations so that the coefficients of one of the variables are
opposites?
(A) Multiply the first equation by 7.
Multiply the second equation by 3.
(B) Multiply the first equation by -2.
Multiply the second equation by 4.
(C) Multiply the first equation by 2.
(D) Multiply the second equation by 4.

What is the equation of the line with a slope of 4 and a y-intercept of —2?

Pablo rented a truck for one day. There was a base fee of $17.95, and there was an additional charge of 82 cents for each
mile driven. Pablo had to pay $131.93 when he returned the truck. For how many miles did he drive the truck?
miles

Solve – 4y – 10 = 4(y - 3)

Solve the following quadratic equation.

(x - 16)2 = 256 The 2 is the exponent so please don't misunderstand it lol, thank you for who ever helps me.

A. x = 30 and x = 8

B. x = -30 and x = -8

C. x = -32 and x = 0

D. x = 32 and x = 0

Help please I don’t understand

Solve the equation.
-5r-1=7r+5

____________________

I need help with my math homework

You can save a significant amount of mortgage interest paid if you make one additional principal and interest payment a year. This will reduce a 30-year mortgage by around 6 years. It also increases your equity in the home faster. If you choose to pay one additional mortgage payment a year by paying 1/12 of it each month (make certain to note the extra money is to reduce principal), how much will you pay each month for a mortgage of $152,000 at 3.5% for 16 years?

Paul spent $48.00 on three tickets to a concert. Janis spent $90.00 on five tickets to the same concert. How much did each ticket cost for the cheaper individual ticket?

In a study investigating the effect of car speed on accident severity, the vehicle speed at impact was recorded for 5,000 fatal accidents. For these accidents, the mean speed was 46 mph and the standard deviation was 13 mph. A histogram revealed that the vehicle speed distribution was mound shaped and approximately symmetric. (Use the Empirical Rule.) (a) Approximately what percentage of vehicle speeds were between 33 and 59 mph

I NEED HELP PLZ ITS FOR MY FINAL

Please answer i need help

PLEASE HELPPPP
Find the equation of the linear function represented by the table below in slope-
intercept form.
X
O
1
2
3
4
y
6
14
22
30
38
Answer: y =
Submit Answer

The length of a rectangle is 3 centimeters less than five times its width. Its area is 14 square centimeters. Find the dimensions of the rectangle.
Find the Width and the Length
W=
L=​

There are 40 marbles in a bin and 25% of the marbles are red how many in the bin are red

I don't understand 1/2 +1/6 what the answer

. Naty bought a dress for $24.95 and a skirt for $14.95. The sales clerk said the total cost including 9.5% sales tax was 49.40. Below are the steps the clerk completed.

Step 1: 24.95 + 14.95 = 39.90 Step 2: 39.90 + 9.5 = 49.40

Are the clerk's steps correct? If she is incorrect, identify her mistake and explain her error. Explain in writing how to accurately calculate the sales tax, total cost, and state the correct total. ( Round final answer to the nearest hundredth)

Are these triangles congruent ?

And what is the theorem ?

I will give a brainlist for the correct answer :)

Which is the best description for the graph?
O The graph is increasing everywhere.
O The graph is decreasing everywhere.
O The graph is increasing, then decreasing.
O The graph is decreasing, then increasing.

Help me please please

Suppose that the water level of a river is 34 feet and that it is receding at a rate of 0.5 foot per day. Write an equation for the water level, L, after d days. In how many days will the water level be 26 feet?

Use x for the unknown number.
Twice an unknown number added to 48 is six times the same unknown number.

What is the length of the line segment with endpoints (-1, -2) and (4, 10)?​

Enuncia 5 vectores que pertenecen a un mismo sub espacio

26. Which is NOT a zero of the following function?
f(x)= x + 3x? – X-3
A. 1
B. -1
C. 3
D. -3