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padilas [110]
3 years ago
11

Q: Form the differential equation representing the family of curves y = a sin (x + b), where a, b are arbitrary constants.​

Mathematics
1 answer:
crimeas [40]3 years ago
8 0

Answer:

y = asin ( x + b)

dy/dx =acos (x+ b)

y²+ (dy/dx)²= a²

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A ladder is 74 inches tall. How tall is it in feet and inches?
vivado [14]

Answer:1 inch = 0.0833333 feet so 74 x 0.0833333 = 6.16667

Step-by-step explanation:

3 0
3 years ago
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27.3= 3/4y<br><br>what does y equal?
12345 [234]
The answer would be 36.4
5 0
4 years ago
8x+3y=4 <br> -7x+5y=-34 <br><br> Elimination using multiplication
irga5000 [103]

Answer:

x= 2    and y = -4

Step-by-step explanation:

8x + 3y = 4 ---------------------------------(1)

-7x + 5y = -34 -----------------------------(2)

Multiply through equation (1) by 5 and multiply through equation(2) by 3

40x + 15y = 20 ----------------------------(3)

-21x + 15y =-102----------------------------(4)

Subtract equation (4) from equation (3)

61x = 122

Divide both-side of the equation by 61

61x/61 = 122/61

(At the left-hand side of the equation 61 will cancel-out 61 leaving us with just x, while at the left-hand side of the equation 122 will be divided by 61)

x = 122/61

x=2

Substitute x= 2 into equation (1)

8x + 3y = 4

8(2) + 3y = 4

16 + 3y = 4

Subtract 16 from both-side of the equation

16-16 + 3y = 4-16

3y = -12

Divide both-side of the equation by 3

3y/3 = -12/3

y = -4

x= 2    and y = -4

4 0
4 years ago
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What is the distance between nicholas's school and the post office?
aleksklad [387]
Part A:

Given that Nicholas's school is located at point (3, 2) and that the post office is located at point (-2, -2), then the distance between Nicholas's school and the post office is given by:

d= \sqrt{(-2-3)^2+(-2-2)^2}  \\  \\ = \sqrt{(-5)^2+(-4)^2} = \sqrt{25+16}  \\  \\  \sqrt{41} =\bold{6.4} \ units



Part B:

If Nicholas is located at point (– 3 , 2), the distance to get to the grocery store located at point (1,-1) is given by:

d= \sqrt{(1-(-3))^2+(-1-2)^2}  \\  \\ = \sqrt{(1+3)^2+(-3)^2} = \sqrt{(4)^2+9}  \\  \\ = \sqrt{16+9} = \sqrt{25} =\bold{5}
4 0
3 years ago
Fred and Frank play a game. Fred picks an even number X and asks Frank to add all even numbers between 0 and X (inclusive) as fa
TiliK225 [7]

Answer:

The even numbers between 0 and X represents an arithmetic sequence with a common difference of 2

The rule of arithmetic sequence = a + d(n - 1)

Where a is the first term and n is the number of terms

So, for the even numbers between 0 and X

The first term = a = 0

d = 2

So, we need to find n at the last term which is X

∴ X = 0 + 2 ( n -1 )

∴ n - 1 = X/2

∴ n = X/2 + 1

The sum of the arithmetic sequence = (n/2) × (2a + (n−1)d)

Substitute with a and d and X

So, the sum = (n/2) * (2*0 + (n−1)*2)

                   = (n/2) * ((n−1)*2)

                   = n(n-1)

                   = (X/2 + 1) * (X/2)

                   = X/2 by (X/2 + 1)

So, The quick way to add all even numbers between 0 and X always works.

8 0
4 years ago
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