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3 years ago

Find the equation of the solution to dydx=x6y through the point (x,y)=(1,3).

1 answer:

7 0

Separate the x's and y's.

dy/y = x^7 dx

Integrate both sides.

ln(abs(y)) = (x^8)/8 + C

To cancel the natural root, make both sides the power to e.

e^ln(abs(y)) = e^((x^8)/8 + C)

abs(y) = e^C * e^((x^8)/8)

y = + or - [e^C * e^((x^8)/8)

Now just bundle the + or - e^C into a single constant. We will call it A.

y = Ae^((x^8)/8)

Now plug in the point (1,3).

3 = Ae^((1^8)/8)

3 = Ae^(1/8)

A = 3/(e^(1/8))

So the equation is:

y = (3/(e^(1/8))*(e^((x^8)/8)

You might be interested in

Pepsi [2]

Answer:

(a)Attached

(b)69 degrees

(b)The ladder is safe

Step-by-step explanation:

(a)See attached diagram

The wall is length |AB| and the ladder is length |AC|

(b)

$sin \theta =\dfrac{|AB|}{|AC|} \\sin \theta =\dfrac{14}{15}\\\theta=arcsin (\dfrac{14}{15})\\\theta=69^\circ$

(c)Jamie wants the angle of the ladder makes with the ground to be no greater than 75 degrees for safety reasons.

Since the angle formed between the ground and the ladder (69 degrees) is less than 75 degrees, the ladder is safe the way it is positioned.

4 0

3 years ago

9. Write an equation of a parabola that opens to the right, has a vertex at the origin, and a focus at (7,0).

Nookie1986 [14]

Answer:

$x = \frac{1}{28} y^{2}$

Step-by-step explanation:

parabola equation with vertex (0 , 0) and focus length |f| = 7

4*f*(x - h) = (y - k)²

4*7*(x-0)=(y-0)²

28x = y²

$x = \frac{1}{28} y^{2}$

6 0

3 years ago

32 and 72 (prime factorization)?

max2010maxim [7]

Yes that is a prime fraction

8 0

3 years ago

Which table of ordered pairs represents a proportional relationship

Citrus2011 [14]

You are right on the answer

5 0

3 years ago

A point x is 34m due to east of a point Y . The bearing of a flagpole from x and Y are N18°W And N40°E respectively .

Murljashka [212]

Answer:

The distance of flag post from Y is 38.13 m

Step-by-step explanation:

Consider point Y at the intersection of both lines as shown below. Now the point X lies 34 meter from point Y in east direction.

Now flag pole at point X lies at a bearing of N18°W. That is at point X from north, flag post makes an angle of 18° towards west.

Similarly flag pole at point Y lies at a bearing of N40°E. That is at point Y from north, flag post makes an angle of 40° towards east.

Consider ∆ AXY as right angle triangle. Therefore measure of angle FXY is,

$\angle AXY=\angle AXF+\angle FXY$

$\therefore 90 \degree=18\degree+\angle FXY$

$\angle FXY=72\degree$

Consider ∆ BYX as right angle triangle. Therefore measure of angle FYX is,

$\angle BYX=\angle BYF+\angle FYX$

$\therefore 90 \degree=40\degree+\angle FYX$

$\angle FYX=50\degree$

Refer attachment 1.

From diagram consider the triangle FYX. To find the third angle that is ∠YFX can be calculated by using angle sum property of triangle.

∠YFX+∠FYX+∠FXY=180°

∠YFX+50°+72°=180°

∠YFX=58°

Refer attachment 2.

Now the distance FY can be calculated using sin rule as follows,

$\frac{\sin X}{FY}=\frac{\sin F}{YX}=\frac{\sin Y}{FX}$

Substituting the values,

$\frac{\sin 72}{FY}=\frac{\sin 58}{34}=\frac{\sin 50}{FX}$

Simplifying first two terms,

$\frac{\sin 72}{FY}=\frac{\sin 58}{34}$

Cross multiplying,

$34\times\sin 72=FY\times \sin 58$

$\dfrac{34\times\sin 72}{\sin 58}=FY$

$FY=38.13$ m

7 0

3 years ago