MATHEMATICS HIGH SCHOOL

In this problem, y = c₁eˣ + c₂e⁻ˣ is a two-parameter family of solutions of the second-order DE y'' − y = 0. Find a solution of the second-order IV P consisting of this differential equation and the given initial conditions. y(-1) = 4, y'(-1) = -4.

Answers

Answer 1
Answer:

Answer:

y=4e^(-(x+1)) will be the solutions.

Step-by-step explanation:

The given equation is y=C_(1)e^(x)+C_(2)e^(-x)

Therefore, for x = -1

4=C_(1)e^(-1)+C_(2)e^(1) ------(1)

Now y'(-1) = -4

y'(x) = C_(1)e^(x)-C_(2)e^(-x) = -4

C_(1)e^(-1)-C_(2)e^(1) = -4 -----(2)

By adding equation (1) and (2)

2C_(1)e^(-1)=0

C_(1)=0

From equation (1),

4=0+C_(2)e^(1)

C_(2)=4e^(-1)

By placing the values in the parent equation

y = 4e^(-1)* e^(-x)

y = 4e^(-(x+1))

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Please help I don't understand this
Which of the following is the equation of a line parallel to the line y=3x+2, passing through the point (10,1)?A. 3x - y=29 B. 3x + y=29 C. -3x-y=29 D. 3x + y=29
24% of 1,321 is how much?
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A plane is flying within sight of the Gateway Arch in St. Louis, Missouri, at an elevation of 30,000 ft. The pilot would like to estimate her distance from the Gateway Arch. She finds that the angle of depression to a point on the ground below the arch is 27°. (Round your answers to the nearest foot.)(a) What is the distance between the plane and the arch? (b) What is the distance between a point on the ground directly below the plane and the arch?

How do you solve 2(10-6x)=x-8x
Show work

Answers

2(10)-2(6x)= x-8x 
20-12x=x-8x 
   +12x+12x

20=13x-8x
20=5x 
4=x
Hey, Lizzy147! 
1st. Distribute 2 to 10 and -6x
20-12x=x-8x 
2nd. Move -12x to the other side.
20=13x-8x
Simple math.
20=5x 
x=4

The total number of fungal spores can be found using an infinite geometric series where a1 = 8 and the common ratio is 4. Find the sum of this infinite series that will be the upper limit of the fungal spores.

Answers

The formula for infinite geometric series is equal to a1 / (1-r) where in this problem a1 is equal to 8 and r is equal to 4. In this case, r is not equal to less than 1. This means the sum should be infinity and cannot be determined definitely. 

Answer:

This infinite geometric series is divergent and thus we cannot find the sum. The sum is infinity.


Step-by-step explanation:

There are two types of geometric series: convergent and divergent.

The sum of an infinite geometric sequence is given by the formula:

Sum = (a)/(1-r)

Where,

r is the common ratio and

|r|<1


If absolute value of r is NOT less than 1, then the series is divergent and sum cannot be found.

For our given problem, r=4 ,  clearly  |4|=4 , which is NOT less than 1, so the series is divergent and sum cannot be found.

What is the equation of the line that passes through the point (-4, 7) and has anundefined slope?

Answers

Answer:

x = -4

Step-by-step explanation:

Since the slope is undefined, the line is a vertical line.  All vertical lines have an equation x = k.  In your problem k = -4, so the equation of the line is x = -4

HELP PLEASE !!!!!!!!!!!!A florist has to order roses and carnations for Valentine’s day. The florist needs to decide how many dozen roses and carnations should be ordered to obtain a maximum profit.

• Roses: The florist’s cost is $20 per dozen;
the profit over cost is $20 per dozen.
• Carnations: The florist’s cost is $5 per
dozen; the profit over cost is $8.
• The florist can order no more than 50 dozen
flowers.
• A minimum of 30 dozen carnations must be
ordered.
• The florist cannot order more than $660
worth of roses and carnations.

A.) How many dozen roses should the florist order? Answer in units of doz

B.) How many dozen carnations should the florist order? Answer in units of doz

Answers

30 dozen carnations.
20 dozen roses.
This means she spends 550, but makes 640. 
I hope this is right?

If each face is a unit square (1x1), what is the surface area of the cube?

Answers

the surface area is 6 because you multiply the area of one side of the cube by the number of sides it has, which is 6.
1 x 6 = 6

Answer:

The unit square would be 6.

Step-by-step explanation:

Compute the following binomial probabilities directly from the formula for b(x; n, p):a. b(3; 8, .35)
b. b(5; 8, .6)
c. P(3<=X<=5) when n=7 and p = .6
d. P(1 <= X) when n=9 and p= .1

Answers

b(x; n, p) = nCx(p^x * (1 - p)^(n - x))

a.) b(3; 8, .35) = 8C3(0.35^3 * 0.65^5) = 56 x 0.042875 x 0.116029 = 0.2786

b.) b(5; 8, .6) = 8C5(0.6^5 * 0.4^3) = 56 x 0.07776 x 0.064 = 0.2787

c.) P(3 <= x <= 5) = P(3) + P(4) + P(5) = 7C3(0.6^3 * 0.4^4) + 7C4(0.6^4 * 0.4^3) + 7C5(0.6^5 * 0.4^2) = (35 x 0.216 x 0.0256) + (35 x 0.1296 x 0.064) + (21 x 0.07776 x 0.16) = 0.193536 + 0.290304 + 0.2612736 = 0.7451
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