The given family of functions is the general solution of the differential equation on the indicated interval. find a member of the family that is a solution of the initial-value problem. y = c1e4x + c2e−x, (−∞, ∞); y'' − 3y' − 4y = 0, y(0) = 1, y'(0) = 2

Answer:

A. $1249.

Step-by-step explanation:

We have been given that Juno deposited $750 in a savings account that earns 4% interest compounded annually. We are asked to find the amount of money in the account after 13 years.

To solve our given problem, we will use compound interest formula. [tex]A=P(1+\frac{r}{n})^{nt}[/tex], where,

A = Amount after t years,

P = Principal amount,

r = Interest rate in decimal form,

n = Number of times interest is compounded per year,

t = Time in years.

Let us convert our given interest rate in decimal form.

[tex]4\%=\frac{4}{100}=0.04[/tex]

Upon substituting our given values in compound interest formula we will get,

[tex]A=\$750(1+\frac{0.04}{1})^{1\cdot 13}[/tex]

[tex]A=\$750(1+0.04)^{13}[/tex]  

[tex]A=\$750(1.04)^{13}[/tex]  

[tex]A=\$750\times 1.665073507310388[/tex]  

[tex]A=\$1248.805130482791\approx \$1249[/tex]  

Therefore, there will be $1249 in Juno's account after 13 years and option A is the correct choice.

The given equation is represented below:

cos(-pi/2)=cos(3pi/2)

The value of cos(-pi/2) is 0 and the value of cos(3pi/2) is also 0

Further a function is defined as an even function if f(x) = f(-x)

Cosine function is an even function.

Therefore it is true and the correct option is c

It is true because the cosine function has a period of 2pi

Hope it helps ..!!

Answer:

Option C - It is true because the cosine function has a period of [tex]2\pi[/tex].              

Step-by-step explanation:

Given :  Marco wrote the equation below.

[tex]\cos (-\frac{\pi}{2})=\cos (\frac{3\pi}{2})[/tex]

To find : Which statement best describes Macro equation?

Solution :

Since, the period of the given cos function is 360°

So, it holds the property of trigonometric :

[tex]\cos \theta=\cos (2\pi+\theta)[/tex] then the function is an even function.

Taking   [tex]\theta =-\frac{\pi}{2}[/tex]

Then , [tex]2\pi+\theta = 2\pi-\frac{\pi}{2}[/tex]

[tex]2\pi+\theta = \frac{4\pi-\pi}{2}[/tex]

[tex]2\pi+\theta = \frac{3\pi}{2}[/tex]

So, the given function is a even function in a period of [tex]2\pi[/tex].

Therefore, Option C is correct.

It is true because the cosine function has a period of [tex]2\pi[/tex].

Answer:

50% probability of a couple having a baby boyboy when their sixth child is​ born, given that the first five were all boys.

Step-by-step explanation:

For each child, there are only two possible outcomes. Either it is a boy, or it is a girl. The probability of a child being a boy or a girl is independent of the other children. So we use the binomial probability distribution to solve this question.

The conditional probability formula is also used.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

And p is the probability of X happening.

Conditional Probability

We use the conditional probability formula to solve this question. It is

[tex]P(B|A) = \frac{P(A \cap B)}{P(A)}[/tex]

In which

P(B|A) is the probability of event B happening, given that A happened.

[tex]P(A \cap B)[/tex] is the probability of both A and B happening.

P(A) is the probability of A happening.

Find the probability of a couple having a baby boyboy when their sixth child is​ born, given that the first five children were all boys.

Event A: First five children being boys.

Event B: Sixth children being a boy.

P(A):

First five children being boys.

P(X = 5) when n = 5.

Equally likely to be boy or girl, so p = 0.5.

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]P(A) = P(X = 5) = C_{5,5}.(0.5)^{5}.(0.5)^{0} = 0.03125[/tex]

Intersection:

Intersection between the first five children being boys and the sixth also being a boy, so [tex]P(X = 6)[/tex] when n = 6.

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]P(A \cap B) = P(X = 6) = C_{6,6}.(0.5)^{6}.(0.5)^{0} = 0.015625[/tex]

Probability:

[tex]P(B|A) = \frac{0.015625}{0.03125} = 0.5[/tex]

50% probability of a couple having a baby boyboy when their sixth child is​ born, given that the first five were all boys.

Let B be the amount Beatrice charges per hour per child

Let x be the number of hours

Let n be the number of children

a)total amount Beatrice charges = T = B*x*n - 10

b)n =4 and T = 100

100 = B*x*4 -40

x = 35/B

c)Let S be the amount she has t o pay to her sister

n = 3 and x = (4+4+5) = 13

so, 13*B*3 -30 -S = 100

S = 39B - 130

The point-slope equation of the line that is perpendicular to y-3=4(x-10) and passes through(-3,7) is:

B. [tex]y-7=\frac{-1}{4} (x+3)\\[/tex]

The slope intercept form is y=mx+b where m is slope.

We have given perpendicular line as:

y-3=4(x-10)

y-3=4x-40

y=4x-37

The slope intercept form of the given line is

y=4x-37

Slope of this line is m=4

Now, as we know the two perpendicular lines have negative reciprocal slope.

Thus the other line have slope [tex]m=-\frac{1}{4}[/tex]

Now. the equation of line passing through point (-3,7) and having slope [tex]\frac{-1}{4}[/tex] is:

[tex]y-7=\frac{-1}{4} (x+3)\\[/tex]

Therefore the correct option is B.

Learn more: brainly.com/question/18595188

Answer:

100 pi cubic feet

Step-by-step explanation:

Final answer:

The banker's interest rounded to the nearest cent is approximately $110.60.

Explanation:

To calculate the banker's interest on a principal of $2,500 at a rate of 9% for 180 days, you would apply the formula for simple interest:

Interest = Principal × rate × time

Since time needs to be expressed in years and the rate as a decimal, convert 180 days into a fraction of a year by dividing by 365:

Time (in years) = 180 / 365 ≈ 0.4932

Convert the rate to a decimal:

Rate (as a decimal) = 9% = 0.09

Now calculate the interest:

Interest = $2,500 × 0.09 × 0.4932 ≈ $110.595

Thus, the banker's interest rounded to the nearest cent is approximately $110.60.

Answer:

The height of the pole is 322.75 feet.

Step-by-step explanation:

Let the triangle Δ ABC with AC be the length of wire and AB be the Height of the pole

Length between the point of attachment of wire from base of the pole = BC = 137 feet

Angle of elevation to the pole = θ = 67°

We have to find the length of the pole that is AB Let the height of pole be h feet.

According to trigonometry :

[tex]\tan C=\frac{\text{perpendicular}}{\text{base}}[/tex]

Here, C = 67° , perpendicular = AB = h , base = BC = 137

Substitute the values,

[tex]\tan 67^{\circ}=\frac{AB}{BC}[/tex]

[tex]\tan 67^{\circ}=\frac{h}{137}[/tex]

[tex]h=\tan 67^{\circ} \times 137[/tex]

[tex]h=322.75[/tex]

Thus, the height of the pole is 322.75 feet.

Answer:60.1

Step-by-step explanation:

cos

Well, to make it simple it's 0.49. Hope it helps!

The equation of the plane in xyz-space that passes through the point p=(5,5,3) and is perpendicular to the vector n=(1,2,5) is x + 2y + 5z = 30.

In mathematics, the equation of the plane can be found using the plane equation Ax + By + Cz = D. Given that the plane goes through point p=(5,5,3) and is perpendicular to vector n=(1,2,5). The vector n actually gives us the coefficients A, B, and C. Meaning A=1, B=2, and C=5. We get D by substituting the given point into the equation (Ax + By + Cz = D) as follows D = Ax + By + Cz = (1*5) + (2*5) + (5*3) = 5 + 10 + 15 = 30. Thus, the equation of the plane is x + 2y + 5z = 30.

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Answer:

Option 3

Step-by-step explanation:

edge 2020

Answer:

Faelyn should realize that her work shows that the polynomial is prime.

Explanation:

The only difference between her factors in Step 2 is that the 4 in the first group is negative, while the 4 in the second group is positive.

Rearranging the polynomial to factor it will not change the end result.

Factoring out a negative will make not only one, but both terms, in one of the binomials the opposite sign; this will not make the factors the same.

Factoring only 2x out of the first group will result in having (3x³+4x); this is not the same either.

She should realize that when this happens, her polynomial is prime.

The precision of what Faelyn should do is that Faelyn should realize that her work shows that the polynomial is prime. Hence, the option A is the correct option.

Factors of the polynomial which are multiplied to produce the original polynomial.

The polynomial which can not be factored is known as prime polynomial.

The standard form of the polynomial with highest power of 2 can be given as,

Given information-

The given polynomial equitation in the problem is,

[tex]6x^4 -8x^2 + 3x^2 + 4[/tex]

         [tex](6x^4- 8x^2) + (3x^2 + 4)[/tex]

       [tex]2x^2(3x^2 - 4) + 1(3x^2 + 4)[/tex]

Faelyn noticed that she does not have a common factor. The polynomial which can not be factored is known as prime polynomial.

Thus Faelyn should realize that her work shows that the polynomial is prime. Hence, the option A is the correct option.

Learn more about the polynomial equation here;

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Final answer:

The vertex of the quadratic function y = (x -7)² + 9 is at the point (7, 9).

Explanation:

Vertex of a quadratic function is the highest or lowest point on the graph of the function. In this case, the quadratic function is in the form y = (x -7)² + 9.

To find the vertex, we notice that the function is in the form y = (x - h)² + k, where (h, k) represents the vertex. Therefore, the vertex of the given quadratic function is at (7, 9).

the answers are (x-1) and (3x-2)