In Problems 41 and 42 solve the given initial-value problem in which the input function g(x) is discontinuous. [Hint: Solve each problem on two intervals, and then find a solution so that y and y are continuous at x p2 (Problem 41) and at x p (Problem 42).] 41. y 4y g(x), y(0) 1, y(0) 2,

Differentiating both sides of

xy = 99

with respect to t yields

x dy/dt + y dx/dt = 0

When x = 11, we have

11y = 99   ==>   y = 9

and we're given that dy/dt = -4 at this point, which means

11 (-4) + 9 dx/dt = 0   ==>   dx/dt = 44/9

[tex]\\ \sf\longmapsto \frac{5}{ \sqrt{7} - \sqrt{3} } + \frac{1}{ \sqrt{7} + \sqrt{3} } \\ \\ \sf\longmapsto \frac{5( \sqrt{7} + \sqrt{3} ) + 1 (\sqrt{7} - \sqrt{3} )}{( \sqrt{7} - \sqrt{3} )( \sqrt{7} + \sqrt{3} )} \\ \\ \sf\longmapsto \frac{5 \sqrt{7} + 5 \sqrt{3} + \sqrt{7} - \sqrt{3} }{( { \sqrt{7} )}^{2} - ( \sqrt{3}) {}^{2} } \\ \\ \sf\longmapsto \frac{5 \sqrt{7} + \sqrt{7} + 5 \sqrt{3} - \sqrt{3} }{7 - 3} \\ \\ \sf\longmapsto \frac{6 \sqrt{7} + 4 \sqrt{3} }{4} [/tex]

Similar triangles are proportional, meaning one will be a factor larger or smaller than the other. This factor will be the same for all of the sides. So, we can say that one corresponding pair of sides is equal to another corresponding pair of sides.

BA / ED = AC / CD

42 / 6 = (64 - x) / (x)

6(64 - x) = 42(x)

384 - 6x = 42x

384 = 48x

x = 8

Hope this helps!

Answer:

The mean number of the students who develop hypertension over a life time is 7.8.

Step-by-step explanation:

For each person, there are only two possible outcomes, either they will develop hypertension, or they will not. The probability of a person developing hypertension is independent of any other person, which means that the binomial probability distribution is used to solve this question.

Binomial probability distribution

Probability of exactly x successes on n repeated trials, with p probability.

The expected value of the binomial distribution is:

[tex]E(X) = np[/tex]

Suppose that the probability that a person will develop hypertension over a life time is 60%.

This means that [tex]p = 0.6[/tex]

13 graduating students from the same college are selected at random.

This means that [tex]n = 13[/tex]

Find the mean number of the students who develop hypertension over a life time

[tex]E(X) = np = 13*0.6 = 7.8[/tex]

The mean number of the students who develop hypertension over a life time is 7.8.

Answer:

C. 10,080

Step-by-step explanation:

We can multiply to find how many minutes there are in 1 day.

24 * 60 = 1,440

Now, we can multiply that value by 7 to find out how many minutes there are in 1 week.

1,440 * 7 = 10,080

Best of Luck!

Answer: -2(d) is the answer.

Step-by-step explanation:

x1 = 3

y1 = -5

x2 = -2

y2 = 5

slope (m) = rise/run = (y2 - y1)/(x2-x1)

                                =(5-(-5))/(-2-3)

                                 =   10/-5

                                 = -2

Answer:

-14 and 4

Step-by-step explanation:

To find the values subtract 9 from -5, as well as add 9 to -5

-5-9= -14

-5+9= 4

Answer:

x = 5±2 sqrt(11)

Step-by-step explanation:

(x-5) ²+5 =49

Subtract 5 from each side

(x-5) ²+5-5 =49-5

(x-5) ² =44

Take the square root of each side

sqrt((x-5) ²) =±sqrt(44)

sqrt((x-5) ²) =±sqrt(4*11)

x-5 = ±2 sqrt(11)

Add 5 to each side

x-5+5 = 5±2 sqrt(11)

x = 5±2 sqrt(11)

Answer:

[tex]\left(x-5\right)^2+5=49[/tex]

Subtract 5 from both sides

[tex]\left(x-5\right)^2+5-5=49-5[/tex]

[tex]\left(x-5\right)^2=44[/tex]

[tex]x-5=\sqrt{44}[/tex]

[tex]44=2^{2} \times11[/tex]

[tex]x-5=\sqrt{11} \sqrt{2^{2} }[/tex]

Radical rule:- [tex]\sqrt[n]{a^{n} } =a[/tex]

[tex]x-5=2\sqrt{11}[/tex]

Add 5 to both sides

[tex]x=2\sqrt{11}+5[/tex]

-------

[tex]x-5=-2\sqrt{11}[/tex]

Add 5 to both sides

[tex]x-5=-2\sqrt{11}[/tex]

Ans: [tex]x=2\sqrt{11}+5,\:x=-2\sqrt{11}+5[/tex]

OAmalOHopeO

Answer:

[tex]here \: the \: two \: sides \: are \: equal \: so \: \\ the \: triangle \: is \: issosceles \\ then \: x = 40 \\ thank \: you[/tex]

Step-by-step explanation:

A=140sq. units

Step-by-step explanation:

ABCD

A=13

B=15

C=14

D=20

C=14×14

=196sqr.units

Complete the square in the denominator to get

tan²(t ) + 14 tan(t ) + 48 = tan²(t ) + 14 tan(t ) + 49 - 1

… = (tan(t ) + 7)² - 1

Substitute u = tan(t ) + 7 and du = sec²(t ) dt. Then the integral becomes

[tex]\displaystyle \int \frac{2\sec^2(t)}{\tan^2(t)+14\tan(t)+48} \,\mathrm dt = 2 \int \frac{\mathrm du}{u^2-1}[/tex]

Separate the integrand into partial fractions:

[tex]\dfrac1{u^2-1} = \dfrac12 \left(\dfrac1{u-1}-\dfrac1{u+1}\right)[/tex]

Then we get

[tex]\displaystyle \int \frac{2\sec^2(t)}{\tan^2(t)+14\tan(t)+48} \,\mathrm dt =  \int \left(\frac1{u-1}-\frac1{u+1}\right)\,\mathrm du \\\\ =\ln|u-1|-\ln|u+1| + C \\\\ = \ln\left|\frac{u-1}{u+1}\right|+C \\\\ = \boxed{\ln\left|\frac{\tan(t)+6}{\tan(t)+8}\right|+C}[/tex]

Answer:

0.0079 = 0.79% probability that she randomly plants the trees so that all 5 sycamores are next to each other and all 5 palm trees are next to each other.

Step-by-step explanation:

A probability is the number of desired outcomes divided by the number of total outcomes.

The trees are arranged, so, to find the number of outcomes, the arrangements formula is used.

Arrangements formula:

The number of possible arrangements of n elements is given by:

[tex]A_n = n![/tex]

Desired outcomes:

5 sycamores(5! possible ways) and then the 5 palm trees(5! possible ways)

5 palm trees(5! possible ways) then the 5 sycamores(5! possible ways).

[tex]D = 2*5!*5![/tex]

Total outcomes:

Arrangements of 10 plants, so:

[tex]T = 10![/tex]

What is the probability that she randomly plants the trees so that all 5 sycamores are next to each other and all 5 palm trees are next to each other?

[tex]p = \frac{D}{T} = \frac{2*5!*5!}{10!} = 0.0079[/tex]

0.0079 = 0.79% probability that she randomly plants the trees so that all 5 sycamores are next to each other and all 5 palm trees are next to each other.

Answer: D

"Separating the students on the list into boys and girls and choosing a sample from each group that is proportional to the size of the group."

Step-by-step explanation:

You are sampling an equal amount of boys and girls since your getting an equal sample of each gender. (Not random)

The option that is not a random sample is:

Separating the students on the list into boys and girls and choosing a sample from each group that is proportional to the size of the group.

Option D is the correct answer.

It is the way of choosing a number of required items from a population given.

Each item has an equal probability of being chosen.

We have,

We will see which option is a sample that is not random.

A. Going through the list and choosing the first 25 names on the list.

Going through the list means every name has an equal chance of getting chosen.

This is a random sample.

B. Writing each student’s name on a card and then drawing out 25 names without looking.

Since we are drawing out 25 names without looking, all the students' names have an equal chance of getting drawn.

This is a random sample.

C. Choosing one student at random from the list and going through the list and choosing every fifth student until she has 25 names.

Choosing one student at random means every student has an equal chance of getting chosen.

This is a random sampling.

D. Separating the students on the list into boys and girls and choosing a sample from each group that is proportional to the size of the group.

The students are separated into boys and girls and the sample is chosen from each group so we are selecting the sample from the separated group.

This can not be a random sampling.

Thus,

The option that is not a random sample is:

Separating the students on the list into boys and girls and choosing a sample from each group that is proportional to the size of the group.

Option D is the correct answer.

Learn more about random sampling here:

https://brainly.com/question/12719656

#SPJ2

Answer:

Step-by-step explanation:

[tex]\tt{ \green{P} \orange{s} \red{y} \blue{x} \pink{c} \purple{h} \green{i} e}[/tex]

Answer:

the square root of 24 is 4.89897948557

Answer:

4.89

Step-by-step explanation:

2root 6........***

Answer:

0.53%

Step-by-step explanation:

hope it is well understood

Answer:

The null hypothesis is [tex]H_0: p = 0.31[/tex]

Step-by-step explanation:

Based on the Nielsen ratings, the local Fox affiliate claims its 10:00 PM newscast reaches 31% of the viewing audience in the area.

From the claim, we get the expected proportion, that is, the value tested at the null hypothesis. Thus, at the null hypothesis, we test if the proportion is of 31%, that is:

[tex]H_0: p = 0.31[/tex]

Answer:

x = 12.15 oz

Step-by-step explanation:

z = 1.8808

 1.8808 = (x - 12)/.08

Answer:

I cannot understand this question

Step-by-step explanation:

I don't know what is in the question

9514 1404 393

Answer:

  491,400 ft·lb

Step-by-step explanation:

The mass of the water is ...

  M = Vρ = LWHρ = (25 ft)(15 ft)(7 ft)(62.4 lb/ft³) = 163,800 lb

The average depth is 3 ft, so the work required is equivalent to that required to raise this mass 3 ft.

  W = (3 ft)(163,800 lb) = 491,400 ft·lb

Let breadth be x

Length=5x

ATQ

[tex]\\ \sf \longmapsto Area=Length\times breadth[/tex]

[tex]\\ \sf \longmapsto 5x(x)=180[/tex]

[tex]\\ \sf \longmapsto 5x^2=180[/tex]

[tex]\\ \sf \longmapsto x^2=\dfrac{180}{5}[/tex]

[tex]\\ \sf \longmapsto x^2=36[/tex]

[tex]\\ \sf \longmapsto x=\sqrt{36}[/tex]

[tex]\\ \sf \longmapsto x=6in[/tex]

Answer:

y=2,4

Step-by-step explanation:

7,25x( y+5,6)=58

7,25y+ 40,6=58

7,25y=58-40,6

y=17,4:7,25

y=2,4

x

3/2

Step One: 1 3/8, transform the number into a improper fraction:

Answer:

70% IS THE ANSWER

Step-by-step explanation:

Hope I helped.

Answer:

70%

Step-by-step explanation

0.7×100=70

Answer:

36 is the answer

Step-by-step explanation:

Answer:

36

Step-by-step explanation:

72: 2×2×2×3×3

108: 2×2×3×3×3

180: 2×2×3×3×5

here, common factors are 2,2,3 and 3 ..

so.. HCF: 2×2×3×3

•°•HCF=36 ..

Answer:

Isaac is 26

Simon is 24

if 8 is 4 I.e 8 divide by 4 is 2

therefore 1 minute is 2 scores

Isaac :13 x 2=26

(do the same to Simon to get his score)

9514 1404 393

Answer:

  8.4 years

Step-by-step explanation:

The value of P compounded continuously at rate r for t years is ...

  A = Pe^(rt)

Solving for t, we find ...

  t = ln(A/P)/r = ln(2)/0.083 ≈ 8.35117

It will take about 8.4 years for the investment to double.

Here we have a problem of maximization and quadratic equations.

The unit prize that maximizes the revenue is $1,500, and the maximum revenue is $18,000.

We know that the revenue equation is:

R(P) = - 8p^2 + 24,000p

Where the variable p is the price.

Now we want to find the value of p that maximizes the revenue.

To do it, we can see that the revenue equation is a quadratic equation with a negative leading coefficient.

This means that the arms of the graph will go downwards, then the maximum point of the graph will be at the vertex.

Remember that for an equation like:

y = a*x^2 + b*x+ c

The x-value of the vertex is at:

x = -b/(2*a)

Then for the equation:

R(P) = - 8p^2 + 24,000p

The vertex is at:

p = -(24,000)/(2*-8) = 1,500

The value of p that maximizes the revenue is p = $1,500

To get the maximum revenue, we need to evaluate the revenue equation in that p value.

R(1,500) =  - 8*(1,500)^2 + 24,000*1,500 = 18,000

And the revenue equation is in dollars, then the maximum revenue is 18,000 dollars.

If you want to learn more, you can read:

https://brainly.com/question/18269297

p = 1500  $    the unit price

R(p) = 18000000 $ maximum revenue

We will use two different procedures to calculate the maximum revenue.

That is equivalent to solve the problem and after that to test the solution

The first one is:

R(p) = - 8*p² + 24000*p

we realize that R(p) is a quadratic function ( a parabola) of the form:

y = a*x² + b*x + c    ( c = 0 in this case)

We also know that  as the coefficient of p² is negative the parabola opens downwards then the vertex is a maximum value for R(p), and the x coordinate of p is:

x = p =  - b/2*a   then by substitution

p = - ( 24000)/ 2 ( - 8)

p = 1500  $   and for that value of p

R(p) = - 8 ( 1500)² + 24000* (1500)  = - 18000000 + 36000000

R(p) = 18000000 $

The second procedure is solving with the help of derivatives.

R(p) =  - 8*p² + 24000*p

Tacking derivatives on both sides of the equation we get:

R´(p) = -16p  +  24000

If R´(p) = 0    then    -16p  +  24000 = 0

p = 24000/ 16         p  =  1500

if we check for the second derivative

R´´(p) = -16          -16 < 0  therefore there is a maximum value for R(p) when p = 1500, and that value is:

By substitution in R(p)

R(p) = -8 *(1500)² + 24000* 1500

R(p) =  - 18000000 + 36000000

R(p) = 18000000 $

Answer

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