Find the maximum or minimum value of y = 3x² + 7x + 9 by completing the squares state the value of x at which the function is maximum or minimum.​

Step-by-step explanation:

we can simplify the stuff inside the parentheses to

[tex] \frac{ {x}^{3} }{2y} [/tex]

now we need to multiply it with itself, giving us

[tex] \frac{ {x}^{6} }{4 {y}^{2} } [/tex]

so yeah, D is the correct answer

Answer:

[tex]y_p(x) =c_1e^{-6x} + c_2e^{-3x}+ e^x + 4x^2[/tex]

Step-by-step explanation:

Given

[tex]y" + 9y' + 18y = 24x^2 + 40x + 8 + 12e^x[/tex] ---- (1)

[tex]y_p(x) = e^x + 4x^2[/tex]

Required

The general solution of [tex]y(x)[/tex]

Let

[tex]y = e^{nx}[/tex] be the trial solution of (1)

So:

[tex]y" + 9y' + 18y = 0[/tex] becomes

[tex]n^2 + 9n + 18 = 0[/tex]

Expand

[tex]n^2 + 6n+3n + 18 = 0[/tex]

Factorize

[tex]n(n + 6)+3(n + 6) = 0[/tex]

Factor out n + 6

[tex](n + 6)(n + 3) = 0[/tex]

Split

[tex]n +6 = 0\ or\ n + 3 = 0[/tex]

Solve for n

[tex]n =-6\ or\ n = -3[/tex]

So:

[tex]y = e^{nx}[/tex] becomes:

[tex]y = c_1e^{-6x} + c_2e^{-3x}[/tex]

[tex]y_p(x) = e^x + 4x^2[/tex] becomes

[tex]y_p(x) =c_1e^{-6x} + c_2e^{-3x}+ e^x + 4x^2[/tex]

Where: [tex]c_1[/tex] and [tex]c_2[/tex] are arbitary constants

Answer:

Since in an orchestra each player plays parallely, i.e. everyone plays the same line simultaneously, hence the length of the play never depends on the number of players playing it. Hence, time taken by 60 players = time taken by 120 players = 40 minutes. So 60 person will play the 9th harmony in same 40 minutes.

Step-by-step explanation:

Answer:

y" - 8y' + 15y = 0

2nd order Homogeneous DE.

Solving Quadratically

k² - 8k + 15 = 0

k= 5 or k= 3.

Two real and Unequal roots.

y= Ae^5x + Be^3x.

Answer:

0.1902 = 19.02% probability of returning a shipment

Step-by-step explanation:

For each alternator, there are only two possible outcomes. Either it is defective, or it is not. The probability of an alternator being defective is independent of any other alternator, which means that the binomial probability distribution is used to solve this question.

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.

1.5% of the alternators will not perform up to specifications.

This means that [tex]p = 0.015[/tex]

Shipment of 100 alternators

This means that [tex]n = 100[/tex]

What is the probability of returning a shipment?

Probability of more than 2 defective, which is:

[tex]P(X > 2) = 1 - P(X \leq 2)[/tex]

In which

[tex]P(X \leq 2) = P(X = 0) + P(X = 1) + P(X = 2)[/tex]. So

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

[tex]P(X = 0) = C_{100,0}.(0.015)^{0}.(0.985)^{100} = 0.2206[tex]

[tex]P(X = 1) = C_{100,1}.(0.015)^{1}.(0.985)^{99} = 0.3360[/tex]

[tex]P(X = 2) = C_{100,2}.(0.015)^{2}.(0.985)^{98} = 0.2532[/tex]

Then

[tex]P(X \leq 2) = P(X = 0) + P(X = 1) + P(X = 2) = 0.2206 + 0.3360 + 0.2532 = 0.8098[/tex]

Then

[tex]P(X > 2) = 1 - P(X \leq 2) = 1 - 0.8098 = 0.1902[/tex]

0.1902 = 19.02% probability of returning a shipment

Answer:

3/35

Step-by-step explanation:

Answer:

10 bars ; width 10

Step-by-step explanation:

Reordering the data given :

2, 3, 8, 9, 10, 14, 14, 15, 15, 17, 18, 20, 22, 24, 26, 29, 36, 39, 39, 39, 41, 43, 44, 50, 50, 52, 52, 52, 60, 60, 60, 62, 65, 69, 71, 72, 77, 78, 82, 86, 87, 87, 91, 93, 93, 97, 98, 98, 98, 98

To know the number of bars and width to use, we need to know the range of the data, from there we can decide the most appropriate width and also the number of bars we get using the width ;

Range = 98 - 2 = 96

By extending the width slightly on either side, we have 0, 100.

If we start from the origin, 0 ; and the maximum data point = 98 ; by slightly extending the width to 100 ; we could make use of a very reasonable width of 10; which is easier to work with than lesser width values ;

Now our range = 100 - 0 = 100

Width = 10

Number of bars = range / bar width

= 100 / 10

= 10 bars

Answer:

572.6

Step-by-step explanation:

400 = 220 [tex]x^{5}[/tex]

ln(400/220) = 5 ln(x)

ln(x) = .1195

x = [tex]e^{.1195}[/tex]

x = 1.127

Y = 220[tex](1.127)^{8}[/tex]

Y= 572.6

9514 1404 393

Answer:

Step-by-step explanation:

Part A:

The two right-angle corners of the triangular bases are at either end of the same edge. This is only shown correctly in Net A.

__

Part B:

See the attached annotated diagram. Dimensions are in inches.

__

Part C:

The total surface area is the sum of the three central rectangles of the net and the two triangles. As shown in the attached, the two triangles can be considered as one rectangle of dimensions 3 in by 4 in.

The total area is ...

  Surface area = base area + face area

  = (3 in)(4 in) + (3 + 4 + 5 in)(7.2 in) = 12 in² +86.4 in²

  Surface area = 98.4 in²

Answer:  Median = 3

Explanation:

Sort the numbers to get {1,2,3,5,6}. The middle most number is 3, so that's the median.

Answer:

14.73.

Step-by-step explanation:

Answer:

See image below for answer:)

Step-by-step explanation:

Answer:

The interval that represents the middle 68% of her commute times is between 33.5 and 42.5 minutes.

Step-by-step explanation:

The Empirical Rule states that, for a normally distributed random variable:

Approximately 68% of the measures are within 1 standard deviation of the mean.

Approximately 95% of the measures are within 2 standard deviations of the mean.

Approximately 99.7% of the measures are within 3 standard deviations of the mean.

In this problem, we have that:

Mean of 38 minutes, standard deviation of 4.5 minutes.

Determine the interval that represents the middle 68% of her commute times.

Within 1 standard deviation of the mean. So

38 - 4.5 = 33.5 minutes

38 + 4.5 = 42.5 minutes.

The interval that represents the middle 68% of her commute times is between 33.5 and 42.5 minutes.

Answer:

use photo math

Step-by-step explanation:

cuz i said so

Answer: 924

Step-by-step explanation:

1. Use the combination formula nCr = n!/(n-r)!r!

Using this formula gets you 16 (n) C 6 (r) = 12!/6!6! Which is also 12 • 11 • 10 • 9 • 8 • 7 • 6 • 5 • 4 • 3 • 2 • 1 / 6 • 5 • 4 • 3 • 2 • 1 • 6 • 5 • 4 • 3 • 2 • 1

2. Cancel out matching multiples that are in the numerator and denominator

This gets you 12 • 11 • 10 • 9 • 8 • 7 / 6 • 5 • 4 • 3 • 2 • 1 or 665280/720 when you simplify which leads you to the answer 924

Hope this helps!

Answer:

924

Step-by-step explanation:

Answer:

I'm sorry but the question is not clear enough for me to understand the question asked snap the entire question

Answer:

The value of the slope is 4

The meaning of the slope is y/x

Step-by-step explanation:

Answer:

20

Step-by-step explanation:

2(3p+4)

Let p=2

2(3*2+4)

Multiply inside the parentheses

2(6+4)

Add inside the parentheses

2(10)

Multiply

20

Hola aquí va la respuesta!!!

[tex]20[/tex]

[tex] \saludos[/tex]

depends on what u believe in if u think he existed then yes if you dont then no

Answer:

f(-1) = 5

Step-by-step explanation:

To "evaluate the function f(x) = -x^2 + 6 at x = -1, we substitute -1 for x in each instance:

f(-1) = -(-1)^2 + 6

According to order of operations rules, exponentiation must be performed before multiplication or division.  '-(-1)^2' thus becomes -1, and so

f(-1) = -(-1)^2 + 6 = -1 + 6 = 5.

Thus, f(-1) = 5

9514 1404 393

Answer:

  7.056 × 10^31

Step-by-step explanation:

The applicable rule of exponents is ...

  (10^a)(10^b) = 10^(a+b)

__

  [tex](1.2\times10^{19})\times(5.88\times10^{12})=(1.2\cdot5.88)\times10^{19+12}\\\\=\boxed{7.056\times10^{31}}[/tex]

As you know, the commutative and associative properties of multiplication let you rearrange the order of the product to any convenient form. Here it is convenient to group the mantissas together and the powers of 10 together.

__

Additional comments

This is a product your scientific or graphing calculator can produce for you. Likely it will display the result in scientific notation because it won't have enough display digits to show you the product any other way. For smaller numbers, you can set the display mode to give you scientific notation.

If you choose to use a spreadsheet to perform this calculation, the numbers would be entered as 1.2e19 and 5.88e12. The result will be something like 7.056e31. You may have to format the display to show 3 decimal places.

Answer:

B)  y < -x + 1

Step-by-step explanation:

you can see from the x-and-y intercepts that the equation of this line is:

y = -x + 1

now you must determine whether the equal sign should be replaced with '<' or '>'

you can use the point (0,0) to see if that makes y > -x + 1 true or false:

0 > 0+1   This is False

so the answer should be:  y < -x + 1

Answer: B

Step-by-step explanation:

Answer:

-5ºC < 5ºC is an inequality that compares temperatures.

B is the correct answer for the multiple choice question.

Answer:

11 2/3%

Step-by-step explanation:

Change in Amount  =335,000 – 300,000

Percent Increase

Original Amount

300,000

35,000

2

=0.11666=11.666%=11-%

300,000

3

(https://imgur.com/a/U6c1pes) - For more clear explanation.

Answer:

Side a = 10.44031

Side b = 10

Side c = 3

Angle ∠A = 90° = 1.5708 rad = π/2

Angle ∠B = 73.301° = 73°18'3" = 1.27934 rad

Angle ∠C = 16.699° = 16°41'57" = 0.29146 rad

Answer:

The smallest possible length is 0.83m

Step-by-step explanation:

Given

[tex]Volume = 565L[/tex]

Required

The smallest length of the tank

Since the tank is cubical, then the volume is:

[tex]Volume = Length^3[/tex]

This gives:

[tex]565L= Length^3[/tex]

Express as [tex]m^3[/tex]

[tex]\frac{565m^3}{1000} = Length^3[/tex]

[tex]0.565m^3 = Length^3[/tex]

Take cube roots of both sides

[tex]0.8267m = Length[/tex]

Rewrite as:

[tex]Length = 0.8267m[/tex]

Approximate

[tex]Length = 0.83m[/tex]

Answer:

yes

Step-by-step explanation:

that's that's I think

Answer:

The answer:

y=(x+2)²+7

Choose (B)

Answer:

[tex]\text{D) }99^{\circ}[/tex]

Step-by-step explanation:

Define a cyclic quadrilateral by a quadrilateral that is circumscribed by a circle. In this case, since the quadrilateral shown is circumscribed by a circle, it is a cyclic quadrilateral.

A property of all cyclic quadrilaterals is that their opposite angles are supplementary, meaning they add up to 180 degrees. Since [tex]\angle G[/tex] and [tex]\angle I[/tex] are opposite angles in the quadrilateral, they must be supplementary. Therefore, we have the equation:

[tex]\angle G+\angle I=180,\\81^{\circ}+\angle I=180,\\\angle I=180-81=\boxed{99^{\circ}}[/tex]

Answer:

1 : 2

Step-by-step explanation: trust

Answer:

3/1 Hope that helps

Step-by-step explanation:

Step-by-step explanation:

hope it help thanks

pls mark me as brainliest