= 1 2 + (2 + tan 1 2 ) where and are constants. Show that (1 + ) ²y/dy²=y
​

Answer:

Step-by-step explanation:

The given function is quadratic.

The maximum of the quadratic function is its vertex.

The x-coordinate is determined by x = - b/(2a)

Apply the x-value and find the value of f:

Answer:

18.25

Step-by-step explanation:

we are given a quadratic function

[tex] f(x) = - 16 {x}^{2} + 20x + 12[/tex]

where:

To find the maximum value of f(x) in other words, the maximum height, in feet, reached by the arrow.

Differentiate both sides:

[tex] f'(x) = \dfrac{d}{dx}( - 16 {x}^{2} + 20x + 12)[/tex]

with sum differentiation rule, we acquire:

[tex] \displaystyle f'(x) = \frac{d}{dx}( - 16 {x}^{2} )+ \frac{d}{dx} 20x + \frac{d}{dx} 12[/tex]

recall that,

utilizing the rules we acquire:

[tex] \displaystyle f'(x) = - 32 {x}^{} + 20 [/tex]

now equate f'(x) to 0:

[tex] \displaystyle - 32 {x}^{} + 20 = 0[/tex]

solving the equation for x yields:

[tex]x _{max}= \dfrac{5}{8} [/tex]

plug in the maximum value of x into the quadratic function:

[tex]f(x )_{max}= - 16 {( \frac{5}{8} )}^{2} + 20( \frac{5}{8} ) + 12[/tex]

simplify:

[tex]f(x )_{max} = 18.25[/tex]

hence,

The maximum height reached by the arrow is 18.25 feet

Check the picture below, so the green line is really the radius of the circle, and we know its center.

[tex]~~~~~~~~~~~~\textit{distance between 2 points}\\\\(\stackrel{x_1}{0}~,~\stackrel{y_1}{-3})\qquad(\stackrel{x_2}{\frac{15}{2}}~,~\stackrel{y_2}{1})\qquad \qquadd = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2}\\\\\\\stackrel{radius}{r}=\sqrt{[\frac{15}{2} - 0]^2 + [1 - (-3)]^2}\implies r=\sqrt{\left( \frac{15}{2} \right)^2 + (1+3)^2}\\\\\\r=\sqrt{\left( \frac{15}{2} \right)^2 +4^2}\implies r=\sqrt{\frac{225}{4} + 16}\implies r=\sqrt{\cfrac{289}{4}}\implies r=\cfrac{17}{2}\\\\[-0.35em]\rule{34em}{0.25pt}[/tex]

[tex]\textit{equation of a circle}\\\\ (x- h)^2+(y- k)^2= r^2 \qquad center~~(\stackrel{0}{ h},\stackrel{-3}{ k})\qquad \qquad radius=\stackrel{\frac{17}{2}}{ r} \\\\\\\ [x-0]^2~~ + ~~[y-(-3)]^2~~ = ~~\left( \cfrac{17}{2} \right)^2\implies x^2+(y+3)^2 = \cfrac{289}{4}[/tex]

QUESTION :> WHATS STATEMENT IS TRUE ?

ANSWER :> A. OR THE RATE OF FUNCTION G IS GREATER THAN THE RATE OF FUNCTION F BECAUSE

2 > (9 — 7).

HOPE IT HELPS

Answer:

x-73

Step-by-step explanation:

Let x=Jose's height.  If it says "less than," then that is subtraction.  Since Jose's height is not defined, there is no specific number that can be used to describe "73 less than twice Jose's height," so I use the variable x, and then subtract 73.

Answer:

96 in³

Step-by-step explanation:

Volume = 2(BHD) / 2

The 2s cancel out

Volume = 3(8)4

Volume = 96

Answer:

g= 81

Step-by-step explanation:

Replace X with 15

g = 6x -9

g = 6(15) - 9

g = 90 - 9

g = 81

Step-by-step explanation:

g=6x-9

putting the value of x

g=6×15-9

g=81

Answer:

1456

Step-by-step explanation:

56x2x13

56x26

1456

Answer:

[tex]1,\!848[/tex].

Step-by-step explanation:

There are two disjoint sets of ways to choose a lineup as required:

Assume that none of Alicia, Amanda, or Anna is to be selected. This lineup of [tex]6[/tex] would then need to be selected from a set of [tex]14 - 3 = 11[/tex] players (which excludes Alicia, Amanda, and Anna.)

The number of ways of selecting (without order) [tex]6[/tex] items out of a set of [tex]11[/tex] (distinct) items is equal to the combination:

[tex]\begin{aligned}\begin{pmatrix}11 \\ 6\end{pmatrix} &= \frac{11!}{(6!)\, (11 - 6)!} \\ &= \frac{11!}{6! \times 5!}\end{aligned}[/tex].

Assume that Alicia is selected, but neither Amanda nor Anna is selected. The other [tex]6 - 1 = 5[/tex] players in this lineup would then need to be selected from a set of [tex]14 - 1 - 2 = 11[/tex] players. (This set of [tex]11[/tex] excludes Alicia, Amanda, and Anna.)

The number of ways to select [tex]5[/tex] items from a set of [tex]11[/tex] items is:

[tex]\begin{aligned}\begin{pmatrix}11 \\ 5\end{pmatrix} &= \frac{11!}{(5!)\, (11 - 5)!} \\ &= \frac{11!}{5! \times 6!} \\ &= \frac{11!}{6! \times 5!}\end{aligned}[/tex].

Similarly, there would be another set of [tex](11!) / (6! \times 5!)[/tex] distinct ways to select the lineup if Amanda is selected, but neither Alicia nor Anna is.

Likewise, the number of ways to select the lineup with Anna but neither Amanda nor Alicia would also be [tex](11!) / (6! \times 5!)[/tex].

These sets of configurations for the lineup are pairwise disjoint from one another. Thus, the total number of ways to select this lineup would be:

[tex]\begin{aligned}& \begin{pmatrix}11 \\ 6 \end{pmatrix} + 3 \times \begin{pmatrix}11 \\ 5 \end{pmatrix} \\ =\; & \frac{11!}{6! \times 5!} + 3 \times \frac{11!}{6! \times 5!} \\ =\; & \frac{4 \times 11!}{6! \times 5!} \\ =\; & \frac{4 \times 11 \times 10 \times 9 \times 8 \times 7}{5 \times 4 \times 3 \times 2} \\ =\; & \frac{11 \times 10 \times 9 \times 8 \times 7}{5 \times 3 \times 2} \\ =\; & 1,\!848\end{aligned}[/tex].

Using it's concept, it is found that the probability that the next trial will result in a 2 and 4 is given by:

A. [tex]\frac{3}{10}[/tex].

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

In an experimental probability, the number of outcomes are taken from previous trials.

In this problem, the table states that of 20 trials, 6 resulted in either (2,4) or (4,2), hence the probability is given by:

p = 6/20 = 3/10.

Which means that option A is correct.

More can be learned about probabilities at https://brainly.com/question/14398287

Answer:

3 miles

Step-by-step explanation:

Range is the biggest number minus the smallest number.

First put the distance in order from least to greatest.

4 miles, 4 miles, 5 miles, 6 miles, 6 miles, 7 miles.

Now subtract the greatest and least amounts.

7 - 4 = 3

Answer:

  (iv)  b

  (v)  c

  (vi)  d

Step-by-step explanation:

The first two questions have to with understanding the meaning of the English words. (It's reading comprehension.)

__

(iv) "no larger than 10" means "less than or equal to 10"

  (b) x ≤ 10

__

(v) "at most 1600" means "less than or equal to 1600"

  (c)  c ≤ 1600

__

(vi) A value of x will be a solution to the inequality if substituting it into the inequality results in a true statement. Here, using x=0 effectively eliminates the x-term from the inequality.

  (a) 0 > 0 . . . false

  (b) 5 < 0 . . . false

  (c) 2 < 0 . . . false

  (d) -2 < 0 . . . true

Answer:

hello

18 % =  24

3 % = ( 3 x 24 ) / 18 = 4

Step-by-step explanation:

Answer:

A

First prove Triangle ABC is congruent to Triangle CDA, and then state AD and BC are corresponding sides of the triangles.

Hope this helps!

Please Mark Brainleast!!!

The sequence to prove that AD = BC is; First prove ABC is similar to CDA, and then state AD and BC are opposite sides of the parallelograms.

From the question, we see that the parallelogram ABCD has a diagonal AC. Thus; AB║ CD and AD║BC.

Now, the parallelogram is divided into two triangles ΔABC and ΔADC by its diagonal AC.

Thus;

∠ACB = ∠DAC  and ∠CAB = ∠ACD  because they are alternate interior angles.

Also, AC = AC  (Reflexive property)

Thus; by ASA congruence postulate, we can say that; ΔABC ≅  ΔADC

Also, by corresponding sides of the congruent triangles are congruent we can say that AD = BC.

Read more baout Quadrilateral proofs at; https://brainly.com/question/2698923

Answer:

The number is 2

Step-by-step explanation:

The equation is: 1/4 (x + 10) = 2x - 1

1/4x + 2.5 = 2x - 1

Multiply everything by 4 to get rid of the fraction

x + 10 = 8x - 4

Subtract x from both sides

10 = 7x - 4

Add 4 to both sides

14 = 7x

Divide both sides by 7

x = 2

The time I would need to leave the hotel if the flight lands at 3:23 p.m is 7 : 09 am

The first step is to add the total hours of the flight to the time of the tax ride and the time you need to get to the airport.

7h + 12 min + 45 + 17 = 8 hours 14 minutes

Now subtact  8 hours 14 minutes  form 3: 23

(12 + 3:23) -  8 hours 14 minutes =7 : 09 am

To learn more about how to calculate time, please check: https://brainly.com/question/26290873

Answer:

3/5

Step-by-step explanation:

6 white cars out of 10 cars would be written as 6/10.

You then would simplify this fraction to 3/5.

So your answer is 6/10 or 3/5.

Answer:

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

It would help if you can actually show the points

Answer:

The cylinder can hold 508.68 in³

Explanation:

The volume of a cylinder can be calculated using the following rule:

Volume of cylinder = πr²h cubic units

where r is the radius of the cylinder and h is its height

Now, we are given that:

height of cylinder = 18 in

diameter of cylinder = 6 in which means that the radius of the cylinder is 3 in

π is 3.14

Substitute with the givens in the above equation to get the volume of the cylinder as follows:

Volume of cylinder = πr²h

Volume of cylinder = 3.14 * (3)² * 18

Volume of cylinder = 508.68 in³

Answer:

180-52=128

Do mark BRAINLIEST

Answer:

The slope of both EF and GH are 2/3

The slope of both FG and EH are -3/2

You can see that these slopes are perpendicular, forming a rectangle

Step-by-step explanation:

To find slope use the slope formula: y1 - y2 / x1 - x2

so first:

8 - 2 / 3 - (-6) = 2/3

(-4) - 2 / (-2) - 7 = 2/3

Then:

8 - 2 / 3 - 7 = -3/2

2 - (-4) / (-6) - (-2) = -3/2

Answer:

893

Step-by-step explanation:

893 is too far away to round to 880. It would actually round to 890.

The last digits of 883 and 882 are small enough to round to 880.

The last digit of 878 is large enough to round to 880.

Answer:

893

Step-by-step explanation:

We round down if the digit is less than 5

We round up if the digit is 5 or more

Rounding to the nearest 10:

893 → 890 (round down as 3 is less than 5)

883 → 880 (round down as 3 is less than 5)

882 → 880 (round down as 2 is less than 5)

878 → 880 (round up as 8 is more than 5)

So the only number that does NOT round to 880 is 893.

Answer:390

Step-by-step explanation:

500*.22=110

500-110=390

390

Answer:

390

Step-by-step explanation:

22% of 500 is 110 so that would make the answer 390 i think

The question asked by Troy is a statistical question because there would be variability in the answers he get fro the 12 maths teachers.

A statisical question is a question that can only be answered through the collection of data. Thhere would be variablility in the results gotten from the data.

A non- statistical question is a question that has only one answer. For example, how old are you? is a non-statistical question.

To learn more about a statisitcal question, please check: https://brainly.com/question/21508412

Answer:

down syndrome

Step-by-step explanation:

To find area of square one :-

Given :

To find :

We know :

Area of square = side²

Therefore:-

→Area of square = 9²

→Area of square = 9 × 9

→Area of square = 81 (unit)²

To find area of square two :-

Given :

To find :

We know :

Area of square = side²

Therefore:-

→Area of square = 11²

→Area of square = 11 × 11

→Area of square = 121 (unit)²

Now it's clearly visible that the whole figure is also. a square .

Therefore AE = CP

Which means area of square three = 81 (unit)²

Now area of shaded figure :-

Answer:

21

Step-by-step explanation:

There is an equal chance of 21 per each choice. So there is an equal amount of chance to land on both yellow or pink.

The value of x from the figure is 17.82 units

1) From the first figure.

Opposite side = x

Adjacent = 12

Using the SOH CAH TOA identity

tan53 = opp/adj

tan53 = x/12

x = 12tan53

x = 15.92 units

2) Using the SOH CAH TOA identity

cos27 = adj/hyp

cos27 = x/20

x = 20cos27

x =  17.82units

Hence the value of x from the figure is 17.82 units

Learn more on SOH CAH TOA here: https://brainly.com/question/20734777