[tex]\lim _{x\to \infty }\left(\frac{tanx-sinx}{x^2}\right)[/tex]

Answer: C

Step-by-step explanation: The y-intercept is 1/5 since the point on the y-axis is (0, 1/5). The slope is 2/3 because the other coordinate is up 2 and right 3 from (0, 1/5) *remember rise over run*. The shading means that the answer (y) must be less than or equal to 2/3x + 1/5, hence it being underneath the line.

Separating variables, we have

[tex]\dfrac{dy}{dx} = \dfrac xy \implies y\,dy = x\,dx[/tex]

Integrate both sides.

[tex]\displaystyle \int y\,dy = \int x\,dx[/tex]

[tex]\dfrac12 y^2 = \dfrac12 x^2 + C[/tex]

Given that [tex]y(0)=-1[/tex], we find

[tex]\dfrac12 (-1)^2 = \dfrac12 0^2 + C \implies C = \dfrac12[/tex]

Then the particular solution is

[tex]\dfrac12 y^2 = \dfrac12 x^2 + \dfrac12[/tex]

[tex]y^2 = x^2 + 1[/tex]

[tex]y = \pm\sqrt{x^2 + 1}[/tex]

and because [tex]y(0)=-1[/tex], we take the negative solution to accommodate this initial value.

[tex]\boxed{y(x) = -\sqrt{x^2+1}}[/tex]

\cos (\tan \left( -1\right) (\frac{x}{2}))

c

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Simplify

1

Combine multiplied terms into a single fraction

\cos (\tan \left( -1\right) \cdot \frac{x}{2})

c

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s

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t

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n

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⋅

2

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\cos (\frac{\tan \left( -1\right) x}{2})

c

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Solution

\cos \left( \frac{\tan \left( -1\right) x}{2}\right)

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Answer:

Step-by-step explanation:

[tex]cos(tan^{-1}(\frac{x}{2} ))\\put~tan^{-1}(\frac{x}{2} )=t\\\frac{x}{2} =tan~t\\sec^2t-tan^2t=1\\sec^2t=1+tan^2t=1+(\frac{x}{2} )^2=\frac{x^2+4}{4} \\sec~t=\pm\frac{\sqrt{x^2+4}}{2} \\cos ~t=\pm\frac{2}{\sqrt{x^2+4}} \\hence~cos(tan^{-1}(\frac{x}{2} ))=cos~t=\pm\frac{2}{\sqrt{x^2+4}}[/tex]

Answer:

-24 would be the temperature

Answer:

-24 BECAUSE I did all the math.

By using trigonometric relations, we will see that the angle that the ladder makes with the ground is 64.2°, so we conclude that the ladder is safe.

Notice that the ladder makes a right triangle with the wall.

Such that the hypotenuse (the ladder itself) measures 15 ft, and one of the catheti (distance between the ground and top of the ladder) measures 13.5ft

If we considerate the angle that the ladder makes with the ground, the known cathetus is the opposite cathetus.

Then we can use the relation:

sin(x) = (opposite cathetus)/(hypotenuse)

Then:

sin(x) = (13.5ft)/(15ft)

If we use the inverse sine function on both sides, we get:

Asin(sin(x)) = Asin( 13.5ft/15ft)

x = Asin(13.5/15) = 64.2°

So the angle is less than 75°, which means that in fact, the ladder is safe.

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Based on the calculations, the coordinates of the point of congruency of the altitudes (H) are (-160/11, 40/11).

A triangle can be defined as a two-dimensional geometric shape that comprises three (3) sides, three (3) vertices and three (3) angles only.

A slope is also referred to as gradient and it's typically used to describe both the ratio, direction and steepness of the function of a straight line.

Mathematically, the slope of a straight line can be calculated by using this formula;

[tex]Slope, m = \frac{Change\;in\;y\;axis}{Change\;in\;x\;axis}\\\\Slope, m = \frac{y_2\;-\;y_1}{x_2\;-\;x_1}[/tex]

Assuming the following parameters for triangle ABC:

For the slope of BC, we have:

Slope of BC = (2 - 8)/(4 - 0)

Slope of BC = -6/4

Slope of BC = -3/2.

For the slope of CA, we have:

Slope of CA = (2 - 0)/(4 - (-2))

Slope of CA = 2/6

Slope of CA = 1/3.

For the slope of AB, we have:

Slope of AB = (8 - 0)/(0 - (-2))

Slope of AB = 8/2

Slope of AB = 4.

Note: The point of concurrency of three altitudes in a triangle is referred to as orthocenter.

Since side AB is perpendicular to side QC, we have:

m₁ × m₂ = -1

Slope of AB × Slope of QC = -1

Slope of QC = (k - 4)/(h - 2)

4 × (k - 4)/(h - 2) = -1

(4k - 16)/(h - 2) = -1

4k - 16 = -h + 2

4k + h = 18    .......equation 1.

Similarly, we have the following:

Slope of BC × Slope of AH = -1

-3/2 × (k)/(h + 2) = -1

3k/(2h + 4) = 1

3k = 2h + 4

3k - 2h = 4     .......equation 2.

Solving eqn. 1 and eqn. 2 simultaneously, we have:

8k + 2h = 36

3k - 2h = 4

11k = 40

k = 40/11.

For the value of h, we have:

h = -4k

h = -4 × (40/11)

h = -160/11

Therefore, the coordinates of the point of congruency of the altitudes (H) are (-160/11, 40/11).

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Based on the given parameters, the length of c is 8.0 units

The given parameters are

Angle c = 76 degrees

Side a = 20

Side b = 13

The length of c is then calculated using the following law of sines

c^2 = a^2 + b^2 - 2absin(C)

Substitute the known values in the above equation

So, we have

c^2 = 20^2 + 13^2 - 2 * 20 * 13 * sin(76)

Express 20^2 as 400

c^2 = 400 + 13^2 - 2 * 20 * 13 * sin(76)

Express 13^2 as 169

c^2 = 400 + 169 - 2 * 20 * 13 * sin(76)

Evaluate the product and sin(76)

c^2 = 400 + 169 - 520 * 0.9703

Evaluate the product

c^2 = 400 + 169 - 504.55

Evaluate the exponents

c^2 = 400 + 169 - 504.55

So, we have

c^2 = 64.45

Evaluate the square root

c = 8.0

Hence, the length of c is 8.0 units

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Answer:

268.08

Step-by-step explanation:

Answer:

803.84 m³

Step-by-step explanation:

The formula to find the volume of a sphere is:

V = 4 π r³

Given that,

radius ⇒ 4m

Let us find the volume now.

V = 4 π r³

V = 4 π × ( 4 )³

V = 4 π × 64

V = 4 π × 64

V = 12.56 × 64

V = 803.84 m³

The probability of being dealt four of a kind or a straight is 0.00416 or 0.416%.

It is defined as the ratio of the number of favourable outcomes to the total number of outcomes, in other words, the probability is the number that shows the happening of the event.

It is given that:

In 5-card poker, find the probability of being dealt the following hand. Refer to the table.

From the table:

Total number of outcomes = 2598960

Total number of favorable outcomes = 624 + 10200 = 10824

The probability of being dealt four of a kind or a straight

P = 10824/2598960

P = 0.00416

In percentage:

P = 0.416%

Thus, the probability of being dealt four of a kind or a straight is 0.00416 or 0.416%.

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Using the Factor Theorem, the equation of h(x) is given as follows:

h(x) = -2(x³ - 2x² - 5x + 6)

The Factor Theorem states that a polynomial function with roots [tex]x_1, x_2, \codts, x_n[/tex] is given by:

[tex]f(x) = a(x - x_1)(x - x_2) \cdots (x - x_n)[/tex]

In which a is the leading coefficient.

Looking at the table, considering the values of x when h(x) = 0, the roots of h(x) are given as follows:

[tex]x_1 = -2, x_2 = 1, x_3 = 3[/tex]

Then the rule is:

h(x) = a(x + 2)(x - 1)(x - 3)

h(x) = a(x² + x - 2)(x - 3)

h(x) = a(x³ - 2x² - 5x + 6)

The h-intercept is of -12, as when x = 0, h = -12, hence this is used to find a as follows:

6a = -12

a = -12/6

a = -2.

Hence the function is given by:

h(x) = -2(x³ - 2x² - 5x + 6)

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Check the picture below, so the ball's path is pretty much like so, and it reaches its hightest at its vertex, so

[tex]~~~~~~\textit{initial velocity in feet} \\\\ h(t) = -16t^2+v_ot+h_o \quad \begin{cases} v_o=\textit{initial velocity}&80\\ \qquad \textit{of the object}\\ h_o=\textit{initial height}&0\\ \qquad \textit{of the object}\\ h=\textit{object's height}&h\\ \qquad \textit{at "t" seconds} \end{cases} \\\\\\ f(t)=80t-16t^2\implies f(t)=-16t^2+80t+0 \\\\[-0.35em] ~\dotfill[/tex]

[tex]\textit{vertex of a vertical parabola, using coefficients} \\\\ y=\stackrel{\stackrel{a}{\downarrow }}{-16}x^2\stackrel{\stackrel{b}{\downarrow }}{+80}x\stackrel{\stackrel{c}{\downarrow }}{+0} \qquad \qquad \left(-\cfrac{ b}{2 a}~~~~ ,~~~~ c-\cfrac{ b^2}{4 a}\right)[/tex]

[tex]\left(-\cfrac{ 80}{2(-16)}~~~~ ,~~~~ 0-\cfrac{ (80)^2}{4(-16)}\right) \implies \left( - \cfrac{ 80 }{ -32 }~~,~~0 - \cfrac{ 6400 }{ -64 } \right) \\\\\\ \left( \cfrac{5}{2}~~,~~100 \right)\implies \underset{~\hfill feet ~~ }{\stackrel{seconds\qquad }{\left( 2\frac{1}{2}~~,~~100 \right)}}[/tex]

Answer:

40

Step-by-step explanation:

19*2 = 38 + 2 = 40

Answer:

Step-by-step explanation:

we have to get k by itself on one side of the equal sign. To do that we have to get rid of 3. To get rid of 3 we have to do the opposite. The opposite of +3 is -3 so we -3 on both sides. 19 - 3 = 16. So k = 16

k+3=19

 -3  -3

   k=16

Hi there,

please see below for solution steps :

‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗

Evaluate by substituting :

[tex]\begin{gathered} \boldsymbol{f(x)=-2x^2-3x+5; \ evaluate \ when \ x=-3} \\\boldsymbol{Write \ -3 \ everywhere \ you \ see \ and \ x :}\\\boldsymbol{f(-3)=-2(-3)^2-3(-3)+5}\\\boldsymbol{Evaluate \ using \ Order \ of \ Operations :}\\\boldsymbol{f(-3)=-2(9)+9+5= > -18+9+5= > -18+14= > -4}\end{gathered}[/tex]

Therefore, the answer is [tex]\LARGE\textbf{-4}[/tex].

I hope the answer - and steps - made sense to you !!

Happy Learning !!

‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗

Using it's concept, your percentage for the month was of 94.12%.

The percentage of an amount a over a total amount b is given by a multiplied by 100% and divided by b, that is:

P = a/b x 100%

In this problem, your goal was of 85, with a grade of 80, hence the percentage is:

P = 80/85 x 100% = 94.12%.

Hence, your percentage for the month was of 94.12%.

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The ski club has 44 members in all

What is population?

Population refers to the total number of items or individuals that form a group.

In this case, the population means the total  number of all members in the  Mogul Runners ski club.

What is sample?

Sample means a fraction of the total population, in other words, the 25% of the members, whose number is 11, that signed up to go for the planned trip.

We can convert 25% to 100% by equation 25% to 11 members that signed up to go for the planned trip.

25% of club members=11 members

divide both sides by 25%

25%/25% of club members=11/25% members

club members=44 members

The ski club has 44 members altogether as computed above.

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Answer:

X = 17√3

Y = 34

Step-by-step explanation:

TO calculate the values of X and y we use SOHCAHTOA.

tan 30 = opposite/adjacent

tan30 = 17/X

Cross multiply

tan30 ×X = 17

Divide bothsides by tan30

X = 17/1/√3

X=17√3

X = 29 ( approximately)

[tex]sin30 = \frac{Opposite}{Hypothenus} \\ \\ sin30 = \frac{17}{y} [/tex]

[tex]sin30 \times y = 17[/tex]

[tex] \frac{sin30 \times y}{sin30} = \frac{17}{sin30} \\ \\ y = \frac{17}{0.5} = 34 \\ y = 34[/tex]

Answer:

C...........................

Answer:

c

Step-by-step explanation:

Step-by-step explanation:

The value of b will be 43° as it is vertically opposite angle.. !!

Step-by-step explanation:

Use this sort of layout, but where x will be an odd number, do not shade it. there should be a pattern of shaded segments followed by unshaded segments repeating

Answer:

inductive reasoning

Step-by-step explanation:

Answer:

B. 1

Step-by-step explanation:

-1*2 = -2

-2+1 = -1

-1+1 = 0

0+1 = 1

Answer:

7,647.4?

Step-by-step explanation:

The standard deviation for the number of people with the genetic mutation is 3.77

The given parameters are:

Sample size, n = 300

Proportion that has the particular genetic mutation, p = 5%

The standard deviation for the number of people with the genetic mutation is calculated as:

Standard deviation = √np(1 - p)

Substitute the known values in the above equation

Standard deviation = √300 * 5% * (1 - 5%)

Evaluate the product

Standard deviation = √14.25

Evaluate the exponent

Standard deviation = 3.77

Hence, the standard deviation for the number of people with the genetic mutation is 3.77

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[tex](x^2 - y^2) \, dx + 2xy \, dy = 0[/tex]

Multiply both sides by [tex]\frac1{x^2}[/tex].

[tex]\left(1 - \dfrac{y^2}{x^2}\right) \, dx + \dfrac{2y}x \, dy = 0[/tex]

Substitute [tex]y=vx[/tex], so [tex]v=\frac yx[/tex] and [tex]dy=x\,dv+v\,dx[/tex].

[tex](1-v^2) \, dx + 2v (x\,dv + v\,dx) = 0[/tex]

[tex](1 + v^2) \, dx + 2xv \, dv = 0[/tex]

Separate the variables.

[tex]2xv\,dv = -(1 + v^2) \, dx[/tex]

[tex]\dfrac{v}{1+v^2}\,dv = -\dfrac{dx}{2x}[/tex]

Integrate both sides

[tex]\displaystyle \int \frac{v}{1+v^2}\,dv = -\frac12 \int \frac{dx}x[/tex]

On the left side, substitute [tex]w=1+v^2[/tex] and [tex]dw=2v\,dv[/tex].

[tex]\displaystyle \frac12 \int \frac{dw}w = -\frac12 \int\frac{dx}x[/tex]

[tex]\displaystyle \ln|w| = -\ln|x| + C[/tex]

Solve for [tex]w[/tex], then [tex]v[/tex], then [tex]y[/tex].

[tex]e^{\ln|w|} = e^{-\ln|x| + C}[/tex]

[tex]w = e^C e^{\ln|x^{-1}|}[/tex]

[tex]w = Cx^{-1}[/tex]

[tex]1 + v^2 = Cx^{-1}[/tex]

[tex]1 + \dfrac{y^2}{x^2} = Cx^{-1}[/tex]

[tex]\implies \boxed{x^2 + y^2 = Cx}[/tex]

Your mistake is in the first image, between third and second lines from the bottom. (It may not be the only one, it's the first one that matters.)

You incorrectly combine the fractions on the left side.

[tex]\dfrac1{-2v} -\dfrac v{-2} = \dfrac1{-2v} - \dfrac{v^2}{-2v} = \dfrac{1-v^2}{-2v} = \dfrac{v^2-1}{2v}[/tex]

Information : The given hyperbola is a horizontal hylerbola with its centre (3 , -5) and one of its focus at (9 , -5) and vertex at (7 , -5) and as we can see that the focus and vertex have same y - coordinates, it must have its Transverse axis on line y = - 5.

Now,

it's vertex is given, I.e (7 , -5)

so, length of semi transverse axis will be equal to distance of vertex from centre, i.e

Now, it's focus can be represented as ;

[tex]\qquad \sf  \dashrightarrow \: (3 + ae, - 5 )[/tex]

so,

and we know, a = 4

[tex]\qquad \sf  \dashrightarrow \: 4e + 3 = 9[/tex]

[tex]\qquad \sf  \dashrightarrow \: 4e = 6[/tex]

[tex]\qquad \sf  \dashrightarrow \: e = \cfrac{3}{2} [/tex]

Now, let's find the measure of semi - conjugate axis (b)

[tex]\qquad \sf  \dashrightarrow \: {b}^{2} = {a}^{2} ( {e}^{2} - 1)[/tex]

[tex]\qquad \sf  \dashrightarrow \: {b}^{2} = 16( \frac{9}{4} - 1)[/tex]

[tex]\qquad \sf  \dashrightarrow \: {b}^{2} = 16( \frac{9 - 4}{4} )[/tex]

[tex]\qquad \sf  \dashrightarrow \: {b}^{2} = 16( \frac{5}{4} )[/tex]

[tex]\qquad \sf  \dashrightarrow \: {b}^{2} = 20[/tex]

[tex]\qquad \sf  \dashrightarrow \: b = \sqrt{20} [/tex]

So, it's time to write the equation of hyperbola, as we already have the values of a and b ~

[tex]\qquad \sf  \dashrightarrow \: \cfrac{ {(x - h)}^{2} }{ {a}^{2} } - \cfrac{( {y - k)}^{2} }{ {b}^{2} } = 1[/tex]

[ plug in the values, and h = x - coordinate of centre, and k = y - coordinate of centre ]

[tex]\qquad \sf  \dashrightarrow \: \cfrac{ ({x-3)}^{2} }{ {16}^{} } - \dfrac{ {(y+5)}^{2} }{ { {20} }^{} } = 1[/tex]

Hello and Good Morning/Afternoon:

Let's solve this problem step-by-step:

Let's find the format of the standard form of hyperbole:

 [tex]\hookrightarrow \frac{(x-h)^2}{a^2}-\frac{(y-k)^2}{b^2} =1[/tex]

Let's find the value of a, b:

             [tex]a = \sqrt{(7-3)^2+(-5--5)^2} =\sqrt{16} =4[/tex]

           ⇒value of c: distance between focus (9, -5) and center (3, -5)

                  [tex]c = \sqrt{(3-9)^2+(-5--5)^2}=\sqrt{36} =6[/tex]

            ⇒ therefore:

                  [tex]b = \sqrt{c^2-a^2} =\sqrt{6^2-4^2}=\sqrt{20}[/tex]

Let's plug everything into our standard form of the equation:

   [tex]\frac{(x-3)^2}{4^2} -\frac{(y--5)^2}{(\sqrt{20})^2 } =1\\\frac{(x-3)^2}{16} -\frac{(y+5)^2}{20 } =1[/tex] <== Answer

Hope that helps!

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Step-by-step explanation:

sin alpha^2 + 2sin alpha* cos alpha + cos alpha^2

sin alpha^2 + cos alpha^2 +2sin alpha* cos alpha

1+ 2sin alpha* cos alpha

1+sin2 alpha

Answer:

Dependent variable: time(months) or [tex]t[/tex]

Independent variable: 6

Step-by-step explanation:

[tex]h=24+6t[/tex]

(h=height)

Answer:

7.....gggggggggggggggh