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Answer:

The trigonometric ratios are presented below:

[tex]\sin \theta = \frac{AC}{\sqrt{AC^{2} + BC^{2}}}[/tex]

[tex]\cos \theta = \frac{BC}{\sqrt{AC^{2} + BC^{2}}}[/tex]

[tex]\cot \theta = \frac{BC}{AC}[/tex]

[tex]\sec \theta = \frac{\sqrt{AC^{2}+BC^{2}}}{BC}[/tex]

[tex]\csc \theta = \frac{\sqrt{AC^{2}+BC^{2}}}{AC}[/tex]

Step-by-step explanation:

From Trigonometry we know the following definitions for each trigonometric ratio:

Sine

[tex]\sin \theta = \frac{y}{h}[/tex] (1)

Cosine

[tex]\cos \theta = \frac{x}{h}[/tex] (2)

Tangent

[tex]\tan \theta = \frac{\sin \theta}{\cos \theta} = \frac{y}{x}[/tex] (3)

Cotangent

[tex]\cot \theta = \frac{\cos \theta}{\sin \theta} = \frac{x}{y}[/tex] (4)

Secant

[tex]\sec \theta = \frac{1}{\cos \theta} = \frac{h}{x}[/tex] (5)

Cosecant

[tex]\csc \theta = \frac{1}{\sin \theta} = \frac{h}{y}[/tex] (6)

Where:

[tex]x[/tex] - Adjacent leg.

[tex]y[/tex] - Opposite leg.

[tex]h[/tex] - Hypotenuse.

The length of the hypotenuse is determined by the Pythagorean Theorem:

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

If [tex]y = AC[/tex] and [tex]x = BC[/tex], then the trigonometric ratios are presented below:

[tex]\sin \theta = \frac{AC}{\sqrt{AC^{2} + BC^{2}}}[/tex]

[tex]\cos \theta = \frac{BC}{\sqrt{AC^{2} + BC^{2}}}[/tex]

[tex]\cot \theta = \frac{BC}{AC}[/tex]

[tex]\sec \theta = \frac{\sqrt{AC^{2}+BC^{2}}}{BC}[/tex]

[tex]\csc \theta = \frac{\sqrt{AC^{2}+BC^{2}}}{AC}[/tex]

Answer:

Fossil > Arrow Head > Pottery > Shell > Fishbone > Fish Hook

Step-by-step explanation:

Arrowhead = ___20___ feet

Fishbone = __-10___ feet

Fish Hook = ___-40__ feet

Fossil = __30___ feet

Pottery = ___10___ feet

Shell = ____0___ feet

If something is above sea level, it would have a positive elevation, and if below sea level, a negative elevation.  And at sea level, you have 0 elevation.

After this, just put them in order of decreasing elevation.  So, the highest elevation is  30ft with the fossil, then 20 with the arrow head, pottery at 10, shell at 0, fishbone at -10, fish hook at -40.

Answer:

3 is the right one

Step-by-step explanation:

Simple math you know

Answer: 61/100 would be the answer

Answer:

A - B = 11x² -9x + 14

A - B = 11x² -9x + 14

Answer: 72

Step-by-step explanation: LxWXH

3x3x8=72

9514 1404 393

Answer:

  table C

Step-by-step explanation:

The rates of change can be computed using the slope formula.

  m = (y2 -y1)/(x2 -x1)

The points used and the resulting "rate of change" are shown in the attachment.

Table C shows a rate of change (1/3) that is less than that of the graph (1/2).

_____

I like to use a spreadsheet for repetitive calculations, especially ones involving negative numbers. This helps prevent errors (and tedium). The formula is entered only once.

The table of values which has a smaller rate of change than the function in the graph is C.

This is defined as the ratio of the vertical change to the horizontal change between any two distinct points on a line.

Slope formula.

m = (y2 -y1)/(x2 -x1)

For table C = 4 -3 / -3 - (-6)

= 1/3

Table C shows a rate of change of 1/3 which is less than that of the graph at 1/2 .

Read more about Slope here https://brainly.com/question/25722412

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Answer:

  63.7% or 33.35 miles

Step-by-step explanation:

The hint suggests that we find the points where the drive begins and ends picking up the transmitter. We suspect both of those points will have irrational coordinates, so finding the distance between them will involve dealing with squares and roots of irrational numbers. We want to see if there's an easier way.

The distance from the transmitter to the path being driven can be found using the "distance to a line" formula. First, we need the equation of the line in general form. In intercept form, it is ...

  y/38 +x/36 = 1

  19x +18y -684 = 0 . . . . . . multiply by LCM(36, 38) and subtract that amount

Then the distance from the origin to the line is ...

  d = |19·0 +18·0 -684|/√(19² +18²) = 685/√685 ≈ 26.1243

The distance (x) along the line from the point where the transmitter is first picked up until the point of closest approach can be found from the Pythagorean theorem:

  x² + (26.1243)² = 31²

  x² = 31² -(684/√685)² = 190429/685

  x ≈  16.6733

The driving distance for which the transmitter is picked up is twice this, so is ...

  2x = 2(16.6733) ≈ 33.3466 . . . miles

The total drive length is also given by the Pythagorean theorem:

  drive length = √(36² +38²) = √2740 ≈ 52.3450 . . . miles

Then the fraction of the drive during which the signal is picked up is ...

  fraction = (33.3466 mi)/(52.3450 mi) ≈ 0.6371 ≈ 63.7%

__

The signal is picked up for 33.35 miles, about 63.7% of the drive.

______

The intercept-form equation for a line is ...

  x/(x-intercept) +y/(y-intercept) = 1

The distance from (x, y) to line ax+by+c=0 is given by ...

  d = |ax+by+c|/√(a²+b²)

The Pythagorean theorem relates legs a, b and hypotenuse c of a right triangle this way:

  c² = a² +b²

Answer:1.50

Step-by-step explanation:None

Answer: the answer is d

Step-by-step explanation:

Answer:

C

Step-by-step explanation:

C= 2* pi*r = 2* pi* 5 ≈ 31.4 cm

Answer:

b and 288

Step-by-step explanation:

ywwwwwwwwwwww

Answer: 9 cherry ice pops

Step-by-step explanation:

if you bought 3 boxes and there is four orange one in each pack the that is

12 and 36 divided by 4 is 9 so there is 9 cherry ice pops

Answer:

37.7

Step-by-step explanation:

Circumference = [tex]2\pi r[/tex]

Circumference = [tex](2)(\pi )(6)[/tex]

Circumference = 37.69911184 / 37.7

Therefore, circumference of the circle with the radius 6 cm is 37.7.

Answer:

37.7

Step-by-step explanation:

formula for circumference of a circle=2πr

2×π×6=37.7cm

Answer:

3

Step-by-step explanation:

because 3x3= 9 and 4x3=12 and 5x3=15

Answer:

268 m²

Step-by-step explanation:

8x26=208

3x10x2=60

208+60=268

Answer:

Step-by-step explanation:

Right side =

sin A / cos A + sinB/ cosB         (sinAcosB + sinB cos A ) *   cosA cosB

-------------------------------------    =          cosA cosB                (sinAcosB - snBcosA )        sinA/cosA -  sinB/cos B

= Left side.

The trigonometry identity [tex]\frac{sin(A+B)}{sin(A-B)}[/tex] is equals to [tex]\frac{tan(A)+tan(B)}{tan(A)-tan(B)}[/tex].

Trigonometric Identities are the equalities that involve trigonometry functions and holds true for all the values of variables given in the equation.

According to the given question.

We have a trigonometric identity.

[tex]\frac{sin(A+B)}{sin(A-B)} =\frac{tan(A)+tan(B)}{tan(A)-tan(B)}[/tex]

To prove the above  trigonometric identity we will show L.H.S = R.H.S

[tex]L.H.S=\frac{sin(A+B)}{sin(A-B)}[/tex]

⇒ [tex]L.H.S = \frac{cosBsinA-sinBcosA}{sinAcosB-cosAsinB}[/tex]

⇒ [tex]L.H.S = \frac{\frac{sinAcosB}{cosAcosB} + \frac{sinBsinA}{cosBcosA} }{\frac{sinAcosB}{cosAcosB}-\frac{cosAsinB}{cosAcosB} }[/tex]     (dividing the numerator and denominator by [tex]cosAcosB[/tex] )

⇒ [tex]L.H.S = \frac{\frac{sinA}{cosA} +\frac{sinB}{cosB} }{\frac{sinA}{cosA}-\frac{sinB}{cosB} }[/tex]

⇒ [tex]L.H.S = \frac{tanA+tanB}{tanA- tanB}= R.H.S[/tex]

Hence, L.H.S = R.H.S

Find out more information about trigonometric identities here:

https://brainly.com/question/12537661

#SPJ3

Answer:

0.5

hope this helps

have  a good day :)

Step-by-step explanation:

Answer:

missing angle=36 degree

Answer:

220 miles

Step-by-step explanation:

.18m + 11d = 61.60

d = 2

.18m + 22 = 61.60

Subtract 22 from both sides

.18m = 39.60

Divide both sides by .18

m = 220

Step-by-step explanation:

By question , it's given that the X intercept is (5,0) and the y intercept is (0,8) . And we need to find the y-intercept of the graph of f(x) + 3 . For that , firstly let's find out the equation of the line.

[tex]\sf\implies y- y_1 = \bigg(\dfrac{y_2-y_1}{x_2-x_1}\bigg) ( x - x_1) \\\\\sf\implies y - 0 = \bigg(\dfrac{0-8}{5-0}\bigg)( x - 5 ) \\\\\sf\implies y = \dfrac{-8}{5}( x - 5 ) \\\\\sf\implies 5y = -8x +40 \\\\\sf\implies 8x + 5y - 40 = 0 [/tex]

Let us say that this is f(x) :-

[tex]\\\\\sf\implies f(x) = 8x + 5y - 40 \\\\\sf\implies \boxed{\sf\red{ f(x)+3 = 8x +5y -37 }}[/tex]

Plot its graph :-

We can either convert it into intercept form but plotting a graph can also be done to find y intercept .

[tex]\implies \boxed{\pink{\sf y - intercept = 7.4}}[/tex]

Refer to attachment for graph .

Hence the y Intercept is 7.4 .

Answer:

16

Step-by-step explanation:

ezz

Answer:

36

Step-by-step explanation:

If 1/3 of x is 12, we can make an equation.

x/3=12

So now we isolate x.

x=36

Answer:

36

Step-by-step explanation:

of means multiply and is means equals

1/3 * n = 12

Multiply each side by 3

3 * 1/3 n = 12 *3

n = 36

Answer:

then 2 are human

Step-by-step explanation:

because 4 are robots

Answer:

The rest are normal students.

6-4= 2 so that's how many normal students there are.

Please add a little bit more detail to the question please :)

Answer:

33 plants

Step-by-step explanation:

6 x 550 = 3300

3300/100 = 33

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Answer:

  1340

Step-by-step explanation:

The perimeter of a rectangle of length L and width W is ...

  P = 2(L+W)

The perimeter of the rectangle outline of the figure is ...

  P = 2(315 +300) = 2·615 = 1230

That outline is the sum of all of the line segments making up the figure except for two lengths of 55 units each. Adding those, we find the perimeter of the figure to be ...

  P = 1230 +2(55) = 1230 +110 = 1340 . . . units

_____

Additional comment

It can be convenient to consider the total of horizontal segments and the total of vertical segments. We have shown in the attachment that, except for the 55-unit "indent", the horizontal and vertical lengths are equivalent to those of an ordinary rectangle. Thinking about the problem in this way makes it unnecessary to do the tedious arithmetic necessary to find each segment length. (Here, there is not enough information to do that anyway.)

Answer:

a = {-5/6 , 1}

Step-by-step explanation:

6a² - a -5 = 0

Factor

(6a + 5)(a - 1) = 0

Root 1

6a + 5 = 0

6a = -5

a = -5/6

Root 2

a - 1 = 0

a = 1

Solution set

a = {-5/6 , 1)