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3 years ago

What do you know about the side lengths and trigonometric ratios in special right triangles

Mathematics

1 answer:

TEA [102]3 years ago

6 0

Explanation:

This looks like an essay question with no right answer.

There are two "special" right triangles:

isosceles 45°-45°-90° triangle with sides in the ratios 1 : 1 : √2

30°-60°-90° triangle with sides in the ratios 1 : √3 : 2

These side lengths give rise to the trigonometric ratios shown below for angles with 30°, 45°, or 60° as reference angles.

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PLEASE HURRY<br><br> 9x^2 + 64 = 0<br><br> I NEED THE WORK SHOWN IN ORDER TO GET CREDIT

seropon [69]

Answer:

x = ± $\frac{8}{3}$ i

Step-by-step explanation:

subtract 64 from both sides

9x² = - 64 ( divide both sides by 9 )

x² = - $\frac{64}{9}$ ( take the square root of both sides )

x = ± $\sqrt{-64/9}$ = ± $\frac{8}{3}$ i

6 0

3 years ago

Read 2 more answers

Using the binomial theorem , obtain the expansion of :

andrezito [222]

Answer:

see explanation

Step-by-step explanation:

Expand both factors and collect like term

Using Pascal' triangle with n = 6 to obtain the coefficients

1 6 15 20 15 6 1

Decreasing powers of 1 from $1^{6}$ to $1^{0}$

Increasing powers of 3x from $(3x)^{0}$ to $(3x)^{6}$

$1+3x)^{6}$

= 1. $1^{6}$ $(3x)^{0}$ + 6. $1^{5}$ $(3x)^{1}$ + 15. $1^{4}$ $(3x)^{2}$ + 20. $1^{3}$ $(3x)^{3}$ + 15.1² $(3x)^{4}$ + 6. $1^{1}$ $(3x)^{5}$ + 1. $1^{0}$ $(3x)^{6}$

= 1 + 18x + 135x² + 540x³ + 1215 $x^{4}$ + 1458 $x^{5}$ + 729 $x^{6}$

--------------------------------------------------------------------------------------

$(1-3x)^{6}$

= 1. $1^{6}$ $(-3x)^{0}$ + 6. $1^{5}$ $(-3x)^{1}$ + 15. $1^{4}$ $(-3x)^{2}$ + 20. $1^{3}$ $(-3x)^{3}$ + 15.1² $(-3x)^{4}$ + 6. $1^{1}$ $(-3x)^{5}$ + 1. $1^{0}$ $(-3x)^{6}$

= 1 - 18x + 135x² - 540x³ + 1215 $x^{4}$ - 1458 $x^{5}$ + 729 $x^{6}$

----------------------------------------------------------------------------------

Collecting like terms from both expressions

$(1+3x)^{6}$ + $(1-3x)^{6}$

= 2 + 270x² + 2430 $x^{4}$ + 1458 $x^{6}$

----------------------------------------------------

(2)

Using Pascal's triangle with n = 5

1 5 10 10 5 1

Decreasing powers of 1 from $1^{5}$ to $1^{0}$

Increasing powers of 2x from $(2x)^{0}$ to $(2x)^{5}$

$(1+2x)^{5}$

= 1. $1^{5}$ $(2x)^{0}$ + 5. $1^{4}$ $(2x)^{1}$ + 10. $1^{3}$ $(2x)^{2}$ + 10. $1^{2}$ $(2x)^{3}$ + 5. $1^{1}$ $(2x)^{4}$ + 1. $1^{0}$ $(2x)^{5}$

= 1 + 10x + 40x² + 80x³ + 80 $x^{4}$ + 32 $x^{5}$

8 0

3 years ago

Please help me :(.....

monitta

Answer:

the answer is C.........

7 0

3 years ago

A large paperclip is 7 1/8 inches long. How many paper clips will it take to lay them end to end to have 45 inches.

aleksandr82 [10.1K]

Answer:

6 Paperclips

Step-by-step explanation:

You first step would be to do 45 divide 7 1/8. Your answer would then be 6 6/19. The last step would be to round 6 6/19. Your answer would then be 6. Your answer would be 6, because you cant have 6/19 of a paper clip.

3 0

3 years ago

Pre calculus, trigonometry Given point M the ordered pair 6 times the square root of 3 comma negative 6 comma which is located o

Nikitich [7]

The possible form of the point (6√3, - 6) in polar form are (r₁, θ₁) = (12, 11π / 6), (r₂, θ₂) = (12, - π / 6).

<h3>How to derive the polar form of a point in rectangular form</h3>

In this problem we find a point in rectangular form, that is, a point of the form (x, y). We are asked to find the polar form of the point, that is, a point described by the following expression:

(r, θ)

Where:

r - Magnitude
θ - Direction, in radians

The magnitude is found by Pythagorean theorem:

r =√(x² + y²)

And the direction of the point is described by the following inverse trigonometric function:

θ = tan⁻¹ (y / x)

If we know that (x, y) = (6√3, - 6), then the point in polar form is:

r = √[(6√3)² + (- 6)²]

r = 12

θ = tan⁻¹ (- 6 / 6√3)

θ = tan⁻¹ (- √3 / 3)

θ = 11π / 6 rad / θ = - π / 6 rad

There are two possible solutions: (r₁, θ₁) = (12, 11π / 6), (r₂, θ₂) = (12, - π / 6).

To learn more on point in polar form: brainly.com/question/13103661

#SPJ1

7 0

1 year ago