Write an integer to describe the situation AND explain the meaning of zero. RISING 7 DEGREES

2〖sen〗^2 x+3 senx+1=0

KonstantinChe [14]

2 sin²(x) + 3 sin(x) + 1 = 0

(2 sin(x) + 1) (sin(x) + 1) = 0

2 sin(x) + 1 = 0 OR sin(x) + 1 = 0

sin(x) = -1/2 OR sin(x) = -1

The first equation gives two solution sets,

x = sin⁻¹(-1/2) + 2nπ = -π/6 + 2nπ

x = π - sin⁻¹(-1/2) + 2nπ = 5π/6 + 2nπ

(where n is any integer), while the second equation gives

x = sin⁻¹(-1) + 2nπ = -π/2 + 2nπ

2 cot(x) sec(x) + 2 sec(x) + cot(x) + 1 = 0

2 sec(x) (cot(x) + 1) + cot(x) + 1 = 0

(2 sec(x) + 1) (cot(x) + 1) = 0

2 sec(x) + 1 = 0 OR cot(x) + 1 = 0

sec(x) = -1/2 OR cot(x) = -1

cos(x) = -2 OR tan(x) = -1

The first equation has no (real) solutions, since -1 ≤ cos(x) ≤ 1 for all (real) x. The second equation gives

x = tan⁻¹(-1) + nπ = -π/4 + nπ

sin(x) cos²(x) = sin(x)

sin(x) cos²(x) - sin(x) = 0

sin(x) (cos²(x) - 1) = 0

sin(x) (-sin²(x)) = 0

sin³(x) = 0

sin(x) = 0

x = sin⁻¹(0) + 2nπ = 2nπ

2 cos²(x) + 2 sin(x) - 12 = 0

2 (1 - sin²(x)) + 2 sin(x) - 12 = 0

-2 sin²(x) + 2 sin(x) - 10 = 0

sin²(x) - sin(x) + 5 = 0

Using the quadratic formula, we get

sin(x) = (1 ± √(1 - 20)) / 2 = (1 ± √(-19)) / 2

but the square root contains a negative number, which means there is no real solution.

2 csc²(x) + cot²(x) - 3 = 0

2 (cot²(x) + 1) + cot²(x) - 3 = 0

3 cot²(x) - 1 = 0

cot²(x) = 1/3

tan²(x) = 3

tan(x) = ± √3

x = tan⁻¹(√3) + nπ OR x = tan⁻¹(-√3) + nπ

x = π/3 + nπ OR x = -π/3 + nπ

7 0

3 years ago

A rectangle that is 2 inches by 3 inches has been scaled by a factor of 7.

loris [4]

Answer:

$New\ Lengths = (14,21)$

$New\ Scale\ Factor = \frac{1}{7}$

Step-by-step explanation:

Given

Rectangle:

Length = 2 in

Width = 3 in

Scale Factor = 7

Solving (a):

The side lengths of the new scale is calculated as follows;

New Lengths = Old Lengths * Scale Factor

$New\ Lengths = (2,3) * 7$

$New\ Lengths = (2 * 7,3* 7)$

$New\ Lengths = (14,21)$

Solving (b): To go back to the original length

Given that the initial scale factor is 7;

The new scale factor is the reciprocal of the old factor;

Hence;

$New\ Scale\ Factor = \frac{1}{7}$

6 0

4 years ago

a street light is at the top of a 18 ft tall pole. a woman 6 ft tall walks away from the pole with a speed of 4 ft/sec along a s

shutvik [7]

The most appropriate choice for similarity of triangles will be given by -

Speed of tip of the shadow of woman = 6 ft/s

What are similar triangles?

Two triangles are said to be similar, if the corrosponding angles of the triangles are same and the corrosponding sides of the triangles are in the same ratio.

Here,

The diagram has been attached here

Let the distance of woman from the pole be x ft and the distance of tip of the shadow to the pole be y ft.

Height of street light = 18 ft

Height of woman = 6ft

The two triangles are similar [As height of woman is parallel to the height of pole]

$\frac{y - x}{6}=\frac{y}{18}\\18y - 18x = 6y\\18y - 6y = 18x\\12y = 18x\\y = \frac{18}{12}x\\y = \frac{3}{2}x\\$

To find the speed, we have to differentiate both sides with respect to time 't'

$\frac{dy}{dt} =\frac{3}{2}\frac{dx}{dt}\\\frac{dy}{dt}=\frac{3}{2} \times 4\\\frac{dy}{dt} = 6$

Speed of tip of her shadow = 6 ft

To learn more about similarity of triangles, refer to the link-

brainly.com/question/14285697

#SPJ4

6 0

1 year ago

The life spans of elephants in a Columbus zoo are normally distributed. The average elephant lives 60 years: the standard deviat

Marta_Voda [28]

did u ever get the answer l need it

5 0

3 years ago

Center (-9,0) radius 1

gogolik [260]

Answer:

Step-by-step explanation:

im guessing you need the equation of the circle?

plugging it into the standard circle equaition you would get (x+9)^2+y^2=1 and then you would just need to rearaange it into standard form

5 0

3 years ago