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3 years ago

May I Please Get Help With Questions 2 and 4

Mathematics

1 answer:

kotegsom [21]3 years ago

8 0

Answer:

22 and 31

Step-by-step explanation:

from the table we know that f(0) = 22 and f(-3) = 31

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Verify each trigonometric equation by substituting identities to match the right hand side of the equation to the left hand side

lorasvet [3.4K]

Answer:

Step-by-step explanation:

cot x sec⁴ x = cot x+2 tan x +tan³x

L.H.S = cot x sec⁴x

=cot x (sec²x)²

=cot x (1+tan²x)² [ ∵ sec²x=1+tan²x]

= cot x(1+ 2 tan²x +tan⁴x)

=cot x+ 2 cot x tan²x+cot x tan⁴x

=cot x +2 tan x + tan³x [ ∵cot x tan x $=\frac{ \textrm{tan x }}{\textrm{tan x}}$ =1]

=R.H.S

(sin x)(tan x cos x - cot x cos x)=1-2 cos²x

L.H.S =(sin x)(tan x cos x - cot x cos x)

= sin x tan x cos x - sin x cot x cos x

$=\textrm{sin x cos x }\times\frac{\textrm{sin x}}{\textrm{cos x} } - \textrm{sinx}\times\frac{\textrm{cos x}}{\textrm{sin x}}\times \textrm{cos x}$

= sin²x -cos²x

=1-cos²x-cos²x

=1-2 cos²x

=R.H.S

1+ sec²x sin²x =sec²x

L.H.S =1+ sec²x sin²x

= $1+\frac{{sin^2x}}{cos^2x}$ [ $\textrm{sec x}=\frac{1}{\textrm{cos x}}$ ]

=1+tan²x $[\frac{\textrm{sin x}}{\textrm{cos x}} = \textrm{tan x}]$

=sec²x

=R.H.S

$\frac{\textrm{sinx}}{\textrm{1-cos x}} +\frac{\textrm{sinx}}{\textrm{1+cos x}} = \textrm{2 csc x}$

L.H.S= $\frac{\textrm{sinx}}{\textrm{1-cos x}} +\frac{\textrm{sinx}}{\textrm{1+cos x}}$

$=\frac{\textrm{sinx(1+cos x)+{\textrm{sinx(1-cos x)}}}}{\textrm{(1-cos x)\textrm{(1+cos x})}}$

$=\frac{\textrm{sinx+sin xcos x+{\textrm{sinx-sin xcos x}}}}{{(1-cos ^2x)}}$

$=\frac{\textrm{2sin x}}{sin^2 x}$

= 2 csc x

= R.H.S

-tan²x + sec²x=1

L.H.S=-tan²x + sec²x

= sec²x-tan²x

= $\frac{1}{cos^2x} -\frac{sin^2x}{cos^2x}$

$=\frac{1- sin^2x}{cos^2x}$

$=\frac{cos^2x}{cos^2x}$

8 0

3 years ago

A cylinder with a height of 12 cm is inscribed in a sphere with a radius of 10 cm. Find the lateral area of the cylinder. Answer

zalisa [80]

Answer:

256π

Step-by-step explanation:

Given that:

The height of the cylinder: 12 cm

The radius of the sphere : 10

Let r is the radius of the cylinder, use Pytagon

10² = r² + 6²

<=> r² = 10² - 6² = 64

<=> r = 8

Hence, the lateral area of the cylinder

L= 2πrh

= 2π8*16

= 256π

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3 years ago

A rectangular pool in your friend' s yard is 150 ft× 400 ft.

Amiraneli [1.4K]

60,000 us the answer.

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3 years ago

What is half of a teaspoon of vanilla

Ksivusya [100]

Answer:

I believe the answer would be: Half of a teaspoon of vanilla.

Step-by-step explanation:

6 0

3 years ago

Graph a parabola whose xxx-intercepts are at x=-3x=−3x, equals, minus, 3 and x=5x=5x, equals, 5 and whose minimum value is y=-4y

DENIUS [597]

Answer:

Vertex: (1, -4)

intercept: (-3, 0)

Step-by-step explanation:

lets be real, you don't care about an explanation you just want the answer.

BUT... the vertex is the Y line and the Intercept is the X line

7 0

3 years ago