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RoseWind [281]
3 years ago
14

Match the right side of the equation to the left side cot x sec^4 x=cot x+ 2 tan x+tan^3 x

Mathematics
1 answer:
Natalka [10]3 years ago
5 0

Step-by-step explanation:

cot x + 2 tan x + tan³ x

Write in terms of sine and cosine:

(cos x / sin x) + 2 (sin x / cos x) + (sin³ x / cos³ x)

Find the common denominator:

(cos⁴ x / (sin x cos³ x) + 2 (sin² x cos² x / (sin x cos³ x)) + (sin⁴ x / (sin x cos³ x))

Add:

(cos⁴ x + 2 sin² x cos² x + sin⁴ x) / (sin x cos³ x)

Factor:

(sin² x + cos² x)² / (sin x cos³ x)

Pythagorean identity:

1 / (sin x cos³ x)

Multiply top and bottom by cos x:

cos x / (sin x cos⁴ x)

Simplify:

cot x sec⁴ x

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What is the distance between two points with coordinates at (8, 40) and (20, 5)?
Alchen [17]

Answer:

37 units

Step-by-step explanation:

The two points form a right triangle so

a²+b²=c² so

(8-20)²(x values)+(40-5)²(y values)=c² (distance) so

12²+35²=c² so

144+1225=c²

1369=c²

c=37 units

7 0
2 years ago
Can someone maybe help?
Rina8888 [55]

Answer:

y= -1/3x+3 the y-intercept is 3 so plot it at (0,3)

Step-by-step explanation:

pls mark brainliest <3

8 0
2 years ago
Which equations represent the asymptotes of the hyperbola (x-1)^2/36-(y-2)^2/64=1 ?
allochka39001 [22]

Answer:

4x+3y=10 and  4x-3y=-2

Step-by-step explanation:

The asymptote equation of a translate hyperbola with equation \frac{(x-h)^2}{b^2}-\frac{(y-k)^2}{a^2}=1 is y=\pm\frac{b}{a}(x-h)+k

The given hyperbola has equation: \frac{(x-1)^2}{36}-\frac{(y-2)^2}{64}=1

Or \frac{(x-1)^2}{6^2}-\frac{(y-2)^2}{8^2}=1

Comparing to \frac{(x-h)^2}{a^2}-\frac{(y-k)^2}{b^2}=1

We have  a=6 and b=8, h=1 and k=2.

We substitute this values to get:

y=\pm\frac{6}{8}(x-1)+2

y=\pm\frac{4}{3}(x-1)+2

3y=\pm4(x-1)+6

We split the plus or minus sign to get:

3y=4x-4+6

3y=4x+2

3y-4x=2

Or

3y=-4(x-1)+6

3y=-4x+4+6

3y+4x=10

5 0
3 years ago
2/5x=42 HELP!!!!!!!!!<br><br><br><br>pls explain i have to show my work-
ICE Princess25 [194]

Answer:

X = 105

Step-by-step explanation:

<u>2x</u> = 42

5

Multiply both sides by 5

5 × <u>2x</u> = 5×42

5

5 cancle 5

2x = 5 × 42

2x = 210

Divide both sides by 2

<u>2x</u> = <u>210</u>

2 2

x = 105

8 0
1 year ago
I need help with 5th grade fractions
nirvana33 [79]

Answer:

i can help

Step-by-step explanation:

4 0
2 years ago
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