How many whole numbers less than 2,700,000 end with 2014?

Tan^2 A/1+cot^2 A + cot^2 A/1+tan^2 A=sec^2 A cosec^2 A-3

omeli [17]

$\frac{tan^2x}{1+cot^2x}+\frac{cot^2x}{1+tan^2x}=sec^2x\ cosec^2x-3\\\\L=\frac{tan^2x(1+tan^2x)+cot^2x(1+cot^2x)}{(1+cot^2x)(1+tan^2x)}=\frac{tan^2x+tan^4x+cot^2x+cot^4x}{1+tan^2x+cot^2x+tanxcotx}\\\\=\frac{tan^2x+cot^2x+tan^4x+cot^4x}{1+tan^2x+cot^2x+1}=\frac{tan^2x+2+cot^2x+tan^4x-2+cot^4x}{tan^2x+cot^2x+2}$

$=\frac{(tanx+cotx)^2+(tan^2x-cot^2x)^2}{(tanx+cotx)^2}=\frac{(tanx+cotx)^2}{(tanx+cotx)^2}+\frac{(tan^2x-cot^2x)^2}{(tanx+cotx)^2}\\\\=1+\frac{(tanx-cotx)^2(tanx+cotx)^2}{(tanx+cotx)^2}=1+(tanx-cotx)^2\\\\=1+tan^2x-2tanx\ cotx+cot^2x=tan^2x+cot^2x+1-2\\\\=\left(\frac{sinx}{cosx}\right)^2+\left(\frac{cosx}{sinx}\right)^2-1=\frac{sin^2x}{cos^2x}+\frac{cos^2x}{sin^2x}-1=\frac{sin^4x+cos^4x}{sin^2x\ cos^2x}-1$

$=\frac{(sin^2x)^2+2sin^2x\ cos^2x+(cos^2x)^2-2sin^2x\ cos^2x}{sin^2x\ cos^2x}-1\\\\=\frac{(sin^2x+cos^2x)^2-2sin^2x\ cos^2x}{sin^2x\ cos^2x}-1=\frac{1^2-2sin^2x\ cos^2x}{sin^2x\ cos^2x}-1\\\\=\frac{1}{sin^2x\ cos^2x}-\frac{2sin^2x\ cos^2x}{sin^2x\ cos^2x}-1=\frac{1}{sin^2x}\cdot\frac{1}{cos^2x}-2-1\\\\=cosec^2x\cdot sec^2x-3=sec^2x\ cosec^2x-3=R$

3 0

3 years ago

Noah bought 15 baseball cards for $9.00. Assuming that each baseball card costs the same amount, answer the following questions.

STatiana [176]

Answer:

270 dollars

Step-by-step explanation:

5 0

3 years ago

Lisa is a single taxpayer whose total income before deductions are $57,392. She was able to reduce her total income by $9,347 by

qaws [65]

Answer:

$5554.91

Step-by-step explanation:

8 0

3 years ago

Read 2 more answers

Find the vertex of this parabola:<br> y = -x2 - 6x - 10

MAVERICK [17]

Answer:-10

Step-by-step explanation: The slope-intercept form is

y

=

m

x

+

b

y

=

m

x

+

b

, where

m

is the slope and

b

is the y-intercept.

y

=

m

x

+

b

y

=

m

x

+

b

Find the values of

m

and

b

using the form

y

=

m

x

+

b

y

=

m

x

+

b

.

m

=

−

6

m

=

-

6

b

=

−

10

b

=

-

10

The slope of the line is the value of

m

, and the y-intercept is the value of

b

.

Slope:

−

6

-

6

y-intercept:

−

10

8 0

3 years ago

Read 2 more answers

A restaurant chef ordered 4 pounds of beef at $3.25 per pound, 6 pounds of potatoes at $1.96 a pound, and 5 pounds of carrots at

zhenek [66]

Answer:

Profit = $18.8 per meal

Step-by-step explanation:

Chef ordered beef = 4 pounds

Cost of beef = $3.25 per pound

Total cost of beef = 4 × 3.25 = $13

Amount of potatoes ordered = 6 pounds

Cost of potatoes = $1.96 per pound

Total cost of potatoes = 6 × 1.96

= $11.76

Amount of carrots ordered = 5 pounds

Cost of carrots = $1.81 per pound

Total cost of carrots = 5 × 1.81 = $9.05

Total amount of beef, potatoes and carrots = $13 + $11.76 + $9.05

= $33.81

Number of meals prepared with material purchased = 28

Per meal cost = $\frac{33.81}{28}$ = $1.2075

Selling price of one meal = $20

Profit per meal = Selling price - Cost price

= 20 - 1.2075

= 18.7925

≈ $18.8

Therefore, he will make $18.8 for each meal.

3 0

3 years ago