All categories

3 years ago

Simplify the expressioncot^2x - cot^2x cos^2x

Mathematics

1 answer:

andrew-mc [135]3 years ago

8 0

Cot^2x - cot^2x cos^2x
= cot^2x - {(cot^2x)(cos^2x)}
= cot^2x { 1 - cos^2x }
= cot^2x { sin^2x }
= (cos^2x/sin^2x) { sin^2x }
= cos^2x

You might be interested in

Roll ends of carpet are on sale for six dollars per square yard. To finish the rough-cut edges, edging material costing 10 cent

tiny-mole [99]

Answer:

Total cost the roll end is $63.8

Step-by-step explanation:

Since dimensions of the roll ends = 9 feet × 10 feet

By converting these dimensions in yards = $\frac{9}{3}\times \frac{10}{3}$ yards [Since 1 feet = $\frac{1}{3}$ yards]

Area of the roll ends = $\frac{9}{3}\times \frac{10}{3}$ = 10 square yards

Cost of the roll ends = $6 per square yards

So cost of these roll ends = 10×6 = $60

To finish the rough-cut edges, edging material costs = $0.10 per feet

Total length to be glued = Perimeter of the carpet

= 2(length + width)

= 2(9 + 10)

= $38

Total cost to glue the edging material = 38×($0.10) = $3.8

Now total cost of the roll end = $60 + $3.8

= $63.8

Therefore, total cost of a roll end = $63.8

5 0

3 years ago

3. C(8, r) = 28; r =

jeka94

Given:

$C(8,r)=28$

To find:

The value of r.

Solution:

Combination formula:

$C(n,r)=\dfrac{n!}{r!(n-r)!}$

We have,

$C(8,r)=28$

Using the combination formula, we get

$\dfrac{8!}{r!(8-r)!}=28$

$\dfrac{8!}{28}=r!(8-r)!$

$\dfrac{8\times 7\times 6!}{28}=r!(8-r)!$

$2\times 6!=r!(8-r)!$

It can be written as:

$2!6!=r!(8-r)!$ $[\because 2!=2\times 1=2]$

Case 1:

$2!=r!$

$r=2$

And,

$6!=(8-r)!$

$6=8-r$

$r=8-6$

$r=2$

Case 2:

$6!=r!$

$r=6$

And,

$2!=(8-r)!$

$2=8-r$

$r=8-2$

$r=6$

Therefore, the value of r is either 2 or 6.

8 0

3 years ago

Can someone answer this plz.

Svetradugi [14.3K]

OK ,

theres 150 fish in the pond mius 8% each day so

150-8%=138
138-8%=129.96

129.96 is your answer

4 0

4 years ago

The measure of an angle is 13°. What is the measure of its complementary angle?

marysya [2.9K]

Answer:

77°

Step-by-step explanation:

Complementary angles formula

90°- x°. (X is the given angle)

So,

90°-13°

= 77°

7 0

3 years ago

Two cars are driving toward each other from opposite directions. If one is driving 55 mph, the other is driving 60 mph and the c

Korvikt [17]

Set 500 to sum of distances traveled by both cars.
$55t + 60t = 500 \\ 115t = 500 \\ t = (500/115) = 4.3$

4 0

3 years ago