Tanx sinx (cos^2x cscx- sinx)

=(sinx/cosx)((cos^2x cscx- sinx)

=(sinx/cosx)((cos^2x 1/sinx- sinx)

=(sinx/cosx)((cos^²x - sin²x)] / sinx

=(sinx/cosx)((cos^²x - sin²x)] / sinx

=(1/cosx)((cos^²x - sin²x)]

=(1/cosx)(2cos²x====> = 2 cos x]

7 0

4 years ago

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A box is formed by cutting squares from the four corners of a 9"-wide by 12"-long sheet of paper and folding up the sides.

koban [17]

Answer:

$V(x) = 4x^3-42x^2 +108x$

Step-by-step explanation:

We are given the following in the question:

Width of sheet = 9 inches

Length of sheet = 12 inches

A square of length x inches is cut from each corner of the sheet to form a box.

Thus, the dimension of the box formed is:

Height = x inches

Width =

$9 - x-x = (9-2x)\text{ inches}$

Length =

$12 - x-x = (12-2x)\text{ inches}$

Volume of box formed =

$\text{Length}\times \text{Width}\times \text{Height}$

Putting values, we get,

$V(x) = (12-2x)(9-2x)x\\V(x) = (12-2x)(9x-2x^2)\\V(x) = 108x-24x^2-18x^2+4x^3\\V(x) = 4x^3-42x^2 +108x$

is the required expression of volume of box in terms of x.

8 0

3 years ago

a triangular sail has sides of 10 ft ,24ft,and 26ft .if the shortest side of a similar sail measures 6ft , what is the measure o

Katarina [22]

Answer:

15.6 ft

Step-by-step explanation:

Since the sails are similar then the ratios of corresponding sides are equal.

Comparing the shortest sides, that is

10 : 6 = 5 : 3

let the longest side be x, then using proportion

$\frac{26}{5}$ = $\frac{x}{3}$ ( cross- multiply )

5x = 78 ( divide both sides by 5 )

x = 15.6

The longest side is 15.6 ft

5 0

4 years ago

Someone help me pls

FrozenT [24]

Answer:

i can np

Step-by-step explanation:

6 0

3 years ago