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dlinn [17]
3 years ago
14

Which of the following expressions is not equal to X^3?

Mathematics
1 answer:
Musya8 [376]3 years ago
6 0

Answer:

D. x. x^7 . x^-4

Step-by-step explanation:

A. X^5 . X^-4 .X^2=X^(5-4+2)= X^3

B. X^-2 .X^9 .x^-4=X^(-2+9-4)= X^3

C.x^0 . x^10 . x^-7=X^(0+10-7)= X^3

D. x. x^7 . x^-4=X^(1+7-4)= X^4

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Answer:

Step-by-step explanation:

Given expression is,

\text{cot}A=\frac{1}{2}(\text{cot}\frac{A}{2}-\text{tan}\frac{A}{2})

To prove this identity we will take the right side of the identity,

\frac{1}{2}(\text{cot}\frac{A}{2}-\text{tan}\frac{A}{2})=\frac{1}{2}(\frac{1}{\text{tan}\frac{A}{2}}-tan\frac{A}{2})

                         =\frac{1}{2}(\frac{1-\text{tan}^2\frac{A}{2}}{tan\frac{A}{2}})

                         =\frac{1}{2}[\frac{2(1-\text{tan}^2\frac{A}{2})}{2tan\frac{A}{2}}]

                         =\frac{1}{2}(\frac{2}{\text{tan}A} ) [Since \text{tan}A=\frac{2\text{tan}\frac{A}{2}}{1-\text{tan}^2\frac{A}{2}}]

                         = cot A

Hence right side of the equation is equal to the left side of the equation.

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3 years ago
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3 years ago
The base of a parallelogram is 18 inches longer than three times the height. The area of the parallelogram is 216 square inches.
nordsb [41]

Answer:

12 inches

Step-by-step explanation:

Let b represent the base

h represents the height

area of the parallelogram = base * height = 216 square inches

From the question'

b = 18 + 3h

Slot in the value of b

216 = (18 + 3h) * h

expand

216 = 18h + 3h^2

subtract 216 from both sides

0 = 18h + 3h^2 - 216

rearrange

3h^2 + 18h - 216 = 0

divide through by 3

h^2 + 6h - 72 = 0

Now, lets solve!

h^2 + 6h - 12h - 72 = 0

h( h + 6 ) - 12(h + 6) = 0

(h - 12) (h + 6) = 0

h - 12 = 0

h = 12

and

h + 6 = 0

h = - 6

Taking the positive value of h

Hence, the height is 12 inches

Lets check

when h = 12 inches

Area of the parallelogram = 18* 12 = 216 square inches     .... correct

when h = -6inches

A = 18 * -6 ≠  216 square inches

So height is 12 inches

5 0
3 years ago
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