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Vlad [161]
3 years ago
7

Rewrite the expression as an algebraic expression in x. tan(sin−1(x))

Mathematics
1 answer:
solmaris [256]3 years ago
7 0
Let tan^{-1} x=\alpha
Then it can be shown by using a right-angled triangle and the rule of Pythagoras that \alpha= tan^{-1} \frac{x}{ \sqrt{1-x^{2}} }
Therefore
tan(sin ^{-1} (x))=\frac{x}{ \sqrt{1-x^{2}} }
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Which of the following illustrates the truth value of the given conditional statement?
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D is the right answer F T - T
8 0
2 years ago
I NEED HELP PLZ ASAP!!!!! In right triangle ABCD above, x = A. 6 B. 8 C. 6√2 D. 10 E. 13
REY [17]

Answer:

x=6

Step-by-step explanation:

Since this is a right triangle we can use  the Pythagorean theorem

a^2 + b^2 = c^2

where a and b are the legs and c is the hypotenuse

x^2 + (x+2)^2 = (2x-2)^2

FOIL (x+2)^2 = x^2 +2x+2x+4 = x^2 +4x+4

FOIL (2x-2)^2 = 4x^2 -4x -4x+4 = 4x^2 -8x+4

Replacing these in to the equation

x^2 +x^2 +4x+4 = 4x^2 -8x+4

Combine like terms

2x^2 +4x +4 = 4x^2 -8x +4

Subtract 4 from each side

2x^2 +4x +4-4 = 4x^2 -8x +4-4

2x^2 +4x = 4x^2 -8x

Subtract 2x^2 from each side

2x^2 -2x^2+4x = 4x^2-2x^2 -8x

4x = 2x^2 -8x

Subtract 4x from each side

4x-4x = 2x^2 -8x-4x

0 = 2x^2 -12x

Factor out a 2x

0 = 2x(x-6)

Using the zero product property

2x =0  x-6 =0

x =0  x-6+6 = 0+6

x = 0  c=6

5 0
3 years ago
"During the winter snow season, the Snowy Mountain Coffee Spot sells hot chocolate for 47 cents. If Katrina paid for a cup of ho
eduard

Answer:

4 dimes an 7 pennies

Step-by-step explanation:

it should be easy

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3 years ago
HELP ASAP!!
viktelen [127]

Answer:

The answer is terminating!

Step-by-step explanation:

repeating never ends

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2 years ago
Read 2 more answers
Jackie scored 81 and 87 on her first two quizzes . Write and solve a compound inequality to find the possible values for a third
asambeis [7]

Answer:

The third score must be larger than or equal to 72, and smaller than or equal 87

Step-by-step explanation:

Let's name "x" the third quiz score for which we need to find the values to get the desired average.

Recalling that average grade for three quizzes is the addition of the values on each, divided by the number of quizzes (3), we have the following expression for the average:

average=\frac{81+87+x}{3}

SInce we want this average to be in between 80 and 85, we write the following double inequality using the symbols that include equal sign since we are requested the average to be between 80 and 85 inclusive:

80\leq average\leq 85\\80\leq \frac{81+87+x}{3} \leq 85\\80\leq \frac{168+x}{3} \leq 85

Now we can proceed to solve for the unknown "x" treating each inaquality at a time:

80\leq \frac{168+x}{3}\\3*80\leq 168+x\\240\leq 168+x\\240-168\leq x\\72\leq x

This inequality tells us that the score in the third quiz must be larger than or equal to 72.

Now we study the second inequality to find the other restriction on "x":

\frac{168+x}{3} \leq 85\\168+x\leq 85 *3\\168+x\leq 255\\x\leq 255-168\\x\leq 87

This ine72\leq x} \leq 87quality tells us that the score in the third test must be smaller than or equal to 87 to reach the goal.

Therefore to obtained the requested condition for the average, the third score must be larger than or equal to 72, and smaller than or equal 87:

4 0
3 years ago
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