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3 years ago

Solve: sin^2 x + sin x cos x = 0

1 answer:

3 0

Sin² x + sin x cos x = 0
sin x ( sin x + cos x ) = 0
sin x = 0 ; x 1 = k π ; k ∈ Z
sin x + cos x = 0 / ²
sin² x + 2 sin x cos x + cos² x = 0
2 sin x cos x + 1 =0
sin ( 2 x ) = - 1
x = 3π / 2 + 2 kπ / : 2
x 2 = 3π / 4 + kπ ; k ∈ Z

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For all values of x, f(x)=2x^2 and g(x)= x+1<br> Solve fg(x) = gf(x)

Andrej [43]

Answer:

-0.25

Step-by-step explanation:

→ Find fg(x)

2 ( x + 1 )² = 2x² + 4x + 2

→ Find gf(x)

2x² + 1

→ Equate them

2x² + 1 = 2x² + 4x+ 2

→ Move everything to the right hand side

0 = 4x + 1

→ Solve

x = -0.25

4 0

2 years ago

Read 2 more answers

Type the correct answer in each box. Use numerals instead of words. If necessary, use / for the fraction bar(s).

ddd [48]

Answer:

$f'(x) = 4x^2 - 3$ for $x \le -3$

Step-by-step explanation:

See attachment for proper question

Given

$f(x) = -\frac{1}{2}\sqrt{x + 3}$

For

$x \ge -3$

Required

Determine the inverse function

$f(x) = -\frac{1}{2}\sqrt{x + 3}$

Replace f(x) with y

$y = -\frac{1}{2}\sqrt{x + 3}$

Swap the positions of x and y

$x = -\frac{1}{2}\sqrt{y + 3}$

Multiply both sides by -2

$-2 * x =-2 * -\frac{1}{2}\sqrt{y + 3}$

$-2x =\sqrt{y + 3}$

Square both sides

$(-2x)^2 =(\sqrt{y + 3})^2$

$4x^2 =y + 3$

Make y the subject

$y = 4x^2 - 3$

The inverse has been solved. So, we need to replace y with f'(x)

$f'(x) = 4x^2 - 3$

Next, is to determine the interval

$x \ge -3$

Change inequality to $\le$

$x \le -3$

Hence, the inverse function is:

$f'(x) = 4x^2 - 3$ for $x \le -3$

7 0

3 years ago

What equation does the graph below represent

Masteriza [31]

Answer:

y=2x

Step-by-step explanation:

6 0

3 years ago

Find the value of 7 + 32 (-5 + 1) ÷ 2.<br> A. 25<br> B. 32<br> C. -11

kobusy [5.1K]

Answer:

as written, -57
as perhaps intended, C. -11

Step-by-step explanation:

The expression shown evaluates as ...

7 + 32(-5 +1)/2 = 7 +32(-4)/2 = 7 -128/2 = 7 -64 = -57

_____

If we assume your "32" is supposed to be 3², or 3^2, then the expression evaluates differently:

7 +3²(-5 +1)/2 = 7 + 9(-4)/2 = 7 -36/2 = 7 -18 = -11 . . . . matches choice C

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When in doubt, you can have the Google calculator evaluate your expression. However, you do have to write it properly and with all the required parentheses.

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3 years ago

Given: x + 2y = -6. Solve for x. Type a numerical answer in the space provided.

Alex Ar [27]

Answer:

x=-2y-6

Step-by-step explanation:

Subtract 2y from both sides, and now you have x=-2y-6.

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3 years ago