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marissa [1.9K]
3 years ago
11

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

Mathematics
1 answer:
ddd [48]3 years ago
7 0

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

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Aleks04 [339]

Answer:

243

Step-by-step explanation:

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7 0
3 years ago
2. There are 42 persons in a mathematics class, and everyone of them drinks either coffee or grape milk at
Basile [38]

Answer:

1.  8

2.  24

Step-by-step explanation:

The number of persons that drink grape milk only :

18 - 10 = 8

The number of persons that drink coffee :

42 - 8 = 34

The number of persons that drink coffee only :

34 - 10 = 24

5 0
2 years ago
Find the distance between the points (6,5√5) and (4,3√2).<br> 2, 2√2, 2√3
FromTheMoon [43]

Answer:

D=\sqrt{(147-30\sqrt{10}}

Step-by-step explanation:

Here we are required to find the distance between two coordinates. We will use the distance formula to find the distance

The distance formula is given as

D=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}

Here we are given two coordinates as

(6,5\sqrt{5} ) , (4,3\sqrt{2} )

Substituting these values in the Distance formula given above we get

D=\sqrt{(6-4)^2+(5\sqrt{5} -3\sqrt{2}) ^2}

D=\sqrt{(2)^2+(5\sqrt{5})^2+(3\sqrt{2})^2-2*5\sqrt{5}*3\sqrt{2}}\\

D=\sqrt{4+125+18-2*15\sqrt{10}}\\D=\sqrt{147-30\sqrt{10}}\\

Hence this is our answer

6 0
3 years ago
In the figure, a square is inside another bigger square.
evablogger [386]

Answer:

Part 1) The length of the diagonal of the outside square is 9.9 units

Part 2) The length of the diagonal of the inside square is 7.1 units

Step-by-step explanation:

step 1

Find the length of the outside square

Let

x -----> the length of the outside square

c ----> the length of the inside square

we know that

x=a+b=4+3=7\ units

step 2

Find the length of the inside square

Applying the Pythagoras Theorem

c^{2}= a^{2}+b^{2}

substitute

c^{2}= 4^{2}+3^{2}

c^{2}=25

c=5\ units

step 3

Find the length of the diagonal of the outside square

To find the diagonal Apply the Pythagoras Theorem

Let

D -----> the length of the diagonal of the outside square

D^{2}= x^{2}+x^{2}

D^{2}= 7^{2}+7^{2}

D^{2}=98

D=9.9\ units

step 4

Find the length of the diagonal of the inside square

To find the diagonal Apply the Pythagoras Theorem

Let

d -----> the length of the diagonal of the inside square

d^{2}= c^{2}+c^{2}

d^{2}= 5^{2}+5^{2}

d^{2}=50

d=7.1\ units

7 0
3 years ago
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