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2 years ago

Find f '(x) for f of x equals the square root of the quantity sine of 8 times x.

Mathematics

1 answer:

11Alexandr11 [23.1K]2 years ago

8 0

$f(x)=\sqrt{\sin{8x}}\\f'(x)=\frac{8\cos{8x}}{2\sqrt{\sin{8x}}}$

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Erik and Caleb were trying to solve the equation: 0=(3x+2)(x-4) Erik said, "The right-hand side is factored, so I'll use the zer

Mumz [18]

Answer:

C) Both

Step-by-step explanation:

The given equation is:

$0=(3x+2)(x-4)$

To solve the given equation, we can use the Zero Product Property according to which if the product <em>A.B = 0</em>, then either A = 0 OR B = 0.

Using this property:

$(3x+2) = 0 \Rightarrow \bold{x = -\frac{2}{3}}\\(x-4) = 0 \Rightarrow \bold{x = 4}$

So, Erik's solution strategy would work.

Now, let us discuss about Caleb's solution strategy:

Multiply $(3x+2)(x-4)$ i.e. $3x^2-12x+2x-8$ = $3x^2-10x-8$

So, the equation becomes:

$0=3x^2-10x-8$

Comparing this equation to standard quadratic equation:

$ax^2+bx+c=0$

a = 3, b = -10, c = -8

So, this can be solved using the quadratic formula.

$x=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}$

$x=\dfrac{-(-10)\pm\sqrt{(-10)^2-4\times3 \times (-8)}}{2\times 3}\\x=\dfrac{-(-10)\pm\sqrt{196}}{6}\\x=\dfrac{10\pm14}{6} \\\Rightarrow x= 4, -\dfrac{2}{3}$

The answer is same from both the approaches.

So, the correct answer is:

C) Both

3 0

2 years ago

Can somebody help me with the problem attached. It is on simplifying rational expressions. Thanks!

liq [111]

The answer is 8 as in eight

3 0

2 years ago

In Jamie's pocket there are 45 coins.

AVprozaik [17]

D:N
2 :3
Add them together to get the total which = 5
5 = 45
2 ?
= 18
No of dimes is 18

7 0

2 years ago

Read 2 more answers

5 increased by t operation and algebraic expressions

zubka84 [21]

increased means addition

so 5+t

5 0

2 years ago

A standard deck of playing cards has 52 cards total that contains 13 of each suit (hearts, diamonds, clubs and spades). What is

schepotkina [342]

Answer:

C 1/2

Step-by-step explanation:

There are 4 suits, 2 suits are red (hearts and diamonds) while 2 are black (clubs and spades)

Since 13 cards are in each suit, 26 cards are red ( 2 * 13)

There are 52 total cards

P (red) = red cards/ total cards

= 26 / 52

= 1/2

8 0

2 years ago