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4 years ago

How do i find the following f(x)?? Pls help

Mathematics

1 answer:

Neporo4naja [7]4 years ago

3 0

Answer:

(a) (f+g)(x) = √(2x) +x²

(b) (f-g)(x) = √(2x) -x²

(d) (f/g)(x) = (√(2x))/x²

Step-by-step explanation:

These are all about the meaning of the notation (f <operator> g)(x). When the operator is an arithmetic operation (addition, subtraction, multiplication, division), the notation means the same thing as ...

f(x) <operator> g(x)

(a) (f+g)(x) = f(x) + g(x)

(f+g)(x) = √(2x) +x²

(b) (f-g)(x) = f(x) -g(x)

(f-g)(x) = √(2x) -x²

(c) (f·g)(x) = f(x)·g(x)

(f·g)(x) = x²√(2x)

(d) (f/g)(x) = f(x)/g(x)

(f/g)(x) = (√(2x))/x²

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Parallel to y=2x-4 through (8,8)

yanalaym [24]

Answer:

y = 2x - 8

Step-by-step explanation:

Parallel lines have SIMILAR RATE OF CHANGES [SLOPES], so 2 remains the same:

8 = 2[8] + b

↑

-8 = b

y = 2x - 8 >> Parallel Equation

I am joyous to assist you anytime.

5 0

3 years ago

The absolute value of a negative fraction is always greater than 1, true of false?!

Fantom [35]

Answer: False

Step-by-step explanation: False because zero is negative or positive. The absolute value of any number could also include the absolute value of 0, which would be 0. Thus, the absolute value of any rational number is not always greater than zero, it can be zero as well. However, it is true that the absolute value of any rational number can never be negative.

Rational Number definition: Rationals contain whole numbers, integers, decimals, fractions, basically most numbers or any numbers.

6 0

3 years ago

Mrs. Santos is buying binders for the students in her class. She determined that 15 binders would cost $22.50.

atroni [7]

Answer:

It will cost $42 for 28 binders

Step-by-step explanation:

We know that 15 binders = 22.50 dollars . We need to find the cost of 18, 30, 28, and 48 binders to figure out if they match up with the statements. One way to do this is to find the cost for one binder, and then multiply that by the number of binders to find the cost for a certain number of binders. For example, if one binder costs 2 dollars, five binders would cost 2 * 5 = 10 dollars.

To figure out how much one binder costs, we can use the division property of equality to divide both sides of our equation (15 binders = 22.50 dollars) by 15. We divide by 15 because anything divided by itself is equal to 1, and that would make it 1 binder = something dollars.

Applying this, we get

(15 binders)/15 = (22.5 dollars)/15

1 binder = 1.5 dollars

For 18 binders, this would cost 1.5 * 18 = 27 dollars. We know this because we add 1.5 dollars for each binder.

For 30 binders, this would cost 30*15=45 dollars

For 28 binders, this would cost 1.5 * 28 = 42 dollars

For 48 binders, this would cost 1.5*48 = 72 dollars

The only one that matches up is 28 binders for 42 dollars

8 0

3 years ago

Need some help with this question please

Serggg [28]

Answer:

$\frac{15}{17}$

Step-by-step explanation:

$\cos( \alpha ) = \frac{ad}{hip} \\ \\ \sin( \alpha ) = \frac{op}{hip}$

Pythagorean theorem

hip² = op² + ad²

17² = x² + 8²

x² = 17² - 8²

$x \: = \sqrt{{17}^{2} - {8}^{2} } \\ x = \sqrt{289 - 64} \\ x = \sqrt{225} \\ x = 15$

$\sin( \alpha ) = - \frac{15}{17}$

$\sin( - \alpha ) = \frac{15}{17}$

4 0

3 years ago

CALCULUS - Find the values of in the interval (0,2pi) where the tangent line to the graph of y = sinxcosx is

Rufina [12.5K]

Answer:

$\{\frac{\pi}{4}, \frac{3\pi}{4},\frac{5\pi}{4},\frac{7\pi}{4}\}$

Step-by-step explanation:

We want to find the values between the interval (0, 2π) where the tangent line to the graph of y=sin(x)cos(x) is horizontal.

Since the tangent line is horizontal, this means that our derivative at those points are 0.

So, first, let's find the derivative of our function.

$y=\sin(x)\cos(x)$

Take the derivative of both sides with respect to x:

$\frac{d}{dx}[y]=\frac{d}{dx}[\sin(x)\cos(x)]$

We need to use the product rule:

$(uv)'=u'v+uv'$

So, differentiate:

$y'=\frac{d}{dx}[\sin(x)]\cos(x)+\sin(x)\frac{d}{dx}[\cos(x)]$

Evaluate:

$y'=(\cos(x))(\cos(x))+\sin(x)(-\sin(x))$

Simplify:

$y'=\cos^2(x)-\sin^2(x)$

Since our tangent line is horizontal, the slope is 0. So, substitute 0 for y':

$0=\cos^2(x)-\sin^2(x)$

Now, let's solve for x. First, we can use the difference of two squares to obtain:

$0=(\cos(x)-\sin(x))(\cos(x)+\sin(x))$

Zero Product Property:

$0=\cos(x)-\sin(x)\text{ or } 0=\cos(x)+\sin(x)$

Solve for each case.

Case 1:

$0=\cos(x)-\sin(x)$

Add sin(x) to both sides:

$\cos(x)=\sin(x)$

To solve this, we can use the unit circle.

Recall at what points cosine equals sine.

This only happens twice: at π/4 (45°) and at 5π/4 (225°).

At both of these points, both cosine and sine equals √2/2 and -√2/2.

And between the intervals 0 and 2π, these are the only two times that happens.

Case II:

We have:

$0=\cos(x)+\sin(x)$

Subtract sine from both sides:

$\cos(x)=-\sin(x)$

Again, we can use the unit circle. Recall when cosine is the opposite of sine.

Like the previous one, this also happens at the 45°. However, this times, it happens at 3π/4 and 7π/4.

At 3π/4, cosine is -√2/2, and sine is √2/2. If we divide by a negative, we will see that cos(x)=-sin(x).

At 7π/4, cosine is √2/2, and sine is -√2/2, thus making our equation true.

Therefore, our solution set is:

$\{\frac{\pi}{4}, \frac{3\pi}{4},\frac{5\pi}{4},\frac{7\pi}{4}\}$

And we're done!

Edit: Small Mistake :)

5 0

3 years ago