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4 years ago

Is sin x cos x ever equal to 1? Provide a reason for you answer.

1 answer:

8 0

When x = 0° : sin x = 0, cos x = 1, therefore sin x * cos x = 0.
Also, when x = 90° : sin x = 1, cos x = 0, so sin x * cos x = 0.
For any value between 0° and 90° , the product of sin and cos is less than 1.
We can show it like this:
sin 2 x = 2 sin x cos x ( trigonometric formula )
sin x cos x = 1
sin 2 x / 2 = 1 / * 2 ( we will multiply both sides of an equation by 2 )
sin 2 x = 2 This is impossible because the maximum value for sin of any angle is 1.
Answer: sin x cos x is never equal to 1.

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18=a Over 2 How do you solve that as a one step

daser333 [38]

Multiply each side by 2

a=36

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4 years ago

Differentiating Exponential functions In Exercise,find the derivative of the function. See Example 2 and 3.

Keith_Richards [23]

Answer: The derivative would be $f'(x)=2(e^{2x}-e^{-2x})$

Step-by-step explanation:

Since we have given that

$f(x)=(e^x+e^{-x})^{\frac{4}{2}}\\\\f(x)=(e^x+e^{-x})^2$

As we will use "Chain Rule"

and at last we will use the identity '' $a^2-b^2=(a-b)(a+b)$ ''

We need to find the derivative of the function:

$f'(x)=2(e^x+e^{-x})(e^x-e^{-x})\\\\f'(x)=2(e^{2x}-e^{-2x})$

Hence, the derivative would be

$f'(x)=2(e^{2x}-e^{-2x})$

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4 years ago

Fgh is first translated using the rule x,y >x+3,y-1this is followed by a 90 degrees counter clockwise rotation centered at th

maw [93]

Answer:

Rule:

$h = (1 - y,x + 3)$

Step-by-step explanation:

I will answer generally, since the coordinates of f, g and h are not given

Given

Point: x, y

Translation Rule

1 : x + 3, y - 1

2: 90 degree counterclockwise

Required

Determine the new coordinates

At the first translation of (x,y) by x + 3, y - 1

The new point is: $(x + 3, y - 1)$

At the second translation (90 degrees counterclockwise)

When a point (x,y) is translated using this rule, it becomes (-y,x)

So, the new point is:

$h = (-(y - 1),x + 3)$

$h = (1 - y,x + 3)$

If the initial point of h is (2,3),

The new point is:

$h = (1 - 3, 2 + 3)$

$h = (- 2, 5)$

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3 years ago

Questions about rational and irrational numbers

FinnZ [79.3K]

Rational numbers are those numbers that are integers and can be expressed in the form of x/y where both numerator and denominator are integers whereas irrational numbers are those numbers which cannot be expressed in a fraction. ... The denominator of a rational number is a natural number(a non-zero number).

Rational numbers and irrational numbers are mutually exclusive: they have no numbers in common. Furthermore, they span the entire set of real numbers; that is, if you add the set of rational numbers to the set of irrational numbers, you get the entire set of real numbers.

Answer: If a number can be written or can be converted to p/q form, where p and q are integers and q is a non-zero number, then it is said to be rational and if it cannot be written in this form, then it is irrational.

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3 years ago

An atom has 24 protons and 12 neutrons what is the chemical symbol for the atom?

kykrilka [37]

Answer:

The element is Chromium.

Explanation:

The atom has 24 protons and 12 neutrons.

We know that Cr has 24 number of protons, to the Chemical is Cr (Chromium)

Again, we know that the atomic number is the number of protons and the atomic mass is the sum of proton and neutron.

So, the atomic number is 24 and the atomic mass is (24+12)= 36

Therefore, the symbol is $\bold^{36} \mathrm{Cr}_{24}\bold$

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3 years ago