Hannah bought a sweater on sale for $24. If that was a fourth of the original price what is the original price?

Mathematics

2 answers:

max2010maxim [7]3 years ago

8 0

Well 24 * 4 is 96. so $96

shepuryov [24]3 years ago

5 0

Answer: 6$

Step-by-step explanation:

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Fatima wants to find the value of sine theta, given cotangent theta = four-sevenths. which identity would be best for fatima to

Olin [163]

By using trigonometric relations, we will find that:

sin(θ) = (√33)/7 = √(33/49)

<h3>How to find the value of the sine?</h3>

Remember that for a right triangle, we have the relations:

cos(a) = (adjacent cathetus)/(hypotenuse)

sin(a) = (opposite cathetus)/(hypotenuse).

Here we know that:

cos(θ) = 4/7

Then we can say that we have a triangle with an adjacent cathetus of 4 units and a hypotenuse of 7 units. Now we need to find the other cathetus.

opposite cathetus = √(7^2 - 4^2) = √33

Then we can write:

sin(θ) = (√33)/7 = √(33/49)

If you want to learn more about trigonometry.

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3 0

2 years ago

F(x) = lnx/x

My name is Ann [436]

$f(x) = \frac{lnx}{x}$

(a) $f'(x) = \frac{d}{dx}[\frac{lnx}{x}]$
Using the quotient rule:
$f'(x) = \frac{\frac{1}{x} \cdot x - lnx}{x^{2}}$
$f'(x) = \frac{1 - lnx}{x^{2}}$

For maximum, f'(x) = 0;
$\frac{1 - lnx}{x} = 0$
$lnx = 1, x = e$

(b) <em>Deduce:
</em> $e^{x} \geq x^{e}, x > 0$
<em>
Soln:</em> Since x = e is the greatest value, then f(e) ≥ f(x) > f(0)
$\frac{ln(e)}{e} \geq \frac{lnx}{x}$
$\frac{1}{e} \geq \frac{lnx}{x}$ , since ln(e) is simply equal to 1

Now, since x > 0, then we don't have to worry about flipping the signs when multiplying by x.
$\frac{x}{e} \geq lnx$
$x \geq elnx$
$x \geq ln(x^{e})$

Taking the exponential to both sides will cancel with the natural logarithmic function in the right hand side to produce:
$e^{x} \geq e^{ln(x^{e}})$
$e^{x} \geq x^{e}$ , as required.