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2 years ago

Differentiate. y = log₅(2x³-1)

Mathematics

2 answers:

likoan [24]2 years ago

8 0

(1/(ln 5))((6x^2)/(2x^3-1))

Sonja [21]2 years ago

8 0

Change the base to ln

remmber
$log_a(b)= \frac{log_c(b)}{log_c(a)}$
ln is just base e

so
$log_5(2x^3-1)= \frac{log_e(2x^3-1)}{log_e(5)} = \frac{ln(2x^3-1))}{ln(5)}$

remember that tthe deritivive of $\frac{f(x)}{g(x)}$ is $\frac{f'(x)g(x)-g'(x)f(x)}{g(x)^2}$
so

let's take the deritivies seperately first
deritivive of ln(2x^3-1) is $\frac{6x^2}{2x^3-1}$
deritivive of ln(5) is 0

$\frac{ln(2x^3-1))}{ln(5)} = \frac{( \frac{6x^2}{2x^3-1})(ln(5))-(0)(ln(2x^3-1))}{(ln(5))^2}$ = $\frac{( \frac{6x^2}{2x^3-1})(ln(5))}{(ln(5))^2}$ = $\frac{ \frac{6x^2}{2x^3-1}}{ln(5)}= \frac{6x^2}{(2x^3-1)(ln(5))}$

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Unity makes $56 a week, plus 15 percent of the cost of meals that she serves. Use the equation, y = 0.15x + 56, to predict what

seropon [69]

X represents the cost of meals served in a week. The cost of meals or worth was $435, therefore, x = 435. 0.15 x 435= 65.25
Since she makes $56 along with 15% of meals served (which is $65.25), you add those together to get her final income the week she serves $435 worth of meals, so...
66.25+56=121.25
Unity makes $121.25 in a week that she serves $435 worth of meals.

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2 years ago

a. In order for ΔABC to be similar to ΔDEF, what must be true about the angles? Be specific. b. If you know that ΔABC is similar

igomit [66]

I) if the triangles are similar then the corresponding angles are congruent. this means that the angles are of the same size.

ii) If ΔABC is similar to ΔDEF, therefore; m∠A = m∠D, m∠B=m∠E, and m∠C=m∠F,
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2 years ago

Will give brainliest, please help

Rus_ich [418]

Answer:

Step-by-step explanation:

A triangle always consists of it being 180 degrees. The box on the triangle on angle A depicts that it is a right angle, 90 degrees. And since Angle B is given at 45, angle C must be 45 degrees as well, since 180-45-90 (triangle angles=given angles for A and B) equal up to 45. When the angles beside the right angle is both identical and the same, the sides that correspond with that triangle is also the same. AC is given at 9 feet, and since Angle C and B both have the same angles, AB must ALSO be a 9ft.

Now, since we know the two sides, it is very easy to find BC, or the hypotenuse of the triangle, using the Pythagorean Theorem: $a^{2} +b^{2} =c^{2}$ , where a and b are sides, and c is the hypotenuse (or the long end) of a right triangle.

We can plug both 9s in for a and b since they're both the same, and it should equal to

9^2+9^2=c^2.

9^2 is 9*9, and that is 81. We have two of these so add them together to find 162. Since c^2 is equal to 162, we would need to square root both sides so we can find a number that equals c.

$\sqrt{162} =c$

We can either plug this into a calculator, and we should get something around 12.72, and that would be the same as C if you plug that value into a calculator.

You can also simplify the radical if you know how to. 162 is 81 times 2 (example) and 81 is 9*9, so we can add that to the outside and 2 is still under the radical. But this would only make sense if you know how to do that.

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Vlad1618 [11]

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