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Readme [11.4K]
3 years ago
5

Differentiate Functions of Other Bases In Exercise, find the derivative of the function.

Mathematics
2 answers:
Klio2033 [76]3 years ago
7 0

Answer:

dy/dx = [1/ln(10)][(2x+6)/(x^2 +6x)]

Step-by-step explanation:

See attachment

WARRIOR [948]3 years ago
3 0

Answer:

\dfrac{dy}{dx} =\dfrac{2 x + 6}{ \log{\left (10 \right )}\left(x^{2} + 6 x\right)}

Step-by-step explanation:

given

y = \log_{10}{(x^2+6x)}

using the property of log \log_ab=\frac{log_cb}{log_ca}, and if c =e,\log_ab=\frac{ln{b}}{ln{a}}, we can rewrite our function as:

y = \dfrac{\ln{\left (x^{2} + 6 x \right )}}{\ln{\left (10 \right )}}

now we can easily differentiate:

\dfrac{dy}{dx} = \dfrac{1}{\ln{10}}\left(\dfrac{d}{dx}(\ln{(x^{2} + 6x)})\right)

\dfrac{dy}{dx} = \dfrac{1}{\ln{10}}\left(\dfrac{2x+6}{x^{2} + 6x}\right)

\dfrac{dy}{dx} =\dfrac{2 x + 6}{ \log{\left (10 \right )}\left(x^{2} + 6 x\right)}

This is our answer!

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What is an absolute value? What does it do? When would we need to use an absolute value
Nana76 [90]
Absolute Value Absolute Value means ...

... only how far a number is from zero:

<span> <span><span> </span> <span> <span> "6" is 6 away from zero,
and "−6" is also 6 away from zero. So the absolute value of 6 is 6,
and the absolute value of −6 is also 6 </span> </span> </span></span>

More Examples:

<span><span>The absolute value of −9 is 9</span><span>The absolute value of 3 is 3</span><span>The absolute value of 0 is 0</span><span>The absolute value of −156 is 156</span></span> No Negatives!

So in practice "absolute value" means to remove any negative sign in front of a number, and to think of all numbers as positive (or zero).

Absolute Value Symbol

To show that we want the absolute value of something, we put "|" marks either side (they are called "bars" and are found on the right side of a keyboard), like these examples:

<span> <span><span> |−5| = 5 |7| = 7 </span> </span></span> Sometimes absolute value is also written as "abs()", so abs(−1) = 1 is the same as <span>|−1| = 1</span>
3 0
3 years ago
Read 2 more answers
Could 18 in, 6 in, 13 in form a triangle
Tanya [424]

Answer: Yes

Step-by-step explanation:

The reason on why it could form a triangle because 18 is the highest side in the triangle and if you have 2 of the smaller sides that are greater than the larger size then you could form a triangle and 13 and 6 equals to 19 so you could make a triangle hopes this helps and have a good day.

7 0
3 years ago
The weights of a certain brand of candies are normally distributed with a mean weight of 0.8544 g and a standard deviation of 0.
aleksandr82 [10.1K]

Answer:

The probability is 0.508 = 50.8%.

Step-by-step explanation:

Normal Probability Distribution:

Problems of normal distributions can be solved using the z-score formula.

In a set with mean \mu and standard deviation \sigma, the z-score of a measure X is given by:

Z = \frac{X - \mu}{\sigma}

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

Normally distributed with a mean weight of 0.8544 g and a standard deviation of 0.0525 g.

This means that \mu = 0.8544, \sigma = 0.0525

If 1 candy is randomly​ selected, find the probability that it weighs more than 0.8535 g.

This is 1 subtracted by the pvalue of Z when X = 0.8535. So

Z = \frac{X - \mu}{\sigma}

Z = \frac{0.8535 - 0.8544}{0.0525}

Z = -0.02

Z = -0.02 has a pvalue of 0.492

1 - 0.492 = 0.508

The probability is 0.508 = 50.8%.

8 0
3 years ago
Please answer this question picture shown !!
Naddik [55]
The answer is choice D because the expression 6x^3+x^2-3 is the same as 6x^3+1x^2+0x+(-3). Notice the coefficients are 6, 1, 0, -3

The expression x-7 is in the form x-k where k = 7. This is the test root which is placed outside of the synthetic division bar as shown in choice D.
4 0
3 years ago
H(a) = 2a +4<br> g(a) = 4a + 2<br> Find (h+g)(a)
hjlf

Answer:

8−4 a

Step-by-step explanation:

x=g(h(a−4))

h(a−4)=−2(a−4)−5 = −2 a+8−5=3−2 a

Apply g.

g(h(a−4))=g(3−2a)=2(3-2a)+2=6−4a+2

3 0
3 years ago
Read 2 more answers
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