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Vadim26 [7]
1 year ago
12

Let g(x) = log7 (x), find g ¹(0)

Mathematics
1 answer:
klasskru [66]1 year ago
6 0

Step-by-step explanation:

The derivative of log is

\frac{d}{dx} ( log_{a}(x) ) =  \frac{1}{x \:  ln(a) }

You can easily derive this using the Change of base rule, and natural log rules

log_{a}(x)  =  \frac{ log_{e}(x) }{ log_{e}(a) }  =  \frac{ ln(x) }{ ln(a) }

Next, we differentiate with respect to x.

\frac{d}{dx} \frac{ ln(x) }{ ln(a) }  =  \frac{1}{ ln(a) }  \times  \frac{d}{dx}  ln(x)

=  \frac{1}{x ln(a) }

So back to the topic at hand,.

a=7, so we get

\frac{1}{x ln(7) }

We plug in 0, we would get undefined

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ABCD is a parallelogram.
Dmitry_Shevchenko [17]

Answer:

Using SAS they are congruent.

Step-by-step explanation:

E is the point where the diagonals AC and BD meet.

Side: AB = CD

Angle: ∠ABE = ∠EDC

Side: BE = DE

Hence by SAS theorem the two triangles are congruent.

7 0
3 years ago
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Let g(x)=Intragal from 0 to x f(t) dt, where r is the function whos graph is shown.
leonid [27]

If

\displaystyle g(x) = \int_0^x f(t) \, dt

then g(x) gives the signed area under f(x) over a given interval starting at 0.

In particular,

\displaystyle g(0) = \int_0^0 f(t) \, dt = 0

since the integral of any function over a single point is zero;

\displaystyle g(4) = \int_0^4 f(t) \, dt = 8

since the area under f(x) over the interval [0, 4] is a right triangle with length and height 4, hence area 1/2 • 4 • 4 = 8;

\displaystyle g(8) = \int_0^8 f(t) \, dt = 0

since the area over [4, 8] is the same as the area over [0, 4], but on the opposite side of the t-axis;

\displaystyle g(12) = \int_0^{12} f(t) \, dt = -8

since the area over [8, 12] is the same as over [4, 8], but doesn't get canceled;

\displaystyle g(16) = \int_0^{16} f(t) \, dt = 0

since the area over [12, 16] is the same as over [0, 4], and all together these four triangle areas cancel to zero;

\displaystyle g(20) = \int_0^{20} f(t) \, dt = 24

since the area over [16, 20] is a trapezoid with "bases" 4 and 8, and "height" 4, hence area (4 + 8)/2 • 4 = 24;

\displaystyle g(24) = \int_0^{24} f(t) \, dt = 64

since the area over [20, 24] is yet another trapezoid, but with bases 8 and 12, and height 4, hence area (8 + 12)/2 • 4 = 40, which we add to the previous area.

5 0
2 years ago
A company is expanding its building area from 14,000 square feet to 17,640 square feet. What is the percentage increase of the a
natali 33 [55]

Answer:

its about 7.9% I think .... ............

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2 years ago
Please answer with proof/work I give points
Phoenix [80]

Answer:

H. 8.874 hours

Step-by-step explanation:

There is a seven, that has the value of 7/100. 7/100 as a decimal is .07 because there is a 7 in the hundredths place. There has to be a number that contains 7/100, or a value in the hundredths place, and that is 8.874.

Hope this helps!

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