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Alexus [3.1K]
3 years ago
14

Ln (3x+1)-ln (5+x) = ln 2

Mathematics
1 answer:
RideAnS [48]3 years ago
3 0
First you would simplify the left side to get,

ln( ( 3x+1 ) / ( 5+x ) ) = ln 2

Then raise both sides as the power of e, so it would basically cancel out the ln's.

3x+1 / 5+x = 2

3x+1 = 2( 5+x )

3x+1 = 10+2x

x = 9
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Write an exponential model given the points ( 7, 12 ) and ( 8, 25 ). Round to the nearest hundredth.
inna [77]

Answer:

The exponential model is y = 0.07\cdot e^{0.73\cdot x}.

Step-by-step explanation:

The exponential model can be modelled by the following mathematical expression:

y = A\cdot e^{B\cdot x} (1)

Where:

x - Independent variable.

y - Dependent variable.

A, B - Coefficients.

If we know that (x_{1}, y_{1}) = (7,12) and (x_{2}, y_{2}) = (8,25), then we get the following system of equations:

A\cdot e^{7\cdot B} = 12 (2)

A\cdot e^{8\cdot B} = 25 (3)

If we divide (3) by (2), we calculate the value of B:

e^{B}=\frac{25}{12}

B = \ln \frac{25}{12}

B \approx 0.734

And by (2), we determine the value of A:

A = 12\cdot e^{-7\cdot B}

A = 0.0704

The exponential model is y = 0.07\cdot e^{0.73\cdot x}.

4 0
3 years ago
The Temperature at 5:00 A.M. Is -38 F. The temperature rises 20 by 11:00 A.M. Use addition to find the temperature at 11:00 A.M.
GarryVolchara [31]
-38F + 20F equals -18F
8 0
3 years ago
Which statements about the pattern are true?
skelet666 [1.2K]
All the correct answers are C and D.
8 0
3 years ago
Read 2 more answers
I would like to know if I am solving correctly so far and what I do after this to continue solving.
12345 [234]
\bf A=\cfrac{13\cdot 3\sqrt{3}}{2}\implies A=\cfrac{39\sqrt{3}}{2}
4 0
4 years ago
For 12-13, use the figure. A bike path crosses a road as shown. Solve for each indicated angle or variable.
Volgvan

Answer:

x=21° and ∠KMH=96°

Step-by-step explanation:

From the given information that a bike path crosses a road and the given figure, we get

∠GMH=∠KMI=84°(Vertically opposite angles)

⇒4x=84°

⇒x=21°

therefore, the value of ∠GMH=4x=4(21)=84°

Now, ∠KMH+∠KMI=180°( Linear pair)

⇒∠KMH+84°=180°

⇒∠KMH=180-84

⇒∠KMH=96°

Thus, the value of ∠KMH is 96°

6 0
3 years ago
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