Enter the rate of change of the table below

Mathematics

1 answer:

poizon [28]2 years ago

4 0

The rate of change is 23

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

goblinko [34]

$D:x-2\ \textgreater \ 0 \wedge 2x-3\ \textgreater \ 0 \wedge x\ \textgreater \ 0\\
D:x\ \textgreater \ 2 \wedge x\ \textgreater \ \dfrac{3}{2}\wedge x\ \textgreater \ 0\\
D:x\ \textgreater \ 2\\\\
\ln (x-2) +\ln (2x-3)=2\ln x \\
\ln (x-2)(2x-3)=\ln x^2\\
(x-2)(2x-3)=x^2\\
2x^2-3x-4x+6=x^2\\
x^2-7x+6=0\\
x^2-x-6x+6=0\\
x(x-1)-6(x-1)=0\\
(x-6)(x-1)=0\\
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\boxed{x=6}$

4 0

3 years ago

Drag the tiles to the correct boxes to complete the pairs. Not all tiles will be used. Match each triangle below with the value

Dmitriy789 [7]

Answer:

30, 9, 15, 29

Step-by-step explanation:

Triangle 1, yellow

b= √34²- 16²= √900= 30

Triangle 2, blue

a= √41²- 40²= √81= 9

Triangle 3, green

c= √12²+9²= √225= 15

Triangle 4, red

c= √21²+20²= √841= 29

8 0

3 years ago

Find the tenth term of the geometric sequence, given the first term and common ratio.

Natalija [7]

Answer:

$a_{10}=\dfrac{1}{128}$

Step-by-step explanation:

In the geometric series:

$a_1=4\\ \\r=\dfrac{1}{2}$

The nth term of the geometric sequence can be calculated using formula

$a_n=a_1\cdot r^{n-1}$

In your case, n = 10, then

$a_{10}\\ \\=4\cdot \left(\dfrac{1}{2}\right)^{10-1}\\ \\=4\cdot \left(\dfrac{1}{2}\right)^9\\ \\=2^2\cdot \dfrac{1}{2^9}\\ \\=\dfrac{1}{2^{9-2}}\\ \\=\dfrac{1}{2^7}\\ \\=\dfrac{1}{128}$