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3 years ago

Find the value of log(4) ∙ log(25) to five decimal places.

Mathematics

1 answer:

Fittoniya [83]3 years ago

8 0

Answer:0.84164

Step-by-step explanation:

Given

$\log \left ( 4\right )\cdot \log \left ( 25\right )$

we know

$\log a^b=b\log a$

Applying this identity we get

$\log \left ( 2\right )^2\cdot \log \left ( 5\right )^2$

$=2\log \left ( 2\right )\times 2\log \left ( 5\right )$

$=4\times \log \left ( 2\right )\cdot \left ( 5\right )$

$=4\times 0.301029\times 0.698970$

$=0.84164$

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Why are the soulution to the proportions 50/x = 10/20 and 10/50= 20/x

Marianna [84]

Answer:

Step-by-step explanation:

You should croos multiply to get 10x = 50 (20) which is 10x = 1000 then divide each side by 10. What do you get for x?

4 0

4 years ago

C=1/21.22.23+1/22.23.24+................+1/200.201.202 . = là dấu nhân

Aneli [31]

It looks like you have to find the value of the sum,

$C = \displaystyle \frac1{21\times22\times23} + \frac1{22\times23\times24} + \cdots + \frac1{200\times201\times202}$

so that the n-th term in the sum is

$\dfrac1{(21+(n-1))\times(21+n)\times(21+(n+1))} = \dfrac1{(n+20)(n+21)(n+22)}$

for 1 ≤ n ≤ 180.

We can then write the sum as

$\displaystyle C = \sum_{n=1}^{180} \frac1{(n+20)(n+21)(n+22)}$

Break up the summand into partial fractions:

$\dfrac1{(n+20)(n+21)(n+22)} = \dfrac a{n+20} + \dfrac b{n+21} + \dfrac c{n+22}$

Combine the fractions into one with a common denominator and set the numerators equal to one another:

$1 = a(n+21)(n+22) + b(n+20)(n+22) + c(n+20)(n+21)$

Expand the right side and collect terms with the same power of n :

$1 = a(n^2+43n+462)+b(n^2+42n+440) + c(n^2+41n + 420) \\\\ 1 = (a+b+c)n^2 + (43a+42b+41c)n + 462a+440b+420c$

Then

a + b + c = 0

43a + 42b + 41c = 0

462a + 440b + 420c = 1

==> a = 1/2, b = -1, c = 1/2

Now our sum is

$\displaystyle C = \sum_{n=1}^{180} \left(\frac1{2(n+20)}-\frac1{n+21}+\frac1{2(n+22)}\right)$

which is a telescoping sum. If we write out the first and last few terms, we have

C = 1/(2×21) - 1/22 + 1/(2×23)

… … + 1/(2×22) - 1/23 + 1/(2×24)

… … + 1/(2×23) - 1/24 + 1/(2×25)

… … + 1/(2×24) - 1/25 + 1/(2×26)

… … + … - … + …

… … + 1/(2×198) - 1/199 + 1/(2×200)

… … + 1/(2×199) - 1/200 + 1/(2×201)

… … + 1/(2×200) - 1/201 + 1/(2×202)

Notice the diagonal pattern of underlined and bolded terms that add up to zero (e.g. 1/(2×23) - 1/23 + 1/(2×23) = 1/23 - 1/23 = 0). So, like a telescope, the sum collapses down to a simple sum of just six terms,

C = 1/(2×21) - 1/22 + 1/(2×22) + 1/(2×201) - 1/201 + 1/(2×202)

which we simplify further to

C = 1/42 - 1/44 - 1/402 + 1/404

C = 1,115/1,042,118 ≈ 0.00106994

4 0

3 years ago

Find the distance between the points A and B given below.

marusya05 [52]

Step-by-step explanation:

Horizontal it is 4

Vertical it is 2

Use of Pythagoras theorem to find AB

AB= root of 4^2 + 2^2

= 4.47

6 0

3 years ago

Read 2 more answers

Find the slope of the line that goes through the given points (8,5) (6,7)

vazorg [7]

To find the slope of a line that goes through given points with known coordinates, you divide the subtraction of the y of the second point minus the y of the first point, by the subtraction of the x of the second point minus the x of the first point:
m = (yB-yA) / (xB-xA)

Let A(8,5) and B(6,7).
With yB = 7; yA = 5; xB = 6; xA = 8
m = (7-5) / (6-8)
m = 2/-2
m = -1

So the slope of the line that goes through the given points (8,5) and (6,7) is m = -1.

I've added a pic of the line with both points under the answer.

Hope this Helps! :)

4 0

3 years ago

Simplify the following algebraic expression.

Harman [31]

Answer:

In the picture

Step-by-step explanation:

I hope that a clear explanation

8 0

3 years ago