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4 years ago

Find the product. a^3b^2 • 4ab^3

Mathematics

1 answer:

attashe74 [19]4 years ago

8 0

Answer:

4a^4·b^5

Step-by-step explanation:

The applicable rule of exponents is ...

(x^a)(x^b) = x^(a+b)

The commutative and associative properties of multiplication apply, so we can write the expression as ...

4·(a^3·a)·(b^2·b^3) = 4·a^(3+1)·b^(2+3) = 4·a^4·b^5

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What is the definite integral of log (tan x) with range from 90 to 0

nasty-shy [4]

Substituting x with π/2 - x gives the equivalent integral,

$\displaystyle\int_0^{\frac\pi2}\log(\tan(x))\,\mathrm dx=-\int_{\frac\pi2}^0\log(\cot(x))(-\mathrm dx)=\int_0^{\frac\pi2}\log(\cot(x))\,\mathrm dx$

So if we let J denote the value of the integral, we have

$J=\displaystyle\int_0^{\frac\pi2}\log(\tan (x))\,\mathrm dx$

$J=\displaystyle\int_0^{\frac\pi2}\log(\cot (x))\,\mathrm dx$

$\implies 2J=\displaystyle\int_0^{\frac\pi2}\left(\log(\tan (x))+\log(\cot (x))\right)\,\mathrm dx$

Condensing the logarithms, we have

log(tan(x)) + log(cot(x)) = log(tan(x) cot(x)) = log(1) = 0

since cot(x) = 1/tan(x), which means

$2J=\displaystyle\int_0^{\frac\pi2}0\,\mathrm dx=0$

and so the original integral has a value of J = 0.

3 0

3 years ago

Inverse property of addition for real numbers

g100num [7]

Answer:

The answer would be -a

Step-by-step explanation:

In the examples,

5 + (-5) = 0

-1.33 + 1.33 = 0

THat means there will be a negative then a positive, or a positive then a negative.

INVERSE is the key word in this problem.

6 0

3 years ago

Ab with endpoints A(4,-6) and B(-4,2)

gayaneshka [121]

Answer: $d_{AB}=11.31\ units$

Step-by-step explanation:

The formula for calculate the distance between two points is:

$d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$

In this case, given the points A(4,-6) and B(-4,2), we can identify that, we just need to substitute values into the formula in order to calculate the distance between the given points.

Thierefore, this is (Rounded to the nearest hundred):

$d_{AB}=\sqrt{(4-(-4))^2+(-6-2)^2}\\\\d_{AB}=11.31\ units$

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4 years ago

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mylen [45]

$y = - \frac{3}{7}x - 3 \\$

Multiply sides by 7

$7y = - 3x - 21$

Plus sides 3x

$3x + 7y = 3x - 3x - 21$

$3x + 7y = - 21$

_________________________________

And we're done.....♥️♥️♥️♥️♥️

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