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3 years ago

How do i simplify log3(81x^4)

Mathematics

1 answer:

DerKrebs [107]3 years ago

3 0

Log(ab) = log(a) +log(b) . . . . . . . . . this is the whole point of logarithms

$\log_{3}(81x^{4})} = \log_{3}(3^{4}) +log_{3}(x^{4}) = 4+4log_{3}(x)$

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What is the sum of the first 60 positive integers?. (Points : 1). 60. . 61. . 1800. . 1830

stira [4]

Hello,

if 0 is a positive integer
sum=0+1+...+59=(0+59)*60/2=59*30=1770
else
sum=1+2+3+...+60=(1+60)*60/2=61*30=1830
end if

Answer D: 1830
In US, 0 is not positive, in Europe yes!!!

4 0

3 years ago

Which rule which allows us to change the sign of an exponent

ruslelena [56]

Answer:

Step-by-step explanation:

Given x³, we can write the equivalent expression -----------

x^(-3)

Given y^(-4) we can rewrite this as ----------

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Here we're applying the "rule of negative exponents."

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2 years ago

A cylinder has height of 10 millimeters and radius 12 millimeters.Find the a.volume and b. surface area.

Sholpan [36]

Answer:

A. Volume = 4,523.9 mm³ (cubic mm)

B. Surface area = 1,658.76 mm² (square mm)

Step-by-step explanation:

A. Lest's calculate the volume of the cylinder:

r = 12 mm, h = 10 mm

Volume = π * r² * h

Volume = 3.1416 * 12² * 10

Volume = 3.1416 * 144 * 10

Volume = 4,523.9 mm³

B. Let's calculate the surface area of the cylinder:

Surface area = 2π * r * h +2π * r²

Surface area =2π * 12 * 10 + 2π * 12²

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Surface area = 753.98 + 904.78 = 1,658.76 mm²

8 0

3 years ago

Box all final answers. Little to no work will reccive little to no credit! I. (5 points) Let A and B be 4 x 4 matrices, with det

FinnZ [79.3K]

Answer: a) -6, b) 32, c) -48, d) 9, e) -12

Step-by-step explanation:

Since we have given that

A and B are 4 × 4 matrices.

Here,

det (A) = -3

det (B) = 2

We need to find the respective parts:

a) det (AB)

$\mid AB\mid=\mid A\mid.\mid B\mid\\\\\mid AB\mid=-3\times 2=-6$

b) det (B⁵ )

$\mid B^5\mid=\mid B\mid ^5=2^5=32$

c) det (2A)

Since we know that

$\mid kA\mid =k^n\mid A\mid$

so, it becomes,

$\mid 2A\mid =2^4\mid A\mid=16\times -3=-48$

d) $\bold{det(A^TA)}$

Since we know that

$\mid A^T\mid=\mid A\mid$

so, it becomes,

$\mid A^TA\mid=\mid A^T\mid \times \mid A\mid=-3\times -3=9$

e) det (B⁻¹AB)

As we know that

$\mid B^{-1}\mid =\mid B\mid$

so, it becomes,

$\mid B^{-1}AB}\mid =\mid B^{-1}.\mid \mid A\mid.\mid B\mid=2\times -3\times 2=-12$

Hence, a) -6, b) 32, c) -48, d) 9, e) -12

6 0

3 years ago

What are the solutionso of 8x^2 = 6 + 22x

liraira [26]

You can get all the terms on one side, and then solve for x by any means:
$0 = -8x^2+22x+6$

Factor out a -2:
$0 = -2(4x^2-11x-3)$

Factor this equation:
$0 = 4x^2-11x-3$

I will use the AC method. To use it, first multiply a and c (in ax^2 + bx +c):
$4*-3 = -12$

Now, look for two numbers that multiply to -12 and add to -11. Obviously these numbers are -12 and 1. (-12*1 = -12 and -12+1 = -11). Now, because of rules, you set it up in a Punnett square:

4x^2 -12x
x -3

Now, we find common factors of the terms in rows:
_x_______-3__
4x| 4x^2 -12x
1 | x -3

So, you can use this to write an equivalent expression to the quadratic given:
$(x-3)(4x+1)$

Now, we known the factors are (solve for x): 3 and -1/4.

3 0

3 years ago

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