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3 years ago

Number 2 says Write the given equation in exponential form. Log8 1/512=-3

Mathematics

1 answer:

MA_775_DIABLO [31]3 years ago

7 0

In exponential form it is given as, 8⁻³ = $$\frac{1}{512}$

<u>Step-by-step explanation:</u>

We have to write the given equation in the exponential form, that is in the form of base to the power value.

Given:

log₈ ( $$\frac{1}{512}$ ) = -3

Here the base is 8.

In the exponential form, it is written as,

base to the power 3 = 512

Here the reciprocal of 512 is given, so,

base to the power -3 = $$\frac{1}{512}$

So the exponential form is given as, 8⁻³ = $$\frac{1}{512}$

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If a line has a slope of -5/6 a line that is parallel has a slope of what

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Hello there! :)

Parallel lines have the same slope.

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2 years ago

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3 years ago

What is 1/3 + 7/12 x 4

vova2212 [387]

$\frac{1}3+\frac{7}{12}*4$

According to the order of operations, you need to multiply first.

When you multiply into a fraction, the numerator (top number) changes.
In this case, you'd multiply the 7 by 4 to get 28.

$\frac{1}3+\frac{28}{12}$

To add fractions, they have to have the same denominator. (bottom number)
Let's find the lowest common denominator of 3 and 12.
Prime factorization of 3: 3
Prime factorization of 12: 2*2*3
Multiply all of these together, ignoring the duplicates.
2*2*3 = 12

How can we change 1/3 to have a denominator of 12?
Well, if you multiply or divide both the numerator and denominator of a fraction by the same number, it will stay equal. For instance, 1/2 = 2/4.
We want the 3 to become 12. That means we'd multiply by 4.
Multiplying 1 by 4 gives us 4.
Thus 1/3 = 4/12.

$\frac{4}{12}+\frac{28}{12}$

Now just add the numerators.

$\frac{32}{12}$

Since the top and bottom are both divisible by 2, we can simplify this by dividing them both by 2.

$\frac{16}6$

And again.

$\frac{8}3$

If you wanted that as an improper fraction, that would be $2\frac{2}3$ .

4 0

3 years ago

Read 2 more answers

Consider the curve defined by the equation y=6x2+14x. Set up an integral that represents the length of curve from the point (−2,

torisob [31]

Answer:

32.66 units

Step-by-step explanation:

We are given that

$y=6x^2+14x$

Point A=(-2,-4) and point B=(1,20)

Differentiate w.r. t x

$\frac{dy}{dx}=12x+14$

We know that length of curve

$s=\int_{a}^{b}\sqrt{1+(\frac{dy}{dx})^2}dx$

We have a=-2 and b=1

Using the formula

Length of curve= $s=\int_{-2}^{1}\sqrt{1+(12x+14)^2}dx$

Using substitution method

Substitute t=12x+14

Differentiate w.r t. x

$dt=12dx$

$dx=\frac{1}{12}dt$

Length of curve= $s=\frac{1}{12}\int_{-2}^{1}\sqrt{1+t^2}dt$

We know that

$\sqrt{x^2+a^2}dx=\frac{x\sqrt {x^2+a^2}}{2}+\frac{1}{2}\ln(x+\sqrt {x^2+a^2})+C$

By using the formula

Length of curve= $s=\frac{1}{12}[\frac{t}{2}\sqrt{1+t^2}+\frac{1}{2}ln(t+\sqrt{1+t^2})]^{1}_{-2}$

Length of curve= $s=\frac{1}{12}[\frac{12x+14}{2}\sqrt{1+(12x+14)^2}+\frac{1}{2}ln(12x+14+\sqrt{1+(12x+14)^2})]^{1}_{-2}$

Length of curve= $s=\frac{1}{12}(\frac{(12+14)\sqrt{1+(26)^2}}{2}+\frac{1}{2}ln(26+\sqrt{1+(26)^2})-\frac{12(-2)+14}{2}\sqrt{1+(-10)^2}-\frac{1}{2}ln(-10+\sqrt{1+(-10)^2})$