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3 years ago

Help. help. help. alegbra ll honors

Mathematics

2 answers:

telo118 [61]3 years ago

7 0

A. 2 or -4

it is undefined when the denominator is 0
set x^2+2x-8 equal to 0

it can be factored as (x-2)(x+4)
so the zeros would be 2 and -4

geniusboy [140]3 years ago

3 0

Answer:

Step-by-step explanation:

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lutik1710 [3]

Left 4. Or x-4 because the way it moves

3 0

3 years ago

1.) Find the length of the arc of the graph x^4 = y^6 from x = 1 to x = 8.

xxTIMURxx [149]

First, rewrite the equation so that y is a function of x :

$x^4 = y^6 \implies \left(x^4\right)^{1/6} = \left(y^6\right)^{1/6} \implies x^{4/6} = y^{6/6} \implies y = x^{2/3}$

(If you were to plot the actual curve, you would have both $y=x^{2/3}$ and $y=-x^{2/3}$ , but one curve is a reflection of the other, so the arc length for 1 ≤ x ≤ 8 would be the same on both curves. It doesn't matter which "half-curve" you choose to work with.)

The arc length is then given by the definite integral,

$\displaystyle \int_1^8 \sqrt{1 + \left(\frac{\mathrm dy}{\mathrm dx}\right)^2}\,\mathrm dx$

We have

$y = x^{2/3} \implies \dfrac{\mathrm dy}{\mathrm dx} = \dfrac23x^{-1/3} \implies \left(\dfrac{\mathrm dy}{\mathrm dx}\right)^2 = \dfrac49x^{-2/3}$

Then in the integral,

$\displaystyle \int_1^8 \sqrt{1 + \frac49x^{-2/3}}\,\mathrm dx = \int_1^8 \sqrt{\frac49x^{-2/3}}\sqrt{\frac94x^{2/3}+1}\,\mathrm dx = \int_1^8 \frac23x^{-1/3} \sqrt{\frac94x^{2/3}+1}\,\mathrm dx$

Substitute

$u = \dfrac94x^{2/3}+1 \text{ and } \mathrm du = \dfrac{18}{12}x^{-1/3}\,\mathrm dx = \dfrac32x^{-1/3}\,\mathrm dx$

This transforms the integral to

$\displaystyle \frac49 \int_{13/4}^{10} \sqrt{u}\,\mathrm du$

and computing it is trivial:

$\displaystyle \frac49 \int_{13/4}^{10} u^{1/2} \,\mathrm du = \frac49\cdot\frac23 u^{3/2}\bigg|_{13/4}^{10} = \frac8{27} \left(10^{3/2} - \left(\frac{13}4\right)^{3/2}\right)$

We can simplify this further to

$\displaystyle \frac8{27} \left(10\sqrt{10} - \frac{13\sqrt{13}}8\right) = \boxed{\frac{80\sqrt{10}-13\sqrt{13}}{27}}$

7 0

3 years ago

Solve and round answer to nearest hundredth please.

MA_775_DIABLO [31]

Answer:

Step-by-step explanation:

Solve this by using natural logs. Taking the natural log of both sides:

$ln(7*16^{8x-8})=ln(3)$

To undo the multiplication, we use addition:

$ln(7)+ln(16)^{8x-8}=ln(3)$

The rule says we can now bring the exponent down in front of the ln:

$ln(7)+(8x-8)ln(16)=ln(3)$

Now we will subtract ln(7) from both sides:

(8x - 8)ln(16) = ln(3) - ln(7)

Now we will divide both sides by ln(16):

$8x-8=\frac{ln(3)-ln(7)}{ln(16)}$ then add 8 to both sides:

$8x=\frac{ln(3)-ln(7)}{ln(16)}+8$ which simplifies to

8x = 7.694401895 so

x = .9618002368 or, rounded,

x = .96

(Rest assured I did the math and checked the answer and it checked out perfectly!) I recommend you learn the laws of natural and common logs cuz they're kinda important!! :)

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3 years ago

A rectangler prism and a cylinder have the same height. the length of each side of the prism base is equal to the diameter of th

nexus9112 [7]

Answer: The rectangular prism?

7 0

3 years ago

What's the difference between two whole number 1/2 percent of 36 and 30% of 10

AlexFokin [52]

Here, we proceed step by step, to obtain our answer,

$\frac{1}{2}$ % of 36 can be written as ,