Part B: Solve 16x2 − 2x − 5 = 0 by using an appropriate method. Show the steps of your work,

A red container has 18 marbles. 5 of the marbles are black. Rest of the marbles are white and red. What additional information i

AveGali [126]

Your answer will be:

The total number of marbles that are not black.

7 0

3 years ago

Read 2 more answers

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

Can someone please help me I’m struggling

blagie [28]

Answer:

point form is (2,-1), equation form is x= 2, y=-1

Step-by-step explanation:

3 0

3 years ago

2x+5y=4 2x-2y=18 using the method of elimination

ExtremeBDS [4]

Answer:

Equation Form:

x=7,y=−2

Step-by-step explanation:

Multiply each equation by the value that makes the coefficients of x

opposite.

(−1)⋅(2x+5y)=(−1)(4)

2x−2y=18

Simplify.

−2x−5y=−4

2x−2y=18

Add the two equations together to eliminate x

from the system.

(−2x−5y=−4) +(2x−2y=18) = (-7y=14)

Divide each term by −7 and simplify.

y=−2

Substitute the value found for y into one of the original equations, then solve for x.

x=7

The solution to the independent system of equations can be represented as a point. (7,−2)

The result can be shown in multiple forms.

Point Form:

(7,−2)

Equation Form:

x=7,y=−2

8 0

3 years ago

Can deltamath see how long you spend on a question? Asking for a friend :)

melisa1 [442]

Answer:

Yes

Step-by-step explanation:

"data includes which problems where attempted, the time at which each problem was attempted, the answers the student submitted and whether they were correct, the duration the student was working on each problem, whether each assignment was completed on time and the completion percentage for each assignment" (paragraph 4).

Its on their privacy policy

5 0

3 years ago