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3 years ago

1.5/4x-1 = 0.4/x+4 find x

Mathematics

1 answer:

vitfil [10]3 years ago

6 0

Step-by-step explanation:

1.5/4x-1=0.4/x+4

We move all terms to the left:

1.5/4x-1-(0.4/x+4)=0

Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R

Domain of the equation: x+4)!=0

x∈R

We get rid of parentheses

1.5/4x-0.4/x-4-1=0

We calculate fractions

(1.5x)/4x^2+(-0.4*4x)/4x^2-4-1=0

We add all the numbers together, and all the variables

(+1.5x)/4x^2+(-0.4*4x)/4x^2-4-1=0

We add all the numbers together, and all the variables

(+1.5x)/4x^2+(-0.4*4x)/4x^2-5=0

We multiply all the terms by the denominator

(+1.5x)+(-0.4*4x)-5*4x^2=0

Wy multiply elements

-20x^2+(+1.5x)+(-0.4*4x)=0

We get rid of parentheses

-20x^2+1.5x-0.4*4x=0

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never [62]

The answer is letter C.

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3 years ago

A person jogs 1/2 miles in 1/12 hours. The person's speed is how many miles per hour?

ipn [44]

Answer:

6 miles per hour

Step-by-step explanation:

speed = distance/time

speed = 1/2÷1/12 which is the same as

1/2 x 12/1 = 6

6 miles per hour.

or ou could change the 1/2 to become 0.5

and the 1/12 to become 0.083333333

and divide 0.5 ÷ 0.083333333 = 6.000000024

rounded to one decima place become 6.0

6 miles per hour

5 0

3 years ago

Calculate s f(x, y, z) ds for the given surface and function. g(r, θ) = (r cos θ, r sin θ, θ), 0 ≤ r ≤ 4, 0 ≤ θ ≤ 2π; f(x, y, z)

Triss [41]

$g(r,\theta)=(r\cos\theta,r\sin\theta,\theta)\implies\begin{cases}g_r=(\cos\theta,\sin\theta,0)\\g_\theta=(-r\sin\theta,r\cos\theta,1)\end{cases}$

The surface element is

$\mathrm dS=\|g_r\times g_\theta\|\,\mathrm dr\,\mathrm d\theta=\sqrt{1+r^2}\,\mathrm dr\,\mathrm d\theta$

and the integral is

$\displaystyle\iint_Sx^2+y^2\,\mathrm dS=\int_0^{2\pi}\int_0^4((r\cos\theta)^2+(r\sin\theta)^2)\sqrt{1+r^2}\,\mathrm dr\,\mathrm d\theta$

$=\displaystyle2\pi\int_0^4r^2\sqrt{1+r^2}\,\mathrm dr=\frac\pi4(132\sqrt{17}-\sinh^{-1}4)$

###

To compute the last integral, you can integrate by parts:

$u=r\implies\mathrm du=\mathrm dr$

$\mathrm dv=r\sqrt{1+r^2}\,\mathrm dr\implies v=\dfrac13(1+r^2)^{3/2}$

$\displaystyle\int_0^4r^2\sqrt{1+r^2}\,\mathrm dr=\frac r3(1+r^2)^{3/2}\bigg|_0^4-\frac13\int_0^4(1+r^2)^{3/2}\,\mathrm dr$

For this integral, consider a substitution of

$r=\sinh s\implies\mathrm dr=\cosh s\,\mathrm ds$

$\displaystyle\int_0^4(1+r^2)^{3/2}\,\mathrm dr=\int_0^{\sinh^{-1}4}(1+\sinh^2s)^{3/2}\cosh s\,\mathrm ds$

$\displaystyle=\int_0^{\sinh^{-1}4}\cosh^4s\,\mathrm ds$

$=\displaystyle\frac18\int_0^{\sinh^{-1}4}(3+4\cosh2s+\cosh4s)\,\mathrm ds$

and the result above follows.

4 0

3 years ago

Best anwser gets brainlist ty show work

jekas [21]

Answer:

$36b^{6}$

Step-by-step explanation:

Using exponential rules, this simplifies to $6^{2} \cdot b^{3\cdot2} = 36b^{6}$ .

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3 years ago

Figure not drawn to scale.

DerKrebs [107]

Though you do not provide a diagram, I am going to give this a try by assuming that O is the center of the circle, OA is a radius, and angle AOB is a central angle that measures 88 degrees.

We want to find out the area of sector AOB. First, we need to find the area of the entire circle. The area of a circle is given by $A= \pi r^{2}$ and since the radius of this circle is equal to 1, the area is $\pi ( 1^{2} )= \pi$

Next we need to know what fraction of the circle sector AOB represents. The distance around the circle is 360 degrees but the central angle that intercepts arc AB is 88 degrees. That meas that the fraction of the circle the sector represents is given by $\frac{88}{360}= \frac{11}{45}$

We multiply this by the area to obtain $\frac{11}{45} \pi$ which is the area of the sector.

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3 years ago