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3 years ago

PLEASE HELP!!!! Solve the equation. Check for extraneous solutions. Type your answers in the blanks. Show your work.

Mathematics

1 answer:

Licemer1 [7]3 years ago

5 0

|4x+3|=9+2x if we square both sides, we can eliminate the absolute values signs...

16x^2+24x+9=81+36x+4x^2 subtract the right side from both sides

12x^2-12x-72=0 now we can factor

12(x^2-x-6)=0

12(x^2+2x-3x-6)=0

12(x(x+2)-3(x+2)=0

12(x-3)(x+2)

So:

x= -2 or 3

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Find the equation of the circle that passes through the points (0,0), (2,0)&(3,-3)

-Dominant- [34]

Answer:

Step-by-step explanation:

A(0,0), B(2,0), C(3,-3)

Perpendicular bisector of AB: x=1

Perpendicular bisector of AC: y=x-3

Center of circle = intersection of perpendicular bisectors = (1,-2)

Radius = √5

(x-1)² + (y+2)² = 5

3 0

3 years ago

Which logorithmic equation is equivalent to the exponential equation below? e^a=60

Alex73 [517]

Answer:

a = ln(60)

Step-by-step explanation:

4 0

3 years ago

Please show work! Factor sin^2Θ + sin^2Θ cos^2Θ

ivanzaharov [21]

Factorization of sin²θ + sin²θ cos²θ gives us; 2sin²θ - sin⁴θ

<h3>How to simplify Trigonometric Functions?</h3>

We want to simplify;

sin²θ + sin²θ cos²θ

Let us factorize out sin²θ to get;

sin²θ(1 + cos²θ)

Now, we know that cos²θ = 1 - sin²θ

Thus;

sin²θ(1 + cos²θ) = sin²θ(1 + 1 - sin²θ)

⇒ sin²θ(2 - sin²θ)

⇒ 2sin²θ - sin⁴θ

Read more about Trigonometric functions at; brainly.com/question/6904750

#SPJ1

5 0

2 years ago

Liam is saving up for a new cell phone. He uses the equation P= I + HB, where P is the cost

Stels [109]

Answer:

$H=\dfrac{P-I}{B}$

Step-by-step explanation:

Given the expression: P= I + HB

Where:

P = cost of the phone Liam is saving for.
I = amount of money he started with.
H = number of hours he babysits
B = hourly rate for babysitting.

We want to find an expression for H, the number of hours Liam will need to babysit to save enough money for a cell phone.

Our goal is to isolate the variable H in the expression P= I + HB.

P= I + HB

Subtract I from both sides

P-I=I-I+HB

HB=P-I

Divide both sides by B

$\dfrac{HB}{B} =\dfrac{P-I}{B}\\\\$Therefore\\\\H=\dfrac{P-I}{B}$

4 0

3 years ago

Find the flux of F = x^3 i + y^3 j + z^3k through the closed surface bounding the solid region x^2 + y^2 ≤ 4, 0 ≤ z ≤ 4

givi [52]

Use the divergence theorem. Let $R$ be the cylindrical region, then

$\displaystyle\iint_{\partial R}\mathbf F\cdot\mathbf n\,\mathrm dS=\iiint_R\nabla\cdot\mathbf F\,\mathrm dV$

(where $\mathbf n$ denotes the unit normal vector to $\partial R$ , but we don't need to worry about it now)

We have

$\mathrm{div }\mathbf F=(\nabla\cdot\mathbf F)(x,y,z)=\dfrac{\partial\mathbf F}{\partial x}+\dfrac{\partial\mathbf F}{\partial y}+\dfrac{\partial\mathbf F}{\partial z}$
$\nabla\cdot\mathbf F=3x^2+3y^2+3z^2$

For the solid $R$ with boundary $\partial R$ , we can set up the following volume integral in cylindrical coordinates for ease:

$\displaystyle3\iiint_R(x^2+y^2+z^2)\,\mathrm dV=3\int_{z=0}^{z=4}\int_{\theta=0}^{\theta=2\pi}\int_{r=0}^{r=2}(r^2+z^2)r\,\mathrm dr\,\mathrm d\theta\,\mathrm dz$
$=\displaystyle6\pi\int_{z=0}^{z=4}\int_{r=0}^{r=2}(r^3+rz^2)\,\mathrm dr\,\mathrm dz$
$=\displaystyle12\pi\int_{z=0}^{z=4}(2+z^2)\,\mathrm dz$
$=352\pi$

5 0

3 years ago