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STALIN [3.7K]
3 years ago
5

Which of the following is an extraneous solution of (45-3x)^1/2=x-9?

Mathematics
1 answer:
Iteru [2.4K]3 years ago
3 0

Answer:

C. x =3

Step-by-step explanation:

Extraneous solution is that root of a transformed equation that doesn't satisfy the equation in it's original form because it was excluded from the domain of the original equation.

Let's solve the equation first

\sqrt{45-3x} = x-9\\Taking\ square\ on\ both\ sides\\{(\sqrt{45-3x})}^2 = {(x-9)}^2\\45-3x = x^2-18x+81\\0 = x^2-18x+81-45+3x\\x^2-15x+36 = 0\\x^2-12x-3x+36 = 0\\x(x-12)-3(x-12) = 0\\(x-3)(x-12)\\x-3 = 0\\=> x =3\\x-12 = 0\\x = 12\\We\ will\ check\ the\ solutions\ one\ by\ one\\So,\\for\ x=3\\\sqrt{45-3(3)} = 3-9\\\sqrt{45-9} = -6\\\sqrt{36}= -6\\6\neq -6\\For x=12\\\sqrt{45-3(12)} = 12-9\\\sqrt{45-36} = 6\\\sqrt{36}= 6\\6=6

Hence, we can conclude that x=3 is an extraneous solution of the equation ..

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When the shaded region below is rotated about the x-axis the resulting solid is a circular cone with radius 2 m and height 3 m.
WARRIOR [948]

Answer:

Therefore, the volume of the cone is V=4π.

Step-by-step explanation:

From task we have a circular cone with radius 2 m and height 3 m. We use the disk method to find the volume of this cone.  

We have the formula:

\boxed{V=\int_0^h\pi \cdot \left(\frac{r}{h}x\right)^2\, dx}

We know that r=2 and h=3, and we get:

V=\int_0^3\pi \cdot \left(\frac{2}{3}x\right)^2\, dx\\\\V=\int_0^3 \pi \frac{4}{9}x^2\, dx\\\\V= \frac{4\pi}{9} \int_0^3 x^2\, dx\\\\V= \frac{4\pi}{9} \left[\frac{x^3}{3}\right]_0^3\, dx\\\\V= \frac{4\pi}{9}\cdot 9\\\\V=4\pi

Therefore, the volume of the cone is V=4π.

7 0
3 years ago
What is the solution set for the following system of equations 5x-3y-10=0 x+y-7=0
garik1379 [7]

(x, y) = ( \frac{31}{8}, \frac{25}{8})

given the 2 equations

5x - 3y - 10 = 0 → (1)

x + y - 7 = 0 → (2)

rearrange (2) to obtain y in terms of x

y = 7 - x → (3)

Substitute y = 7 - x into (1)

5x - 3(7 - x) - 10 = 0

5x - 21 + 3x - 10 = 0

8x - 31 = 0 ( add 31 to both sides )

8x = 31 ( divide both sides by 8 )

x = \frac{31}{8}

Substitute this value into (3) for y

y = 7 - x = \frac{56}{8} - \frac{31}{8} = \frac{25}{8}


6 0
3 years ago
The population of a town has grown at an annual rate of 2.7%. How long does it take for it’s population of 18,450 people to doub
charle [14.2K]
It would take 26 years.

The equation will be in the form y = a(1+r)ˣ, where a is the initial population, r is the growth rate as a decimal number, and x is the amount of time.  Using our information we have

y = 18450(1+0.027)ˣ = 18450(1.027)ˣ

We want the population to be doubled; 18450*2 = 36900:
36900 = 18450(1.027)ˣ

Divide both sides by 18450:
36900/18450 = 18450(1.027)ˣ/18450
2 = 1.027ˣ

Using logarithms, we have
\log_{1.027}2=x
\\
\\x=26.017
3 0
3 years ago
HELP PLEASE 9TH GRADE MATH
Neko [114]

Answer:

B

Step-by-step explanation:

Perpendicular lines have a reciprocal slope with the opposite sign. The y-intercept does not matter

5 0
3 years ago
Which expression is equivalent to 3(5x-4)
erastovalidia [21]

Answer:

15x - 12

Step-by-step explanation:

3(5x - 4)

15x - 12 using the distributive property

BRAINLIEST IS APPRECIATED

4 0
3 years ago
Read 2 more answers
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