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3 years ago

What are the solutions to the equation and check for extraneous solutions: 16=(x-2)^2/3

Mathematics

1 answer:

GuDViN [60]3 years ago

5 0

Answer:

we have x = -62 or x = 66

Step-by-step explanation:

16=(x-2)^2/3

I would take square root first

4 = (x - 2)^ (1/3)

or -4 = (x - 2)^(1/3)

.....

4^3 = x - 2

64 = x - 2

x = 66

or -4 ^3 = x - 2

-64 = x - 2

x = -62

we have x = -62 or x = 66

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How could the fact 36/6=6 help you estimate the quotient of 364,573/64?

butalik [34]

Because when you round 364,573 to the nearest thousand , you get 360,000 and when you round 64 , you get 60 and if you take away the zeros, the equation is basically 36÷6

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3 years ago

3. A prop for the theater club’s play is constructed as a cone topped with a half-sphere. What is the volume of the prop? Round

Mariana [72]

The volume of the prop is calculated to be 2,712.96 cubic inches.

<u>Step-by-step explanation:</u>

Step 1:

The prop consists of a cone and a half-sphere on top. We will have to calculate the volumes of the cone and the half-sphere separately and then add them to obtain the total volume.

Step 2:

The volume of a cone is determined by multiplying $\frac{1}{3}$ with π, the square of the radius (r²) and height (h). Here we substitute π as 3.14. The radius is 9 inches and the height is 14 inches.

The volume of the cone : $V=\pi r^{2} \frac{h}{3}$ = $3.14 \times 9^{2} \times \frac{14}{3}$ = 1,186.92 cubic inches.

Step 3:

The area of a half-sphere is half of a full sphere. The volume of a sphere is given by multiplying $\frac{4}{3}$ with π and the cube of the radius (r³).

Here the radius is 9 inches. We take π as 3.14.

The volume of a full sphere = $V=\frac{4}{3} \pi r^{3}$ = $\frac{4}{3} \times 3.14 \times 9^{3}$ = 3,052.08 cubic inches.

The volume of the half-sphere = $\frac{3,052.08}{2}$ = 1,526.04 cubic inches.

Step 4:

The total volume = The volume of the cone + The volume of the half sphere,

The total volume = 1,186.92 + 1,526.04 = 2,712.96 cubic inches.

5 0

3 years ago

Un paese contava 12000 abitanti all'inizio del 2007 durante l'anno i nati sono 1,7 % del totale degli abitanti e morti sono 2% c

grandymaker [24]

Step-by-step explanation:

12000 abitanti all'inizio del 2007

nati: 1.7% × 12000 = 204

morti: 2% × 12000 = 240

popolazione all'inizio del 2008: 12000 + 204 - 240 = 11964

6 0

2 years ago

Question 7

Kipish [7]

Answer:

true

Step-by-step explanation:

-7=4*-3+5

-7=-12+5

4 0

2 years ago

Engineers want to design seats in commercial aircraft so that they are wide enough to fit 99% of all males. (accommodating 100

Helga [31]

Hip Breadths and Aircraft Seats
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3 years ago