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3 years ago

What is the volume of the sphere below?

Mathematics

2 answers:

WINSTONCH [101]3 years ago

5 0

Answer:

The correct option is C.

Step-by-step explanation:

The radius of the sphere is 5 units.

The volume of a sphere is

$V=\frac{4}{3}\pi r^3$

Where, r is radius of the sphere.

$V=\frac{4}{3}\pi (5)^3$

$V=\frac{4}{3}\pi (125)$

$V=\frac{500}{3}\pi$

The volume sphere is $\frac{500}{3}\pi$ .

Therefore correct option is C.

jek_recluse [69]3 years ago

3 0

Volume = (4/3) * pi * 5^3

= 500 pi / 3

C

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The graph of a function is a parabola that has a minimum at the point (-3,9). Which equation could represent the function?

Scilla [17]

Answer:

$g(x)=2(x+3)^2+9$ , which corresponds to answer D.

Step-by-step explanation:

Recall that the maximum or minimum of a parabola is always located at its vertex. Notice that all quadratic functions listed are given in what is called "vertex" form, since they explicitly show the vertex coordinates in their formulation:

$f(x)=a(x-x_v)^2+y_v$ where $x_v$ , and $y_v$ stand for the x and y coordinates respectively of the vertex.

Examining all four options, we notice that in all four cases listed, the $y_v$ is correct (equal to positive 9), so we proceed to examine what the $(x-x_v)^2$ expression should look like for $x_v=-3$ :

Notice that when replace $x_v$ with "-3", we end up with a sign change:

$(x-x_v)^2\\(x-(-3))^2=(x+3)^2$

Therefore we find that the last two options can be candidates. Then we recall that the question also states that this should be a minimum. Then, for a parabola to have a minimum, its branches must go upwards, and this corresponds to a case in which the factor $a$ (leading coefficient) multiplying (x-x_v)^2 is positive. So in looking for such condition, we find that the very last option is the only one that verifies such.

Then, $g(x)=2(x+3)^2+9$ is the option we select.

4 0

4 years ago

The 90km/h bus runs between the two stations in 2 hours and 20 minutes.

AnnZ [28]

Answer:

1. distance is 210km

2. distance is 163•3km

Step-by-step explanation:

SPEED=DISTANCE÷TIME

90km/h= X ÷ 2 hrs and 20mins

CHANGE 20 MINS INTO HRS

1 hr = 60mins

? = 20mins

20mins * 1hr= 1/3hr

60mins

Speed=distance÷time

90km/h= X ÷ 21/3

Distance= speed * time

X = 90km/h * 21/3hrs

distance is 210km

Speed=distance ÷

70km/h= X ÷ 21/3hrs

Distance=speed * time

X = 70km/h * 21/3hrs

6 0

2 years ago

Write the equation of the line that passes through the point (-2,4) and has a slope of 4.

zheka24 [161]

Answer:

y-4x+12=0

Step-by-step explanation:

(x1,y1)=(2,-4) and m=4

y-y1=m(x-x1)

y-(-4)=4(x-2)

y+4=4x-8

y-4x+4+8=0

y-4x+12=0

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3 years ago

What is the degree of polynomial f (x) = 2x² - 5x+6 ?

valentina_108 [34]

Answer:

Step-by-step explanation:

The degree of a polynomial is its highest exponent value: in this case, thats just two!

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