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4 years ago

What is the sum of 4.9 × 10^2 and 6.8 × 10^3?

1 answer:

5 0

The correct answer is letter choice E.
The answer is letter choice E because 4.9 times 10 to the 2nd power which is 490. Then you calculate 6.8 times 10 to the 3rd power which is 6800.
After you calculate these two equations you then add the answer which is 6800+490 which equals (=) 7290.
Letter choice E is the only accurate answer to equal to 7290. How I figured this out is by calculating 7.29 times 10 to the 3rd power the correct answer to this equation is 7290.
It matches equivalently with the problem so the answer is E.

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write the standard form of the equation of the circle for which the endpoints of a diameter are (0,0) and (4,-6)

Elenna [48]

Given:

The endpoints of a diameter are (0,0) and (4,-6).

To find:

The equation of the circle.

Solution:

The endpoints of a diameter are (0,0) and (4,-6). So, the length of the diameter is

$d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$

$d=\sqrt{(-6-0)^2+(4-0)^2}$

$d=\sqrt{36+16}$

$d=\sqrt{52}$

$d=2\sqrt{13}$

Now, radius is half of the diameter.

$r=\dfrac{2\sqrt{13}}{2}$

$r=\sqrt{13}$

Center of the circle is the midpoint of the endpoints of a diameter.

$Center=\left(\dfrac{x_1+x_2}{2},\dfrac{y_1+y_2}{2}\right)$

$Center=\left(\dfrac{0+4}{2},\dfrac{0+(-6)}{2}\right)$

$Center=\left(\dfrac{4}{2},\dfrac{-6}{2}\right)$

$Center=\left(2,-3\right)$

Standard form of a circle is

$(x-h)^2+(y-k)^2=r^2$

where, (h,k) is center and r is radius.

The center of the circle is (2,-3) and radius is $\sqrt{13}$ . So,

$(x-2)^2+(y-(-3))^2=(\sqrt{13})^2$

$(x-2)^2+(y+3)^2=13$

Therefore, the standard form of the circle is $(x-2)^2+(y+3)^2=13$ .

5 0

3 years ago

A melting spherical block of ice has its surface area changing at the rate of 24 inch2 /sec at the time the radius is 3 inches.

emmainna [20.7K]

The surface area of the sphere is:
A = 4 * pi * r ^ 2
Deriving we have:
A '= 8 * pi * r * r'
We clear the speed:
r '= A' / (8 * pi * r)
Substituting values:
r '= 24 / (8 * pi * 3)
r '= 1 / pi inch / sec
Then, the volume of the sphere is:
V = (4/3) * (pi) * (r ^ 3)
Deriving we have:
V '= (3) * (4/3) * (pi) * (r ^ 2) * (r')
Substituting values:
V '= (3) * (4/3) * (pi) * (3 ^ 2) * (1 / pi)
Rewriting:
V '= (4) * (9)
V '= 36 inch3 / sec
Answer:
the volume of the ice is changing at 36 inch3 / sec at that moment

4 0

3 years ago

There are 8 times as many females as males on the maths course at university. What fraction

Serga [27]

Answer:

8/9 of the course are males.

4 0

3 years ago

JOD, hele he earns $8 per hour. His employer always rounds up to the nearest quarter of an hour. For example, if

Nesterboy [21]

Answer:

where is the question at?