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3 years ago

Find the zeros (x-3)(x+5)=0

1 answer:

3 0

The product is equal zero if one of the factors is equal zero.Therefore:
$(x-3)(x+5)=0\iff x-3=0\ \vee\ x+5=0\\\\\boxed{x=3\ \vee\ x=-5}$

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A spherical balloon currently has a radius of 19cm. If the radius is still growing at a rate of 5cm or minute, at what rate is a

miv72 [106K]

Answer:

22670.8 cm³/min

Step-by-step explanation:

Given:

Radius of the balloon at a certain time (r) = 19 cm

Rate of growth of radius is, $\frac{dr}{dt}=5\ cm/min$

The rate at which the air is pumped in the balloon can be calculated by finding the rate of increase in the volume of the balloon.

So, first we find the volume of the sphere in terms of 'r'. As the balloon is spherical in shape, the volume of the balloon is equal to the volume of a sphere. Therefore,

Volume of balloon is given as:

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

Now, rate of increase of volume is obtained by differentiating both sides of the equation with respect to time 't'.

Differentiating both sides with respect to time 't', we get:

$\frac{dV}{dt}=\frac{d}{dt}(\frac{4}{3}\pi r^3)\\\\\frac{dV}{dt}=\frac{4\pi}{3}(3r^2)(\frac{dr}{dt})\\\\\frac{dV}{dt}=4\pi r^2(\frac{dr}{dt})$

Now, plug in 19 cm for 'r', 5 cm per minute for $\frac{dr}{dt}$ and solve for $\frac{dV}{dt}$ . This gives,

$\frac{dV}{dt}=4\pi (19 cm)^2(5\ cm/min)\\\\\frac{dV}{dt}=4\times 3.14\times 361\times 5\ cm^3/min\\\\\frac{dV}{dt}=22670.8\ cm^3/min$

Therefore, the rate at which the air is being pumped into the balloon is 22670.8 cm³/min.

4 0

3 years ago

PLEASE ANSWERRR NOW!!!

finlep [7]

The answer is [ yes; ΔJLK ~ ΔMLN by AA Similarity ]

AA similarity states that both triangles have corresponding angles that equal the same measure. Even though the question doesn't state the measure of the angles, the angles look the same.

ASA similarity states that two angles and a side equal the same in both triangles. Both triangles in the image aren't the same size, so, this is also false.

Best of Luck!

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hope this helps!
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Answer specify

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