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3 years ago

Simplify 9 log9 (7) is the answer 7

1 answer:

3 0

$log_ab=c\ \ \ \Leftrightarrow\ \ \ a^c=b\\\\log_97=x\ \ \ \Leftrightarrow\ \ \ 9^x=7\\\\9^x=7\ \ \ (and \ \ \ x=log_97)\ \ \ \Rightarrow\ \ \ 9^{\big{log_97}}=7$

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The volume of a cone of radius r and height h is given by V=πr²h³. If the radius and the height both increase at a constant rate

Aloiza [94]

Answer:

The volume of cone is increasing at a rate 1808.64 cubic cm per second.

Step-by-step explanation:

We are given the following in the question:

$\dfrac{dr}{dt} = 12\text{ cm per sec}\\\\\dfrac{dh}{dt} = 12\text{ cm per sec}$

Volume of cone =

$V = \dfrac{1}{3}\pi r^2 h$

where r is the radius and h is the height of the cone.

Instant height = 9 cm

Instant radius = 6 cm

Rate of change of volume =

$\dfrac{dV}{dt} = \dfrac{d}{dt}(\dfrac{1}{3}\pi r^2 h)\\\\\dfrac{dV}{dt} = \dfrac{\pi}{3}(2r\dfrac{dr}{dt}h + r^2\dfrac{dh}{dt})$

Putting values, we get,

$\dfrac{dV}{dt} = \dfrac{\pi}{3}(2(6)(12)(9) + (6)^2(12))\\\\\dfrac{dV}{dt} =1808.64\text{ cubic cm per second}$

Thus, the volume of cone is increasing at a rate 1808.64 cubic cm per second.

5 0

3 years ago

Select the correct answer <br><br> what is the solution for x in the equation <br><br> 5/3x+4=2/3x

max2010maxim [7]

Answer:

x = -4

Step-by-step explanation:

4 = 2/3x - 5/3x

4 = -3/3x

4 = -x

-4 = x

4 0

2 years ago

What is the volume of a rectangular prism with length 13 cm, height 7 cm, and width 5 cm? 455 cm³ 455 cm 455 cm²

Rama09 [41]

Answer:

$455 cm^3$

Step-by-step explanation:

A three dimensional configuration with its face shaped of rectangle is called a Cuboid. So, the prism is in the shape of a cuboid.

The volume of a cuboid = Length *Breadth*Height

$=13cm*5cm*7cm\\=455cm^3$

The volume of the cuboid shaped prism is $455 cm^3$

7 0

3 years ago

What is the slope of this line??

Rom4ik [11]

Answer:

the slope is 0 sinse the line is parallel to x axis

8 0

3 years ago

50 is 20% of what number

Tresset [83]

20% of a number is 1/5th of it so 50 × 5 is 250

6 0

3 years ago