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2 years ago

14

By first calculating the size of angle LMN,

1 answer:

Naily [24]2 years ago

4 0

Step-by-step explanation:

Hope it helps.... that is how I did it

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The radius of the base of a cylinder is increasing at a rate of 7 millimeters per hour. The height of the cylinder is fixed at 1

Ilya [14]

Answer:

The rate of change of the volume of the cylinder at that instant = $791.28\ mm^3/hr$

Step-by-step explanation:

Given:

Rate of increase of base of radius of base of cylinder = 7 mm/hr

Height of cylinder = 1.5 mm

Radius at a certain instant = 12 mm

To find rate of change of volume of cylinder at that instant.

Solution:

Let $r$ represent radius of base of cylinder at any instant.

Rate of increase of base of radius of base of cylinder can be given as:

$\frac{dr}{dt}=7\ mm/hr$

Volume of cylinder is given by:

$V=\pi\ r^2h$

Finding derivative of the Volume with respect to time.

$\frac{dV}{dt}=\pi\ h\ 2r\frac{dr}{dt}$

Plugging in the values given:

$\frac{dV}{dt}=\pi\ (1.5)\ 2(12)(7)$

$\frac{dV}{dt}=252\pi$

Using $\pi=3.14$

$\frac{dV}{dt}=252(3.14)$

$\frac{dV}{dt}=791.28\ mm^3/hr$ (Answer)

Thus rate of change of the volume of the cylinder at that instant = $791.28\ mm^3/hr$

6 0

2 years ago

What is 6 divided by 0.12

wolverine [178]

Answer:

50

Step-by-step explanation:

6/0.12=50

7 0

2 years ago

Write a division equation that shows 3 items being divided equally among 4 people. Express the answer as a fraction

madreJ [45]

Answer:3/4

Step-by-step explanation:

3 divided by 4=3/4

3 0

3 years ago

Read 2 more answers

3logbase5(x^2+9)-6=0

Pavlova-9 [17]

$3\log_5(x^2+9)-6=0$
$3\log_5(x^2+9)=6$
$\log_5(x^2+9)=2$
$5^{\log_5(x^2+9)}=5^2$
$x^2+9=25$
$x^2=16$
$x=\pm\sqrt{16}$
$x=\pm4$

5 0

3 years ago

Seven less than negative two times a number is greater than or equal to 41

kotegsom [21]

$Solution, -2n-7\ge \:41\quad :\quad \begin{bmatrix}\mathrm{Solution:}\:&\:x\le \:-24\:\\ \:\mathrm{Interval\:Notation:}&\:(-\infty \:,\:-24]\end{bmatrix}$

$Steps:$

$\mathrm{Add\:}7\mathrm{\:to\:both\:sides}, -2n-7+7\ge \:41+7$

$\mathrm{Simplify}, -2n\ge \:48\\\\$

$\mathrm{Multiply\:both\:sides\:by\:-1\:\left(reverse\:the\:inequality\right)}, \left(-2n\right)\left(-1\right)\le \:48\left(-1\right)$

$\mathrm{Simplify}, 2n\le \:-48$

$\mathrm{Divide\:both\:sides\:by\:}2, \frac{2n}{2}\le \frac{-48}{2}$

$\mathrm{Simplify}, n\le \:-24$

The correct answer is $n\le \:-24$

I hope this helps!!!

4 0

3 years ago