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3 years ago

What is the value of the digit 5

Mathematics

1 answer:

gulaghasi [49]3 years ago

7 0

The value digit of 5 is ten thousand

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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

3 years ago

Sqrtx^2+6x+9 if x≥3<br><br><br><br> please help quick idk how to do this at all

katrin [286]

Answer:

x+3

Step-by-step explanation:

sqrt(x^2+6x+9)

factor

We know this is a perfect square trinomial

sqrt(( x+3)^2)

Taking the square root of a square

x+3

7 0

3 years ago

Solve the system, using any method. y = x + 2 and x + 2y = 25

Leni [432]

$Elimination\ method\\\\\left\{\begin{array}{ccc}y=x+2&|subtract\ "x"\ from\ both\ sides\\x+2y=25\end{array}\right\\+\left\{\begin{array}{ccc}-x+y=2\\x+2y=25\end{array}\right|add\ the\ equations\ sides\ \\\----------\\.\ \ \ \ \ \ \ 3y=27\ \ \ \ \ |divide\ both\ sides\ by\ 3\\.\ \ \ \ \ \ \ \ \ \ y=9\\\\subtitute\ y=9\ to\ second\ equation\\x+2(9)=25\\x+18=25\ \ \ \ \ \ \ |subtract\ 18\ from\ both\ sides\\x=7\\\\Solution:x=7\ and\ y=9\to(7;\ 9)$