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3 years ago

Kamal wrote the augmented matrix below to represent a system of equations.

Mathematics

2 answers:

atroni [7]3 years ago

8 0

Answer:

Step-by-step explanation:

edge

Sergio039 [100]3 years ago

7 0

Answer:

$\left[\begin{array}{cccc}1&0&1&|-1\\-3&-9&3&|27\\3&2&0&|-2\end{array}\right]$

Step-by-step explanation:

Given [Missing from the question]

$\left[\begin{array}{cccc}1&0&1&|-1\\1&3&-1&|-9\\3&2&0&|-2\end{array}\right]$

Required

$R_2 \to -3R_2$

This implies that, we form a new matrix where the second row of the new matrix is a product of -3 and the second row of the previous matrix.

So, we have:

$Initial =\left[\begin{array}{cccc}1&0&1&|-1\\1&3&-1&|-9\\3&2&0&|-2\end{array}\right]$

$New =\left[\begin{array}{cccc}1&0&1&|-1\\-3*1&-3*3&-3*-1&|-3*-9\\3&2&0&|-2\end{array}\right]$

$New =\left[\begin{array}{cccc}1&0&1&|-1\\-3&-9&3&|27\\3&2&0&|-2\end{array}\right]$

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An open cylinderical tank of radius 70cm contains 385 liters of a liquid find the volume of liquid In a tank

san4es73 [151]

Answer:

5.5

Step-by-step explanation:

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3 years ago

What is 8/28 in simplest form??

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3 years ago

If P(A)=0.4, P(A and B)=0.2,and P(A or B)=0.5, What is P(B)

Vladimir [108]

Answer:

$\boxed{\ P(B)=0.3 \ }$

Step-by-step explanation:

Hi,

We know that

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6 0

3 years ago

The radius of a cone is increasing at a constant rate of 7 meters per minute, and the volume is decreasing at a rate of 236 cubi

storchak [24]

Answer:

The rate of change of the height is 0.021 meters per minute

Step-by-step explanation:

From the formula

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

Differentiate the equation with respect to time t, such that

$\frac{d}{dt} (V) = \frac{d}{dt} (\frac{1}{3}\pi r^{2}h)$

$\frac{dV}{dt} = \frac{1}{3}\pi \frac{d}{dt} (r^{2}h)$

To differentiate the product,

Let r² = u, so that

$\frac{dV}{dt} = \frac{1}{3}\pi \frac{d}{dt} (uh)$

Then, using product rule

$\frac{dV}{dt} = \frac{1}{3}\pi [u\frac{dh}{dt} + h\frac{du}{dt}]$

Since $u = r^{2}$

Then, $\frac{du}{dr} = 2r$

Using the Chain's rule

$\frac{du}{dt} = \frac{du}{dr} \times \frac{dr}{dt}$

∴ $\frac{dV}{dt} = \frac{1}{3}\pi [u\frac{dh}{dt} + h(\frac{du}{dr} \times \frac{dr}{dt})]$

Then,

$\frac{dV}{dt} = \frac{1}{3}\pi [r^{2} \frac{dh}{dt} + h(2r) \frac{dr}{dt}]$

Now,

From the question

$\frac{dr}{dt} = 7 m/min$

$\frac{dV}{dt} = 236 m^{3}/min$

At the instant when $r = 99 m$

and $V = 180 m^{3}$

We will determine the value of h, using

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

$180 = \frac{1}{3}\pi (99)^{2}h$

$180 \times 3 = 9801\pi h$

$h =\frac{540}{9801\pi }$

$h =\frac{20}{363\pi }$

Now, Putting the parameters into the equation

$\frac{dV}{dt} = \frac{1}{3}\pi [r^{2} \frac{dh}{dt} + h(2r) \frac{dr}{dt}]$

$236 = \frac{1}{3}\pi [(99)^{2} \frac{dh}{dt} + (\frac{20}{363\pi }) (2(99)) (7)]$

$236 \times 3 = \pi [9801 \frac{dh}{dt} + (\frac{20}{363\pi }) 1386]$

$708 = 9801\pi \frac{dh}{dt} + \frac{27720}{363}$

$708 = 30790.75 \frac{dh}{dt} + 76.36$

$708 - 76.36 = 30790.75\frac{dh}{dt}$

$631.64 = 30790.75\frac{dh}{dt}$

$\frac{dh}{dt}= \frac{631.64}{30790.75}$

$\frac{dh}{dt} = 0.021 m/min$

Hence, the rate of change of the height is 0.021 meters per minute.

3 0

3 years ago

a rectangular prism has a volume of 810 cubic meters. it has a length of 10 meters and a width of 9 meters. What is the height o

Ainat [17]

Answer:

The height of the prism is 9 meters

Step-by-step explanation:

* Lets describe the rectangular prism

- The rectangular prism has six rectangular faces

- Two of them are bases and the other four are side faces

- The rectangular prism has three dimensions length, width , height

- The volume of any prism = Area of the base × its height

∵ The base of the rectangular prism is a rectangle

∵ Area any rectangle = length × width

∴ The volume of the rectangular prism V = length × width × height

* Lets solve the problem

∵ The volume of the prism is 810 meter³

∵ Its length is 10 meter

∵ Its width is 9 meters

∵ V = length × width × height

- Substitute the values of the volume , the length and the width in

the equation of V

∴ 810 = 10 × 9 × h

∴ 810 = 90 × h

- Divide both sides by 90

∴ 9 = h

∴ The height of the prism is 9 meters

6 0

4 years ago