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2 years ago

Which statement best reflects the solution(s) of the equation?

Mathematics

1 answer:

e-lub [12.9K]2 years ago

4 0

Answer:

There's only one solution x = 2

Thr solution x = 1 is an extraneous solution.

Step-by-step explanation:

$\frac{1}{x - 1} + \frac{2}{x} = \frac{x}{x - 1} \\ \frac{2}{x} = \frac{x}{x - 1} - \frac{1}{x - 1} \\ \frac{2}{x} = \frac{x - 1}{x - 1} \\ \frac{2}{x} = 1 \\ 2 = x$

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Given the arc length of a circle is 127π centimeters and the subtended angle is 60˚. Find the Circumference of the circle.

Mumz [18]

The circumference of the circle is 762π cm.

<h3>What is length of arc of a circle?</h3>

The length of arc a circle can is determined with the radius and central angle of the arc.

The radius of the circle is calculated as follows;

$L = \pi r \times \frac{ \theta }{180} \\\\
\pi r \theta = 180 L\\\\
\pi r = \frac{180 L}{\theta}$

The circumference of the circle is calculated as follows;

$C = 2\pi r\\\\
C = 2(\pi r)\\\\
C = 2(\frac{180 \ L}{\theta } )\\\\
C = 2(\frac{180 \times 127\pi}{60 } )\\\\
C = 762 \pi \ cm$

Learn more about circumference of a circle here: brainly.com/question/9782777

4 0

2 years ago

A is an m×n matrix.Check the true statements below:A. The kernel of a linear transformation is a vector space.B. If the equation

Bess [88]

Answer:

Results are (1) True. (2) False. (3) False. (4) True. (5) True. (6) True.

Step-by-step explanation:

Given A is an $m\times n$ matrix. Let $T :U\to V$ be the corresponding linear transformationover the field F and $\theta$ be identity vector in V. Now if $x\in Ker( T)\implies T(x)=\theta$ .

(1) The kernel of a linear transformation is a vector space : True.

Let $x,y\in Ker( T)$ , then,

$T(x+y)=T(x)+T(y)=\theta+\theta=\theta\impies x+y\in Ker( T)$

hence the kernel is closed under addition.

Let $\lambda\in F, x\in Ker( T)$ , then

$T(\lambda x)=\lambda T(x)=\lambda\times \theta=\theta$

$\lambda x\in Ker(T)$ and thus Ket(T) is closed under multiplication

Finally, fore all vectors $u\in U$ ,

$T(\theta)=T(\theta+(-\theta))=T(\theta)+T(-\theta)=T(\theta)-T(\theta)=\theta$

$\implies \theta\in Ker(T)$

Thus Ker(T) is a subspace.

(2) If the equation Ax=b is consistent, then Col(A) is $\mathbb R^m$ : False

if the equation Ax=b is consistent, then Col(A) must be consistent for all b.

(3) The null space of an mxn matrix is in $\mathbb R^m$

: False

The null space that is dimension of solution space of an m x n matrix is always in $\mathbb R^n$ .

(4) The column space of A is the range of the mapping $x\to Ax$

: True.

(5) Col(A) is the set of all vectors that can be written as Ax for some x. : True.

Here Ax will give a linear combination of column of A as a weights of x.

(6) The null space of A is the solution set of the equation Ax=0.

: True

5 0

3 years ago

Please solve (-3×+15)+(-3×+2)

koban [17]

(-3x + 15) + (-3x + 2)
Simplify by combining like terms.
-6x + 17

-6x + 17

3 0

3 years ago

Read 2 more answers

Let A(t) be the area of a circle with radius r(t), at time t in min. Suppose the radius is changing at the rate of drdt=6 ft/min

mylen [45]

Answer:

The rate of change is $108\pi$ ft^(2)/min

Step-by-step explanation:

The area of a circle is given by the following equation:

$A(t) = \pi r^{2}$

To solve this question, we have to realize the implicit differentiation in function of t. We have two variables, A and r. So

$\frac{dA(t)}{dt} = 2\pi r \frac{dr}{dt}$

We have that:

$\frac{dr}{dt} = 6, r = 9$ .

We want to find $\frac{dA}{dt}$

$\frac{dA(t)}{dt} = 2\pi*9*6$

$\frac{dA}{dt} = 108\pi$

Since the area is in square feet, the rate of change is in ft^(2)/min.

So the rate of change is $108\pi$ ft^(2)/min

5 0

3 years ago

What statement is true?

givi [52]

Answer:

$\frac{18}{32}>\frac{16}{32}$

Step-by-step explanation:

We need to find which statements are true.

Solution to find the same we will solve each statement and will conclude the same.

1. $\frac{14}{21}>\frac{17}{24}$

Now On solving we get;

$\frac{14}{21} = 0.66$

$\frac{17}{24}=0.70$

So we can see that 0.70 > 0.66

Hence The given statement is False.

2. $\frac{18}{32}>\frac{16}{32}$

Now On solving we get;

$\frac{18}{32}=0.5625$

$\frac{16}{32}= 0.5$

So we can see that 0.5625 > 0.5

Hence The given statement is True.

3. $\frac{20}{15}$

Now On solving we get;

$\frac{20}{15} = 1.33$

$\frac{28}{23}=1.2$

So we can see that 1.33 > 1.2

Hence The given statement is False.

4. $\frac{29}{35}$

Now On solving we get;

$\frac{29}{35}= 0.82$

$\frac{20}{30}= 0.66$

So we can see that 0.82 > 0.66

Hence The given statement is False.

7 0

3 years ago