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4 years ago

SOMEONE HELP PLEASE

Mathematics

2 answers:

gulaghasi [49]4 years ago

8 0

Answer:

So the correct answer is option B- ( b - a )

Step-by-step explanation:

Given that M and N are the mid-points of RT and ST.

We are to find the length of MN.

As shown in the figure,

the co-ordinates of the point T are (2c, 2d),

the co-ordinates of the point S are (2b, 0),

and

the co-ordinates of the point R are (2c, 2d).

Since M is the mid-point of TR, so the co-ordinates of M are

$\left(\dfrac{2c+2a}{2},\dfrac{2d+0}{2}\right)$ =(c+a,d).

Also, N is the mid-point of TS, the co-ordinates of N are

$\left(\dfrac{2c+2b}{2},\dfrac{2d+0}{2}\right)$ =c+b,d)(.

Therefore, the length of the line segment MN calculated using distance formula will be

MN= $\sqrt{(c+b-c-a)^2+(d-d)^2}=\sqrt{(b-a)^2}$ =b-a.

Thus, the required length of MN is (b - a) units.

Option (B) is correct.

yan [13]4 years ago

7 0

I have this same question, can anyone answer it?

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I can't figure out how to do (i + j) x (i x j)for vector calc

Vinil7 [7]

In three dimensions, the cross product of two vectors is defined as shown below

$\begin{gathered} \vec{A}=a_1\hat{i}+a_2\hat{j}+a_3\hat{k} \\ \vec{B}=b_1\hat{i}+b_2\hat{j}+b_3\hat{k} \\ \Rightarrow\vec{A}\times\vec{B}=\det (\begin{bmatrix}{\hat{i}} & {\hat{j}} & {\hat{k}} \\ {a_1} & {a_2} & {a_3} \\ {b_1} & {b_2} & {b_3}\end{bmatrix}) \end{gathered}$

Then, solving the determinant

$\Rightarrow\vec{A}\times\vec{B}=(a_2b_3-b_2a_3)\hat{i}+(b_1a_3+a_1b_3)\hat{j}+(a_1b_2-b_1a_2)\hat{k}$

In our case,

$\begin{gathered} (\hat{i}+\hat{j})=1\hat{i}+1\hat{j}+0\hat{k} \\ \text{and} \\ (\hat{i}\times\hat{j})=(1,0,0)\times(0,1,0)=(0)\hat{i}+(0)\hat{j}+(1-0)\hat{k}=\hat{k} \\ \Rightarrow(\hat{i}\times\hat{j})=\hat{k} \end{gathered}$

Where we used the formula for AxB to calculate ixj.

Finally,

$\begin{gathered} (\hat{i}+\hat{j})\times(\hat{i}\times\hat{j})=(1,1,0)\times(0,0,1) \\ =(1\cdot1-0\cdot0)\hat{i}+(0\cdot0-1\cdot1)\hat{j}+(1\cdot0-0\cdot1)\hat{k} \\ \Rightarrow(\hat{i}+\hat{j})\times(\hat{i}\times\hat{j})=1\hat{i}-1\hat{j} \\ \Rightarrow(\hat{i}+\hat{j})\times(\hat{i}\times\hat{j})=\hat{i}-\hat{j} \end{gathered}$

Thus, (i+j)x(ixj)=i-j

8 0

1 year ago

A country is planning to decrease government spending in order to reduce the national debt. If the outlined changes are put into

SOVA2 [1]

<u>Answer</u>

Graph D represents the national debt of the country over the next years.

<u>Solution-</u>

The country's debt will decrease exponentially by one-third each year.

Current debt is $60 billion.

This problem can be treated as an exponential decay problem.

The general exponential decay function is,

$y=a(r)^{-x}$

Where,

a = initial value,

r = rate of change,

-ve sign of x represents the decrease in value of y as x increases.

Here, the rate of change is 3 as each year the debt becomes on third, and initial value of debt is $60, so

$y=60(3)^{-x}$

Plotting a graph taking number of year on x-axis and debt on y-axis, we can generate a graph for this function.

Putting different values of x, we can get the values of y. So the graph must have (0, 60), (1, 20), (2, 6.66), (3, 2.22), (4, 0.74), (5, 0.24) points on it.

Option B and C are incorrect, as they do not start from 60. (they don't have (0,60) on their curve)

Between option A and D, curve in D has all the points on it. So D is the correct graph.

5 0

3 years ago

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