A spherical balloon is inflated so that its volume is increasing at the rate of 3 cubic feet per minute. How fast is the radius of the balloon increasing when the radius is 2 feet?

a. First ball 200 m/s and second ball 400 m/s both in same direction

b. First ball 200 m/s opposite direction and second ball 0 m/s at rest

Now for elastic collision there is a formula including mass and velocity of first and second body.

Now,

m1 = mass of first body

m2 = mass of second body

u1 = initial velocity of first body

u2 = initial velocity of second body

v1= final velocity of first body

v2 = final velocity of second body

Formula for final velocities of both bodies are

v1 = [(m1-m2)/m1+m2)]*u1 + [(2m2)/(m1+m2)]*u2

v2 = [(2m1)/(m1+m2)]*u1 + [(m2-m1)/m2+m1)]*u2

Now according to given data

u1 = 200 m/s

u2 = 0 m/s

For a)

consider m2 = 0 kg (in comparison, first ball is much massive, so the mass of second ball is negligible)

Now by putting values of m2, u1 and u2, we get

v1  = u1

v2 = 2u1

Since u1 = 200 m/s

v1 = 200 m/s

v2 = 400 m/s and both will move in same direction that is from where first body was coming towards second body.

For b)

Consider m1 = 0 Kg for same assumption

Now by putting values of m1, u1 and u2, we get

v1 = -u1

v2 = 0

So v1 = 200 m/s in opposite direction after collision with massive body

v2 = 0 m/s which means that massive body will not move after collision and will be at rest but smaller body will move in opposite direction after collision in double speed.

learn more about of speed here

https://brainly.com/question/14845553

#SPJ4

Answer:

65%

Step-by-step explanation:

If I’m wrong please feel free to report me

The most likely to be the standard deviation(σ) of the normal distribution is equals to the fifteen. So, the right answer of problem is option(B).

A normal distribution, distributes the data symmetrically without skew. In this distribution, half the values fall below the mean and half are above the mean. This distribution is described by two values: the mean and the standard deviation.

We have, a doctor collects large set of heart rate measurements.

Mean of data, μ = 110 beats per minute

lower bound of Confidence interval

= 65 beats per minute

Upper bound confidence interval

= 155 beats per minute

So, confidence interval is (65,155)

Z-statistic value = 3

Using the Standard deviations in normal distribution Formula,

σ = (x - μ)/Z

Substitute all known values in above formula, we get

=> σ = (155 - 110)/3

=> σ = 45/3 = 15

Hence, the required standard deviation of the distribution is 15 .

To learn more about Standard deviations refer:

https://brainly.com/question/24298037

#SPJ4

Complete question:

A doctor collects a large set of heart rate measurements that approximately follow a normal distribution. He only reports 3 statistics, the mean = 100 beats per minute, the minimum = 64 beats per minute, and the maximum = 150 beats per minute. Which of the following is most likely to be the standard deviation of the distribution?

A. 5

B. 15

C. 90

The given linear equation  4x + 3.5 = 2(2x + 2) has no solution.

What is linear equation?

Equation shows the equality between two algebraic expressions by connecting the two algebraic expressions by an equal to sign.

A one degree equation is known as linear equation.

The given linear equation is

4x + 3.5 = 2(2x + 2)

Now,

4x + 3.5 = 2(2x + 2)

4x + 3.5 = 4x + 4

3.5 = 4 which is not possible

So the equation does not have any solution

To learn more about linear equation, refer to the link-

https://brainly.com/question/2030026

#SPJ1

Answer:

19 and 20

Step-by-step explanation:

Take the square root of 389

[tex]\sqrt{389} = 19.723...[/tex]

0.2019 is a fraction of the toasters that can be expected to fail during the fourth year of use  for  the given statistical studies

As it is the fraction of toasters that can be expected to fail during the fourth year of use. This is determined from a statistical study, which indicates that the fraction of electric toasters manufactured by a certain company that is still in working condition after t years of use is approximately 0.3012. To calculate the fraction of toasters expected to fail during the fourth year of use, we simply subtract 0.3012 from 1, which gives us 0.2019. This means that, according to the statistical study, approximately 20% of the electric toasters manufactured by the company can be expected to fail during the fourth year of use.

To know more  about statistical studies  refer to the link brainly.com/question/29220644

#SPJ4

Answer: 400% decrease

Step-by-step explanation: 8 divided by 2 is 4, converted to percent is 400%

Answer:

The answer to the previous question is -14. This is the result of evaluating the expression 3(x^2-6)+4xy when x=2 and y=-2.

Step-by-step explanation:

The given expression is 3(x^2-6)+4xy. Plugging in the values for x and y, we get 3(2^2-6)+4(2)(-2) = 3(-2)+(-8) = -6-8 = -14. Therefore, the result is -14 when x=2 and y=-2.

If f is a function from [0,1] to R and f is continuous, then there exists an x in [0,1] such that f(x) = 0.

What is a function?

In mathematics, a function is a rule that assigns a unique output to each input in a set. A function is continuous if the output value changes smoothly as the input value changes, without any sudden jumps or breaks.

To prove that if f is a function from [0,1] to R and f is continuous, then there exists an x in [0,1] such that f(x) = 0, we can use the intermediate value theorem.

The intermediate value theorem states that if a function f is continuous on a closed interval [a,b], and if y is any value between f(a) and f(b), then there exists at least one x in the interval [a,b] such that f(x) = y.

In our case, f is a function from [0,1] to R, which is a closed interval, and f is continuous on this interval. Therefore, the intermediate value theorem applies to f.

To prove that there exists an x in [0,1] such that f(x) = 0, we can use the intermediate value theorem with y = 0. Since 0 is between f(0) and f(1), the intermediate value theorem guarantees that there exists at least one x in [0,1] such that f(x) = 0.

Hence, if f is a function from [0,1] to R and f is continuous, then there exists an x in [0,1] such that f(x) = 0.

To learn more about the function, visit:

https://brainly.com/question/11624077

#SPJ4

Choose a row or column and perform Gaussian Elimination to reduce the matrix to row/column echelon form.Once the matrix is in row/column echelon form, the determinant can be found by multiplying the diagonal elements.

Let's take the matrix

A =

[1, 2, 3]

[4, 5, 6]

[7, 8, 9]

Choose the first column and perform Gaussian Elimination to reduce the matrix to row echelon form:

A =

[1, 2, 3]

[0, -3, -6]

[0, -6, -12]

The determinant of the matrix is found by multiplying the diagonal elements, which in this case is (1)(-3)(-12) = 36.

Learn more about matrix here

https://brainly.com/question/28180105

#SPJ4

The z-score of the number of books the newest employee sold is +1.80.

To find the z-score of the number of books the newest employee sold, you will need to know the mean and standard deviation of the number of books sold by the sales staff. You can then use the following formula to calculate the z-score:

z-score = (observation - mean) / standard deviation

Plugging in the values given in the problem, we get:

z-score = (number of books sold - mean) / standard deviation = (+1.80 - mean) / standard deviation

Solving for the number of books sold, we get:

number of books sold = mean + (z-score * standard deviation) = mean + (+1.80 * standard deviation)

number of books sold = +1.80

Learn more about z-score, here https://brainly.com/question/15016913

#SPJ4

Total 48 routes are possible for the hiking group to go from the town to

the village to the waterfall to their campsite.

Selections and combinations are synonyms. Combinations represent the choosing of items from a predetermined group of items. We're not trying to arrange anything here.

The combination formula is used to determine how many options there are for choosing things from a collection so that the order in which they are chosen is irrelevant. Combination, to put it simply, is the choosing of items or things from a bigger group when the order doesn't important.

Given:

Total Van to choose= 4

Total Bicycle to choose= 2

Total trails to choose = 6

So, the possible routes that can be chosen for hiking

= 4x 2 x 6

= 8 x 6

= 48 ways

Hence, there 48 possible ways.

Learn more about Combination here:

https://brainly.com/question/13387529

#SPJ1

a) Six-week learning and memory test: Both groups had a six-week learning and memory test.

b) According to Table A, the first five ginkgo trees are 103, 105, 107, 108, and 109.

(A) By randomly allocating people to treatment & control groups, randomized controlled trials are a form of experimental investigation that seeks to reduce bias. In this instance, the treatment group took tablets containing ginkgo extract, whereas the control group took pills containing a placebo. Prior to the initiation of therapy & again after six weeks, both groups underwent memory and learning tests.

The experiment's design may be summarized as follows:

Choosing the research population is folks over 60 who are in good health

Calculate the sample size: 230 people

Place individuals in control and treatment groups at random: The ginkgo group received half of the participants, while the placebo group received the other half.

Administering care: Pills containing ginkgo extract were given to the ginkgo group, whereas placebo pills were given to the placebo group.

Prior to starting therapy, both groups had their learning and memory skills tested.

Both groups underwent learning and memory ability tests six weeks later.

(b) According to the basic random sample applet, the first 20 members of the ginkgo Biloba subpopulation are:

11, 13, 15, 16, 18, 19, 20, 21, 22, 24, 25, 26, 27, 28, 29, 30, 32, 33, 34, 35

first 20 subjects using a placebo Those that participated are 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 14, 17, 23, 31, 36, 37, 38, 39, and 40. 

5 people: 103, 105, 107, 108, and 109

Learn more about the Simple Random Sample at

https://brainly.com/question/13219833

#SPJ4

An interval to estimate the true average tip is  (14.84,13.76).

The square root of the variance is used to calculate the standard deviation, a statistic that expresses how widely distributed a dataset is in relation to its mean. By calculating the deviation of each data point from the mean, the standard deviation may be determined as the square root of variance.

confidence interval = sample mean ± standard deviation /(n)^1/2

substitute the values in it then

confidence interval = 14.3  ± 2.7/(25)^1/2

confidence interval = 14.3 ± 2.7/5

confidence interval = 14.3 ± 0.54

confidence interval = 14.3 + 0.54 , confidence interval = 14.3 - 0.54

confidence interval = (14.84,13.76)

So, an interval to estimate the true average tip is  (14.84,13.76).

To learn more about mean visit:

brainly.com/question/14882017

#SPJ4

Answer:

B

Step-by-step explanation:

You always choose the most limited domain in these answers. And for c(x) the domain is all real numbers except 2, and the domain for d(x) is all real numbers.

So the domain is all real numbers except for 2 (most limited)

The domain of the function is all real values of x except x = 2. Therefore, option B is the correct answer.

Functions are the fundamental part of the calculus in mathematics. The functions are the special types of relations. A function in math is visualized as a rule, which gives a unique output for every input x.

Given that, c(x)=5/(x-2) and d(x)=x+3.

Here, (c·d)(x)=c(x)×d(x)

= 5/(x-2) × (x+3)

= 5(x+3)/(x-2)

= (5x+15)/(x-2)

Find the domain by finding where the expression is defined.

Interval Notation: (-∞,2)∪(2,∞)

Set-Builder Notation: {x|x≠2}

Therefore, option B is the correct answer.

To learn more about the function visit:

https://brainly.com/question/28303908.

#SPJ5

(a) The height of the slide is 34.64 feet .

(b) The angle of depression is θ = tan⁻¹(34.64/d)

(c) The interval for which the rider travels horizontally is (60 , 74.3) .

In the question ,

it is given that ,

the length of the ladder is = 40 feet .

the angle of elevation is 60° .

From the figure given below.

Part(a) :

Let the height of the slide be = h.

From the triangle ABC ,

Sin(60°) = h/l

So , h = 40×0.8660

h = 34.64 feet .

Part(b) :

let θ be the angle of depression .

So , From the triangle DEF ;

tanθ = DF/DE

tanθ = h/d

So , θ = tan⁻¹(34.64/d)

Part(c) :

Safety restrictions require the angle of depression of the slide to be no less than 25 and no more than 30° .

let  θ = 25° , then

tanθ = 34.64/d

So , tan25° = 34.64/d

d = 34.64/tan25°

d = 34.64/0.4663

Simplifying further ,

we get ,

d = 74.3 feet .

and θ = 30° , then

tan30° = 34.64/d

d = 34.64/tan30°

d = 34.64/0.5773

So , d = 60 feet .

So , the interval for which the rider travels horizontally is (60 , 74.3) .

Therefore , (a) The required height is 34.64 feet , (b) angle of depression is tan⁻¹(34.64/d) and (c) the interval is (60 , 74.3) .

Learn more about Trigonometry here

https://brainly.com/question/10643592

#SPJ4

The integral is thus. [tex]\int\limits{f(t)} \, dt[/tex]and limits will be 14 and 0

Describe statistics using an example.

A statistic is a numerical expression of a sample characteristic. The average amount of points obtained by students in one math class at the conclusion of the term, for instance, is an example of a statistic if we see that class as a sample of the population of all math classes.

Estimating the entire amount of coal generated in the US between 1997 and 2009 is the goal.

The information shows how much cola is produced year, in billions of tons.

The right-hand sum and the left-hand sum must be calculated in order to estimate the amount of coal produced.

with n = 7 and a hand sum

(2009 - 1997)/7 = Delta*t

The difference between every two years in the table is 2, which is another way to calculate Ar. So. t*delta = 2

The total on the left is.

The formula is: Delta*t[1.09 + 1.094 + 1.121 + 1.072 + 1.132 + 1.147] = 2[1.09 + 1.094 + 1.121 + 1.072 + 1.132 + 1.147] =13.312.

The amount on the right is.

Delta*I[1.094 plus 1.121 plus 1.072 plus 1.132 plus 1.147 plus 1.073] = 2[1.094 plus 1.121 plus 1.072 plus 1.132 + 1.147 + 1.073] = 13.278

Thus, using the left-hand addition, the total amount of coal produced in the United States between 1997 and 2009 is 13.312; using the right-hand sum, it is 13.278.

To show the production of coal from 1997 to 2009, create an integral.

Production of coal lasted for 14 years, from 1997 to 2009 (2009 – 1997 = 14). As r = f(t) (t).

The integral is thus. [tex]\int\limits{f(t)} \, dt[/tex]and limits will be 14 and 0

Learn more about statistics

https://brainly.com/question/15525560

#SPJ1

Answer:

54

Step-by-step explanation:

To evaluate the numerical expression for (22+5) / (12-9)x6, we need to follow the order of operations. The first step is to perform any operations inside parentheses, so we start by calculating the expressions inside the parentheses on the left-hand side of the equation: (22+5) = 27. Then we move to the right-hand side of the equation and perform the operations inside the parentheses there: (12-9) = 3. Next, we perform any multiplications or divisions in the order that they appear from left to right, so we divide 27 by 3 to get 9. Finally, we perform any remaining multiplications or divisions in the order that they appear from left to right, so we multiply 9 by 6 to get the final result: 54. Therefore, the numerical expression for (22+5) / (12-9)x6 is 54.

The eigenvalue of T are 0,1,2,3,4 and the corresponding eigenvectors are of the form c, cx, cx2, cx3, cx4, where c ∈ R and c≠ 0.

A typical element p of P4(R) is given by expression p(x)= a0 +a1x+a2x2 +a3x3 +a4x4,

where a0,  .... , a4 ∈ R.

With that expression, the eigenvalue-eigenvector equation Tp = λp, which in

this case is xp′(x) = λp(x), becomes

a1x+2a2x2 +3a3x3 +4a4x4 = λ(a0 +a1x+a2x2 +a3x3 +a4x4)

Comparing coefficients in the equation above, we see that the eigenvalue-eigenvector equation is equivalent to the system of equations

0 = λa0 a1 = λa1 2a2 = λa2 3a3 = λa3

4a4 = λa4.

From the equations above, we can see that if j ∈ {0, 1, 2, 3, 4} and aj≠ 0, then we have λ = j and ak = 0 for any k≠ j. Thus the eigenvalue of T are 0,1,2,3,4 and the corresponding eigenvectors are of the form c, cx, cx2, cx3, cx4, where c ∈ R and c≠ 0.

To learn more about the eigen vectors

https://brainly.com/question/22491077

#SPJ4

For the given data AB||CD , ∠CBD ≅ ∠ADB the triangle ABD is congruent to triangle CDB by SAS theorem of congruency.

As given in the question,

From the diagram it is given,

AB || CD

In  ΔABD and  ΔCDB

AB = CD  (Given)

∠CDB = ∠ABD (Given)

BD = BD (common side between two triangle)

so by SAS Congruence rule we have,

ΔABD ≅ ΔCDB.

SAS rule

According to the SAS congruence rule, if two sides and the included angle of one triangle are equal to two sides and the included angle of another triangle, the triangles are congruent.

Therefore, ΔABD ≅ ΔCDB using SAS congruence rule.

Learn more about SAS rule here :-

https://brainly.com/question/29549193

#SPJ4

Is 6.6 greater than -2.0? Yes, true. A positive number is always larger than a negative number.

Answer:

Yes, 6.6 is greater than -2.0

Step-by-step explanation:

If you ever have a positive and a negative number, the positive will be greater every time. ( 6.6 > -2.0 )

Answer:

Increasing on the interval:  (-2, 0) ∪ (2, ∞)

Decreasing on the interval:  (-∞, -2) ∪ (0, 2)

Step-by-step explanation:

A function is increasing when f'(x) > 0

A function is decreasing when f'(x) < 0

Therefore, to find the intervals for which the function is increasing and decreasing, differentiate the given function.

[tex]\boxed{\begin{minipage}{5.4 cm}\underline{Chain Rule for Differentiation}\\\\If $y=f(u)$ and $u=g(x)$ then:\\\\$\dfrac{\text{d}y}{\text{d}x}=\dfrac{\text{d}y}{\text{d}u}\times\dfrac{\text{d}u}{\text{d}x}$\\\end{minipage}}[/tex]

Given function:

[tex]f(x)=(x^2-4)^{\frac{2}{3}}[/tex]

[tex]\begin{aligned}\textsf{Let} \; u &= (x^2-4) \quad &\implies y&=u^{\frac{2}{3}}\\\\\implies \dfrac{\text{d}u}{\text{d}x}&=2x \quad &\implies \dfrac{\text{d}y}{\text{d}u}&=\dfrac{2}{3}u^{-\frac{1}{3}}=\dfrac{2}{3} (x^2-4)^{-\frac{1}{3}}\end{aligned}[/tex]

Therefore:

[tex]\implies \dfrac{\text{d}y}{\text{d}x}=\dfrac{\text{d}y}{\text{d}u}\times\dfrac{\text{d}u}{\text{d}x}[/tex]

[tex]\implies \dfrac{\text{d}y}{\text{d}x}=\dfrac{2}{3} (x^2-4)^{-\frac{1}{3}} \times 2x[/tex]

[tex]\implies f'(x)=\dfrac{4}{3}x (x^2-4)^{-\frac{1}{3}}[/tex]

[tex]\implies f'(x)=\dfrac{4x}{3 \sqrt[3]{x^2-4}}}[/tex]

Stationary points occur when f'(x) = 0:

[tex]\implies \dfrac{4x}{3 \sqrt[3]{x^2-4}}}=0[/tex]

[tex]\implies 4x=0[/tex]

[tex]\implies x=0[/tex]

Therefore, the function has is a stationary point (turning point) when x = 0.

The derivative is undefined when the denominator equals zero.

The denominator equals zero when x² = 4, so when x = ±2.

The derivative is positive when x > 2 and negative when x < -2.

Therefore, determine the nature of the derivative in the intervals between the stationary point x = 0 and x = ±2.

[tex]\implies f'(-1)=\dfrac{4(-1)}{3 \sqrt[3]{(-1)^2-4}}}=\dfrac{\rm negative}{\rm negative}= \rm positive > 0[/tex]

[tex]\implies f'(1)=\dfrac{4(1)}{3 \sqrt[3]{(1)^2-4}}}=\dfrac{\rm positive}{\rm negative}= \rm negative < 0[/tex]

Therefore, the function is:

The correct options are:

b) If A and B are independent , then P(A|B)=P(A)

c) If A and B are disjoint, then they cannot be independent

d) If A and B are disjoint, then P(A cap B)=0

Explanation:

a) If A and B are disjoint, then P(A) and P(B) must not equal each other because the sets have no elements in common. This means that the probability of any given event happening in either set is 0, and so P(A) and P(B) cannot be the same.

b) If A and B are independent, then P(A|B) = P(A) because the event that occurs in A has no impact on the probability of the event occurring in B. This is because the two events do not affect each other, so the probability of one happening does not change with the occurrence of the other.

c) If A and B are disjoint, then they cannot be independent because the two sets have no elements in common. This means that the events in A can affect the probability of events in B and vice versa. For example, if an event in A occurs, then it is impossible for an event in B to occur at the same time. This means that the events are not independent.

d) If A and B are disjoint, then P(A cap B) = 0 because the two sets have no elements in common.

e) They must not be independent because, Disjoint events are events that have no elements in common, so they cannot be independent since they are not related in any way. This means that the probability of A given B is also zero, which means that A and B cannot be independent.

To know more about probability visit here:

https://brainly.com/question/13604758

#SPJ4

a) Alex is closer to the state record.

b) The 8th grade should be awarded the 100 points.

The amounts are obtained applying the proportion for the unit conversion between feet and inches, as follows:

12 inches = 1 feet.

Alex jumped 38 feet 11 2/3 inches, hence the distance that Alex jumped, in feet, is given as follows:

38 + (11.67/12) = 38.98 feet.

(also conversion of mixed number to decimal, 11 and 2/3 = 11 + 2/3 = 11.67).

Alex' difference to the record of eight graders is given as follows:

40.17 - 38.98 = 1.19 feet.

Eric's difference to the record of seventh graders is given as follows:

38 + (1.6/12) - 36.89 = 1.24 feet.

1.19 feet is a smaller difference than 1.24 feet, hence Alex is closer to the state record.

As Alex was closer, and he is an eight grader, this means that the 8th grade should be awarded the 100 points.

More can be learned about proportions at https://brainly.com/question/24372153

#SPJ1

well, we simply add 4% to the 80 bucks, is all

[tex]\begin{array}{|c|ll} \cline{1-1} \textit{\textit{\LARGE a}\% of \textit{\LARGE b}}\\ \cline{1-1} \\ \left( \cfrac{\textit{\LARGE a}}{100} \right)\cdot \textit{\LARGE b} \\\\ \cline{1-1} \end{array}~\hspace{5em}\stackrel{\textit{4\% of 80}}{\left( \cfrac{4}{100} \right)80}\implies 3.2~\hfill \underset{total~cost}{\stackrel{80~~ + ~~3.2}{\text{\LARGE 83.2}}}[/tex]

We will need 40ml of 2% alcohol and 60ml of 7% alcohol to generate a solution of 100ml of 5% alcohol.

What is alchohol ?

Alcohol has addictive qualities and is a harmful, psychoactive drug. Alcoholic drinks are a common aspect of the social environment for many people in many modern nations. This is especially true for those who frequent highly visible, globally influential social settings where drinking often goes hand in hand with socialising. It is simple to ignore or minimise the harm that drinking does to one's health and society under this situation.

Let x and y be the quantities of the 2% and 7% alcohol solutions to be used to make 100ml of 5%, here we get the equation as,

[tex]x+y=100\\y=100-x[/tex]

Now, we can solve the problem to determine how many solutions there are:

[tex]2x+7y=5*100\\2x+7(100-x)=500\\-5x=-200\\x=40\\y=100-x\\y=100-40\\y=60[/tex]

We will need 40ml of 2% alcohol and 60ml of 7% alcohol to generate a solution of 100ml of 5% alcohol.

To learn more about alcohol checkout https://brainly.com/question/11908844

#SPJ4

Answer:

Step-by-step explanation:

To find the distance between the complex numbers -3 + 5i and 2 - 9i, we can use the distance formula for complex numbers, which is given by:

d = sqrt((a - b)^2 + (c - d)^2)

where a, b, c, and d are the real and imaginary parts of the two complex numbers. In this case, a = -3, b = 2, c = 5, and d = -9, so we can substitute these values into the distance formula to get:

d = sqrt((-3 - 2)^2 + (5 + 9)^2)

= sqrt((-5)^2 + (14)^2)

= sqrt(25 + 196)

= sqrt(221)

= 11

Therefore, the distance between -3 + 5i and 2 - 9i is 11.

The nonzero vector orthogonal to the plane through the points P,Q and R is -7i + 7j -21k and the area of the triangle is 11.6 square units.

(a)Given points are P(-1,3,1) , Q(0,7,2) and R(4,2,-1)

PQ = Q - P

= (0 - (-1))i + (7 - 3)j + (2 -1)k

=i + 4j + k

PR = R - P

= (4 - (-1))i + (2 - 3)j + (-1 - 1)k

5i -j - 2k

The orthogonal vector is PQ x QR

[tex]\left[\begin{array}{ccc}i&j&k\\1&4&1\\5&-1&-2\end{array}\right][/tex]

(-8 + 1)i - (-2 - 5)j + (-1 -  20))k

-7i + 7j - 21k

Therefore the nonzero vector orthogonal to the plane through the points P,Q and R is -7i + 7j - 21k

(b) The area of the triangle with the vertices P,Q and R is the half of the length of the cross product of PQ and QR.

Area = 1/2| PQ x QR|

= 1/2 √(7² + (-7)² + (-21)²)

= 1/2 √(49 + 49 + 441)

= 1/2 (23.21)

= 11.60

= 11.60 square units.

Therefore The non zero vector is  -7i + 7j - 21k and the area of the triangle is 11 .6 square units.

To learn more about vector refer here

https://brainly.com/question/3184914

#SPJ4