Find the volume of a square based pyramid with a base length of 7 and a height of 12

The value of y² is 1/5 ln(3+x¹⁰) + C

What is the separation of variables?

Separation of variables, in mathematics, is any of several strategies for rewriting equations so that each of two variables appears on a different side of the problem. These strategies are used to solve ordinary and partial differential equations.

Here, we have

Given: (3+^10)(/) = ^9/

We have to solve the differential equation by using the separation of variables.

Rewrite as y dy = x⁹/3+x¹⁰ dx

As (3+x¹⁰)' = 10x⁹, we solve

y²/2 = 1/10 ln(3+x¹⁰) + C

y² = 1/5 ln(3+x¹⁰) + 2C

Since C is any constant, y²  = 1/5 ln(3+x¹⁰) + C

Hence, the value of y² is 1/5 ln(3+x¹⁰) + C

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The missing length is given as follows:

LN = 44.

The theorem used to solve this problem is given as follows:

A line parallel to one side of a triangle divides the other two proportionately.

The parallel lines for this triangle are given as follows:

VU and LM.

Hence the proportional relationship regarding the remaining side lengths is given as follows:

x/24 = 11/8

Applying cross multiplication, we have that:

8x = 24 x 11

x = 3 x 11

x = 33.

Hence the missing length is given as follows:

LN = 33 + 11

LN = 44.

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This means E is the same fraction of the b metres above the floor, so is ab/a+b metres above the floor.

What is equal angles ?

Equal angles can be defined as the angles which are equal .

Given ,

The picture shows two ladders propped against facing walls. The end of the first ladder is 5m above the base of the second wall. The second

ladder is 5m above the base of the first wall.

the angles ∠BAD and ∠ADC are alternate angles, and therefore equal. Likewise, angles ∠ABC and BCD are also alternate and therefore equal.

∠BEA and ∠CED are opposite, which means that they are equal. You can see these equal angles in the diagram on the right.

This means that the triangles ABE and DCE have the same angles as each other, and are therefore similar.

so,

This means:

AE/ED=AB/DC=5m/10m=1/2

Therefore AE=1/3 AD.

This means E is 1/3 of the way up from the floor to D, so is at a height of

This means E is 13 of the way up from the floor to D, so is at a height of 10m/ 3=3 1/3m

If instead B is a metres above the floor, then:

AE/ED=AB/DC=a/10

Therefore AE=a/10+a AD.

This means E is the same fraction of the 10m above the floor, so is 10a/10+a metres above the floor.

If instead D is b metres above the floor, then:

AE/ED=AB/DC=a/b

Therefore AE=a/a+b AD.

This means E is the same fraction of the b metres above the floor, so is ab/a+b metres above the floor.

Therefore, This means E is the same fraction of the b metres above the floor, so is ab/a+b metres above the floor.

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Answer:

Step-by-step explanation:

Answer:

244.5

Step-by-step explanation:

Use A Budgeting Calc This Anwser Is Correct

A. To find the correlation coefficient, we can use the formula:

r = (n * Σxy - Σx * Σy) / √ ((n * Σx² - (Σx)²) * (n * Σy² - (Σy)²))

Where n is the number of data points.

Plugging in the values for the given data set:

r = (12 * 712.94 - 1451.9 * 511.6) / √ ((12 * 1297.14 - 1451.9²) * (12 * 636.35 - 511.6²))

r = -0.636

So, the correlation coefficient is -0.636.

B. To find the proportion of the variation in y that can be explained by the variation in x, we can use the formula:

r² = r²

r² = (-0.636) ²

r² = 0.40496

So, 40.5% of the variation in y can be explained by the variation in the values of x.

C. To find the regression line,we can use the formula:

y = a + bx

Where a is the y-intercept and b is the slope of the line.

To find b, we can use the formula:

b = (n * Σxy - Σx * Σy) / (n * Σx² - (Σx)²)

Plugging in the values for the given data set:

b = (12 * 712.94 - 1451.9 * 511.6) / (12 * 1297.14 - 1451.9²)

b = -0.856

To find a, we can use the formula:

a = (Σy - b * Σx) / n

Plugging in the values for the given data set:

a = (511.6 - -0.856 * 1451.9) / 12

a = 55.54

So, the regression line is:

y = 55.54 - 0.856x

The negative slope of -0.856 means that as x increases, y decreases, which is consistent with the negative correlation coefficient of -0.636. The y-intercept of 55.54 means that when x is 0, y is predicted to be 55.54.

Complete question:

Run a regression analysis on the following bivariate set of data with y as the response variable.

x y

43.8 54.1

41.3 51.2

35.3 60.1

48.1 44.9

42.8 51.8

44.7 50.8

39.4 56.6

38.2 56.6

40.7 53.5

45.3 51.1

45 46.7

41.1 52.2

A. Find the correlation coefficient and report it accurate to three decimal places.

r = ________________

B. What proportion of the variation in y can be explained by the variation in the values of x? Report answer as a percentage accurate to one decimal place.  (If the answer is 0.84471, then it would be 84.5%...you would enter 84.5 without the percent symbol.)

r² =_______________ %

C. Based on the data, calculate the regression line (each value to three decimal places)

y =___________ x + _______________

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The surface area of the hexagonal pyramid is S = 575.9 inches²

The total surface area is the summation of the areas of the base and the three other sides. A = B + ( 1/2 ) ( P x h ), where B is the area of the base of the pyramid, P is the perimeter of the base, and h is the slant height of the pyramid

Surface Area of Pyramid = B + ( 1/2 ) ( P x h )

Given data ,

Let the surface area of the hexagonal pyramid be S

Now , the equation will be

The base of the hexagonal pyramid a = 10 inches

The height of the lateral face h = 6 inches

The base area of the pyramid = ( 3√3 / 2 )a²

The lateral surface area of the pyramid = 3a √ ( ( 3a²/4 ) + h² )

So , The total surface area of hexagonal pyramid is S

S = ( 3√3 / 2 )a² + 3a √ ( ( 3a²/4 ) + h² )

Substituting the values in the equation , we get

The base area of the pyramid = 259.8 inches²

The lateral surface area of the pyramid = 3 ( 10 ) √ ( 3 ( 100/4 ) + 36 )

On simplifying the equation , we get

The lateral surface area of the pyramid = 316.1 inches²

Total surface area of hexagonal pyramid S = 259.8 inches² + 316.1 inches²

The total surface area of hexagonal pyramid S = 575.9 inches²

Hence , the surface area of the pyramid is 575.9 inches²

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Answer:

12x^4y^7

Step-by-step explanation:

base(b)=8x^3y^5

height(h) =3xy^2

Area= (b x h)/2 =12x^4y^7

Answer:

[tex]A = 12x^4y^7[/tex]

Step-by-step explanation:

The formula for the area of a triangle is:

[tex]A = \dfrac{1}{2}bh[/tex]

where [tex]b[/tex] is the length of the triangle's base and [tex]h[/tex] is the length of the triangle's height.

In this problem, we are given the length of the base of the triangle as [tex]8x^3y^5[/tex] and the length of the height of the triangle as [tex]3xy^2[/tex].

Thus, the area of the given triangle is:

[tex]A = \dfrac{1}{2} \cdot 8x^3y^5 \cdot 3xy^2[/tex]

We can simplify this by combining like terms and using the exponent addition rule ([tex]x^a \cdot x^b = x^{a+b}[/tex]).

[tex]A =\left(\dfrac{1}{2} \cdot 8 \cdot 3 \right)(x^3 \cdot x)(y^5 \cdot y^2)[/tex]

[tex]A = (4 \cdot 3)(x^{3 + 1})(y^{5+2})[/tex]

[tex]A = 12x^4y^7[/tex]

The rule for converting a binary number to  Decimal point is to multiply each binary digit by two to the power of its position from the right, and add all the resulting values together. For example, 42 in binary is 101010, so the conversion is 1*2^5 + 0*2^4 + 1*2^3 + 0*2^2 + 1*2^1 + 0*2^0 = 32 + 8 + 2 = 42.

1. Start with the rightmost binary digit (the ones place) and multiply it by 2^0.

2. Move to the next digit to the left (the twos place) and multiply it by 2^1.

3. Continue this process until you reach the leftmost binary digit.

4. Add all the products together to get the decimal equivalent.

For example, 42 in binary is 101010, so the calculations are: 0*2^0 + 1*2^1 + 0*2^2 + 1*2^3 + 0*2^4 + 1*2^5 = 0 + 2 + 0 + 8 + 0 + 32 = 42.

The rule for converting a binary number to decimal is to multiply each binary digit by two to the power of its position from the right, and add all the resulting values together. To do this, start with the rightmost binary digit (the ones place) and multiply it by 2^0. Then move to the next digit to the left (the twos place) and multiply it by 2^1. Continue this process until you reach the leftmost binary digit. Add all the products together to get the decimal equivalent. For example, 42 in binary is 101010, so the calculations are:

0*2^0 + 1*2^1 + 0*2^2 + 1*2^3 + 0*2^4 + 1*2^5 = 0 + 2 + 0 + 8 + 0 + 32 = 42.

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The trip would have taken 8.89 hours instead of 8 hours.

Distance traveled can be calculated by multiplying the speed at which the object is traveling by the amount of time the object has been in motion.

For example, if a car is traveling at 60 miles per hour for two hours, the distance traveled would be 120 miles.

To calculate distance more accurately, you can use the formula d = rt, where d is the distance, r is the rate of speed, and t is the time in which the object has been in motion.

It is important to note that this formula assumes a constant speed throughout the duration of the journey.

It is also important to remember that the unit of measurement used for both the speed and the time must be the same. Therefore, if the speed is in miles per hour, the time must also be in hours.

In order to calculate this, we need to first calculate the time it took for the family to travel the first 600km at 90km/h. This can be calculated using the formula:

Time = Distance / Speed

So, the time it took for the family to travel the first 600km is:

Time = 600km / 90km/h = 6.67 hours

Then, we can calculate the time it would have taken for the family to travel 800km at 90km/h using the same formula:

Time = 800km / 90km/h = 8.89 hours

Therefore, the trip would have taken 8.89 hours, which is 0.89 hours longer than the original trip which took 8 hours.

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Answer:

y = [tex]-\frac{3}{4}[/tex] x

Step-by-step explanation:

y = mx + b , where "m" is a slope and "b" is an y-intercept.

If a║b ⇒ [tex]m_{a}[/tex] = [tex]m_{b}[/tex] and [tex]b_{a}[/tex] ≠ [tex]b_{b}[/tex]

( [tex]x_{1}[/tex] , [tex]y_{1}[/tex] )

y - [tex]y_{1}[/tex] = m( x - [tex]x_{1}[/tex] )

~~~~~~~~~~~~

y = [tex]-\frac{3}{4}[/tex] x + 1

( 8 , - 6 )

y - ( - 6 ) = [tex]-\frac{3}{4}[/tex] ( x - 8 )

y + 6 = [tex]-\frac{3}{4}[/tex] x + 6

y = [tex]-\frac{3}{4}[/tex] x

The two cuts that are being roasted for each time-temperature combination are an example of replication.

Option (c) is correct.

What is temperature?

Temperature is a measure of the average thermal energy of the particles in a substance. It is a scalar quantity, meaning it has only a magnitude and not a direction. The most commonly used unit of temperature measurement is the degree Celsius (°C) or the degree Fahrenheit (°F), but it can also be measured in Kelvin (K) in scientific and engineering applications.

Given options are:

(a) The two cuts that are being roasted for each time-temperature combination are an example of conduction

(b) The two cuts that are being roasted for each time-temperature combination are an example of convection

(c) The two cuts that are being roasted for each time-temperature combination are an example of replication

(d) None of the above

(c) The two cuts that are being roasted for each time-temperature combination are an example of replication.

In the question it is given that  From 10 identical cuts of lamb, 2 are randomly selected to roast using each of the time-temperature combinations in the same oven. Here it is an act of copying the exact sahpe size of the lamb in all cuts, which is nothing but replication. Moreover, this replication can help in proper comparision.

Hence, The two cuts that are being roasted for each time-temperature combination are an example of replication.

Option (c) is correct.

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Answer:

sum of their present ages is 5 + 20 = 25 years.

Step-by-step explanation:

The father's current age is 4x (because he is four times as old as his son)

Five years ago, the father's age was (4x - 5) and the son's age was (x - 5)

Ten years from now, the father's age will be (4x + 10) and the son's age will be (x + 10)

From the second statement, we know that:

(4x - 5) = 1.5(x - 5)

And from the third statement, we know that:

(4x + 10) = 1.5(x + 10)

We can solve these equations simultaneously to find the present ages of the father and the son.

Solving the first equation:

4x - 5 = 1.5x - 7.5

2.5x = 12.5

x = 5

So the son's current age is 5 years old.

The father's current age is 4x = 4(5) = 20 years old.

So, the sum of their present ages is 5 + 20 = 25 years.

Answer:Use a graphing utility to graph the function and approximate (to two decimal places) any relative minima or maxima. (If an answer does not exist, enter DNE.)

f

(

x

)

=

x

3

−

3

x

2

−

x

+

3

relative minimum

(

x

,

y

)

=

c

Step-by-step explanation:

The correct static test is [tex]$z=\frac{0.30-0.25}{\sqrt{\frac{0.30(0.70)}{80}}}$[/tex]

Number of residents in a certain area with wingspan measurements larger than 10 inches = =30% = 0.30

[tex]$=p_o=30 \%=0.30$[/tex]

20 of the 80 bats in a n=80 random sample from outside the area have wingspan measurements larger than 10 inches to ascertain whether there is any variation in the proportion of bats with a wing span more than 10 inches that live outside the region and those that do.

In response to the query;

an investigation using a one-sample z-test,

The following definition applies to the hypothesis:

[tex]$p=\frac{x}{n}$[/tex]

[tex]$p=\frac{20}{80}$[/tex]

H0: The fraction of bats with a wingspan larger than 10 inches that reside outside of the region and those that do so are equal.

= p - p₀ = 0.

Ha! There is a discrepancy between the percentage of bats with a wingspan larger than 10 inches that reside outside of the region and those that do.

= p - p₀ ≠ 0.

n = 80 , X = 20 , p₀ = 0.30

The analysis will be conducted using the z-test for a single proportion.

Following is a sample of the percentage of bats residing outside the area whose wingspan is larger than 10 inches:

The test statistic is,

[tex]& z=\frac{p-p_0}{\sqrt{\frac{p_0\left(1-p_0\right)}{n}}} \\[/tex]

[tex]& z=\frac{0.25-0.30}{\sqrt{\frac{0.30(1-0.30)}{80}}}[/tex]

The correct test statistic is

[tex]$=\frac{0.30-0.25}{\sqrt{\frac{0.30 \times 0.70)}{80}}}$[/tex]

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Answer: The commutative property is applied when finding the GCF by  taking the factor that has more than 1 factor other than itself(composite) and multiply them until you can no longer multiply. You then take the factors that are in common and multiply them.

Step-by-step explanation: my teacher made me use this way.

Answer:

see below

Step-by-step explanation:

3²-5 = -5x-3

9-5 =- 5x-3

-5x = 7

so x= -7/5

The sampling distribution of the sample mean based on samples of size 2 for a population can be approximated by a normal distribution.

The histogram of the sampling distribution would therefore look like a bell-shaped curve. The mean of the sampling distribution is equal to the population mean, and the standard deviation of the sampling distribution is equal to the population standard deviation divided by the square root of the sample size (in this case, 2).

Therefore, the formula for the sampling distribution of the sample mean for a population of size 2 is:

Mean = Population Mean

Standard Deviation = Population Standard Deviation / √2

The histogram of the sampling distribution would look like a bell-shaped curve with the mean and standard deviation determined by the formula above.

Therefore, the histogram most likely representing the sampling distribution of the sample mean based on samples of size 2 for the population is a bell-shaped curve with the mean and standard deviation determined by the formula above.

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The side length of the original cube is 8.90 inches

Let x be the side length of the original cube. After cutting off the top, the remaining rectangular box has dimensions of x-5, x-5, and x.

The volume of this rectangular box is:

(x-5)(x-5)(x) = x³ - 10x² + 25x

x³ - 10x² + 25x = 135

x³ - 10x² + 25x -135 = 0

Use cubic formula.

x =8.90

Therefore, the side length of the original cube is 8.90 inches

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According to the given data, the firm in question must be a price-taker, which is a perfectly competitive firm.

A price-taker is basically an individual or a particular company that must accept prices that are prevailing in a market and lacks the market share to be able to influence the market price on its own. All the economic participants can be considered to be price-takers in a market consisting of perfect competition.

In the given data set, the marginal revenue is constant which is very typical for competitive firms. This happens because the market decides the optimal price level and companies do not have much say over the price. This is a way by which they can maximize profits.

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The amount in the account after 6 years if the account is compounded semiannually, quarterly, or monthly is 6724.4,  6736.7, and 6664.9.

What is compound interest?

Compound interest, also known as interest on principal and interest, is the practice of adding interest to the principal amount of a loan or deposit.

Here, we have

Given: A principal of $5000 is invested in an account paying an annual rate of 7%.

We have to find the amount in the account after 6 years if the account is compounded semiannually, quarterly, or monthly.

A) Compounded semi-annually:

 = 5000*(1 + 0.05/2)^(2*6) = 6724.4

B) Compounded quarterly:

 = 5000*(1 + 0.05/4)^(4*6) = 6736.7

C) Compounded monthly:

 = 5000*(1 + 0.05/12)^(12*6) = 6664.9

Hence, the amount in the account after 6 years if the account is compounded semiannually, quarterly, or monthly is 6724.4,  6736.7, and 6664.9.

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The principal amount that Jenna put in the bank is $625.

Borrowers must pay lenders simple interest as a fee in exchange for a loan. Compound interest is excluded from the calculation and just the original principal is used. Simple interest applies to all loans, not just specific ones. Additionally, it refers to the kind of interest that banks give their customers on their savings accounts.

Given interest earned = $125

time = 4 years

rate = 5%

let the principal be p

this is the case of simple interest,

SI = (p*r*t)/100

substitute the values

125 (p* 5 * 4)/100

125 x 100 = p x 20

p = 12500/20

p = $625

Hence principal amount is $625.

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According to the solving the exponential form of the given number is as follows:

= 6² × 7⁴

= (-104)³

Bases and powers are employed in the exponential form to write numbers. It informs us of the amount of times we must actually multiply a number in order to obtain the answer. When we write the number 125 as 53, for instance, we can see that it is the third power of 5, or the number 125, which looks to be a typical three-digit number when observed.

When a single integer is multiplied by itself a certain number of times, x, the equation y takes on the base component b to the power of x, which is the quantity being multiplied, and is known as the exponential form.

The exponential form of the given number is :

= 6х6х7х7x7x7

= 6² × 7⁴

The exponential form of the given number is :

= -104 x -104 x -104

= (-104)³

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Charisse needs to stain an area of 174 square feet.

The total surface area of the shed's walls that needs to be stained is the sum of the areas of the four walls, minus the area of the front door.

The area of one wall is 8 feet × 6 feet = 48 square feet.

Since there are 4 walls, the total area of all walls is 48 square feet × 4 = 192 square feet.

The area of the front door is 3 feet  × 6 feet = 18 square feet

Now we can subtract the area of the door from the total area of all walls:

192 square feet - 18 square feet = 174 square feet

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Answer:

216

Step-by-step explanation:

2017-2007=10

8*10=80

80% of 120= 96

120+96=216

The standard deviation is 4.0, while mean is 10.2.

Data dispersion in regard to the mean is quantified by a standard deviation, or. Data are said to be more closely grouped around the mean when the standard deviation is low and more dispersed when the standard deviation is high.

Mean = 10.2

The standard deviation is 4.0.

Age in the mean is the average age.

Mean = (16 + 10 + 5 + 7 + 13)/5

Mean = 51/5 = 10.2

The variance's square root will reveal the standard deviation.

(16 - 10.2) + (10 -10.2) + (5-10.2) + (7-10.2)+( 13-10.2) ( 13-10.2)

5.8 + 0.2 -5.2 - 3.2 + 2.8

each number into squares

33.64 + 0.04 + 27.04 + 10.24 + 7.84

Variation: 78.8/5 = 15.76

Standard deviation = 3.969 = 4.0.

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The complete question is,

16, 10, 5, 7, 13

What is the porcupines' typical age based on your sample? Where can I find the standard deviation? in a circle tenths of a percent, closest.

Selecting elements from an ordered sampling frame is a statistical approach used in survey methodology known as systematic sampling and in the given situation (D) systematic sampling would be the best.

Systematic sampling is a statistical technique used in survey methodology that involves choosing components from an ordered sampling frame.

An equiprobability approach is the most typical type of systematic sampling.

This method treats the list's evolution in a cyclical manner, returning to the top after it has been completed.

The sampling process begins with the random selection of one element from the list, followed by the selection of every kth element in the frame, where k is the sampling interval, also known as the skip, and is equal to:
k = N/n.

Therefore, in the given situation (D) systematic sampling would be the best.

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Answer:

Step-by-step explanation:

d = 6 would not be a solution to the inequality below because it would make the inequality untrue! Plugging in, we get:

13 < d + 3

13 < 6 + 3
13 < 9
We know that 9 is not a solution to the inequality!

To solve, we isolate the d, and from there we can find all values that are a solution to the inequality to the solution!

[tex]13 < d + 3\\\\13 - 3 < d\\\\10 < d[/tex]

Thus, one can say that the solutions to the inequality are: [R, d > 10]!

For each month, you will pay $700 in interest.

What is simple interest?

Simple interest is a method of calculating the interest on a loan or investment where the interest is determined based on the initial principal (the original amount of the loan or investment) and a fixed interest rate. The interest is calculated based on the amount of time the principal is invested or borrowed.

The formula for simple interest is:

I = Prt

Where:

I is the interest

P is the principal

r is the annual interest rate (expressed as a decimal)

t is the time (in years)

For example, if you have a home mortgage of $140,000 with a fixed APR of 6% for 30 years, the simple interest calculation for each month will be:

I = (140,000 x 0.06) / 12 = $700

Hence, for each month, you will pay $700 in interest.

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if b is the span of the given vectors, so we can express b as the linear combination of the other given two vector.

given that,

[tex]a_{1} =\left[\begin{array}{ccc}-1&\\3&\\-1\end{array}\right] , a_{2} =\left[\begin{array}{ccc}-2\\-3\\6\end{array}\right] , b=\left[\begin{array}{ccc}-6\\9\\2\end{array}\right] \\\\\\\\\\\\\\\\\\\\\\\\[/tex]

We have determined that b is span of given vector a1 and a2.

we can write.   [tex]a_{1} =(-1,-3,-1) ,a_{2}=(-2,-3,6) , b=(-6,9,2)[/tex] .

A vector is a quantity that has magnitude and direction.

if x,y,z...., v are vectors and a,b,c....k are scalars then the linear combination is ax+by+cz+......+kv  

The set of linear combinations is called span for set of vectors.

So, b is span of given vector.

[tex]b=(c)a_{1} +(d)a_{2}[/tex]   ...... equation (A)

where c and d are scalars.

Now,

[tex](-6,9,2)=c(-1,3,-1)+d(-2,-3,6)\\(-6,9,2)=(-c,3c,-c)+(-2d,-3d,6d)\\(-6,9,2)=(-c-2d,3c-3d,-c+6d)\\[/tex]

equating the equations,

[tex]-c-2d=-6\\3c-3d=9\\-c+6d=2\\[/tex]

now we shall solve the above linear equations.[tex]subtract \\-c-2d-(-c+6d) = -6-2\\-8d=-8\\d=1\\now, \-c=-6+2d\\c=6-2=4\\c=4[/tex]

So, value of scalars c, d satisfied equation A,

thus, b is span of given vector a1 and a2.

The complete question is.

Determine if b is in the span of the other given vectors. If so, write b as a linear combination of the other vectors. a1=[-1 3 -1], a2=[-2 -3 6]= [-6 9 2]

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