What is the value of (23)2?

The volume of the Parallelepiped with adjacent edges pq, pr,and ps = 136

Geometrically, the Scalar triple product:

\({\displaystyle \mathbf {a} \cdot (\mathbf {b} \times \mathbf {c} )} \mathbf{a}\cdot(\mathbf{b}\times \mathbf{c})\)

is the (signed) volume of the parallelepiped defined by the three vectors given. Here, the parentheses may be omitted without causing ambiguity, since the dot product cannot be evaluated first. If it were, it would leave the cross product of a scalar and a vector, which is not defined.

Given three vectors, there is a product, called scalar triple product, that gives , the volume of the parallelepiped that has the three vectors as dimensions.

So,

Given : p(-2,1,0) , q(3,4,3), r(1,4,-1), s(3,6,4).

pq =  ( -2-3 ,1-4 ,0-3) = (-5,-3,-3)

pr= (-2-1, 1-4, 0+1) = (-3,-3,1)

ps= ( -2-3, 1-6, 0-4) = (-5,-5,-4)

pq = (-5  ,  -3  , -3)

pr = (-3,  -3,  1)

ps= (-5,  -5,  -4)

The scalar triple product is given by the determinant of the matrix (3×3)

that has in the rows the three components of the three vectors:

\(\left[\begin{array}{ccc}-5&-3&-3\\-3&-3&1\\-5&-5&-4\end{array}\right] \\\\-5(12+5)-3(12+5)-3(15-15)\\-5(17)-3(17)-3(0)\\-85-51\\-136\\\)

So, The volume never be negative then by applying vector

v = |-136|

v= 136

the volume of the parallelepiped with adjacent edges pq, pr,and ps = 136

To learn more about Scalar triple product: brainly.com/question/13419505

#SPJ4

The answer is:  " \(42\frac{2}{3}\) miles per hour " .

_______

Step-by-step explanation:

This is a "unit rate" problem.

"Find the rate in miles per "single [unit] hour."

 {GIven:  "5 1/3 mi per 7 1/2 min."}.

_______

Using a technique unknown as "dimension analysis" ;

let us convert the given value; in "mi / min" ;

 to its value in "mi/hr" (our answer):

_______

→    " 5 1/3  mi        60 min                  ,    

      ________  *   ______   =   ?      mi / hr ?  "

       7 1/2 min           1 hr

_______

Note:  The units of "min" ["minute(s)"] ; cancel out to "1" ;

               →  {since:  "min/min = 1 " ;

  and we have:  " [ (5  1/3 * 60) / (7 1/2) ] mi / hr. " ;

_______

   →   " 5  1/3 =  [ (3*5) + 1 ] / 3 " ;

                                  = " (15 + 1) /3 " ;

                                  = " 16 / 3 " ;  → (as an "improper fraction") ;

   →   " 7  1/2 =  [ (2*7) + 1 ] / 2 " ;

                                  =  " (14 + 1) / 2) " ;

                                  = "  15 / 2 " ;   → (as an "improper fraction") ;

_______

So we have:

   →   " \((\frac{16}{3}*\frac{60}{1})\) ÷ \(\frac{15}{2}\) " ;

Note: Dividing by a value is the same value as multiplying by the reciprocal of that value.

 In this case:  The reciprocal of:  " \((\frac{15}{2}\)\()\) " ;  is:  " \((\frac{2}{15})\) " ;

_______

So, we can rewrite the expression:

_______

   →   " \((\frac{16}{3}*\frac{60}{1}) * \frac{2}{15}\) " ;

_______

     =  " \(\frac{(16*60*2)}{(3*1*15)}\) " ;

 →   "    ( 16 * 60 * 2)      "

             (3 * 15)    

 →   Take note of the "60" in the numerator;  and the "15" in the denominator ;

  " (60 ÷ 15 = 4) " ;  

 so we can change the "60" to a "15" and cancel out the "15" ; since:

  " (15 ÷ 15 = 1 ) " ;  

_______

And rewrite:

_______

   →   "    ( 16 * 4 * 2)      "  

                    3       ;

_______

\(= \frac{(16 * 4 * 2)}{3} = \frac{(64*2)}{3} = \frac{128}{3} =\)  (128 ÷ 3) =  " \(42\frac{2}{3}\) " .

_______

The answer is:  " \(42\frac{2}{3}\) miles per hour " .

_______

Hope this is helpful!

 Best of luck to you!

_______

Step-by-step explanation:

\( { ({3}^{3} )}^{4} \)

\( = {3}^{3 \times 4} \)

\( = {3}^{12} \)

\(or \)

\( = 531441\)

The circulation of the vector field F is 0.

To find the circulation of the vector field F = 3yi + 7zj + 2xk around the given triangle using Stokes' theorem, we need to evaluate the surface integral of the curl of F over the surface bounded by the triangle.

The curl of a vector field F = P i + Q j + R k is given by the determinant:

curl F = (∂R/∂y - ∂Q/∂z) i + (∂P/∂z - ∂R/∂x) j + (∂Q/∂x - ∂P/∂y) k

In this case, we have F = 3yi + 7zj + 2xk, so we compute:

∂R/∂y = 0, ∂Q/∂z = 0, ∂P/∂z = 0, ∂R/∂x = 0, ∂P/∂y = 3, ∂Q/∂x = 0

Therefore, the curl of F is:

curl F = 3j

The triangle is formed by the three given points: (6, 0, 0), (6, 0, 4), and (6, 2, 4). We need to find the surface bounded by this triangle.

To apply Stokes' theorem, we need to find the surface area vector and its magnitude.

The surface area vector is given by the cross product of two tangent vectors to the triangle, and its magnitude is equal to the area of the triangle.

The tangent vectors can be obtained by subtracting the position vectors of the points. Let's call the points A, B, and C, where A = (6, 0, 0), B = (6, 0, 4), and C = (6, 2, 4).

Tangent vector AB = B - A = (6, 0, 4) - (6, 0, 0) = (0, 0, 4)

Tangent vector AC = C - A = (6, 2, 4) - (6, 0, 0) = (0, 2, 4)

Now we can calculate the cross product:

Surface area vector = AB x AC = (0, 0, 4) x (0, 2, 4) = (-8, 0, 0)

The magnitude of the surface area vector is |Surface area vector| = \(\sqrt((-8)^2 + 0^2 + 0^2) = 8.\)

Stokes' theorem states that the circulation of F around the closed curve C is equal to the surface integral of curl F over the surface bounded by C.

In this case, the curve is the triangle, and the surface is the one we determined in Step 3.

The circulation is given by:

Circulation = ∬S (curl F) · dS

Substituting curl F = 3j and dS = Surface area vector = (-8, 0, 0), we have:

Circulation = ∫∫S (0, 3, 0) · (-8, 0, 0) dA

           = ∫∫S 0 dA

           = 0

Therefore, the circulation of the vector field F around the given triangle is 0.

Learn more about Stokes' theorem

brainly.com/question/10773892

#SPJ11

Answer:

c

Step-by-step explanation:

I hope this helpssssssss

Answer:

Just say no thanks i have a bf

Step-by-step explanation:

Answer:

40% is bigger

Step-by-step explanation:

40% ⇒ 40/100

1/4 ⇒ 25/100

40>25

∴ 40% is bigger

The parent would have to earn at least $4.166

$2,475 * 12 months = $29,700

$4,000 savings goal to the family's yearly income

$29,700 + $4,000 = $33,700

yearly income for second parent

80 hours/month * 12 months = 960 hours/year

If offer of daycare is accepted

$33,700 (total income) - $29,700 (first parent's income)

= $4,000

$4,000 / 960 hours = $4.166

this is the minimum wage

The parent would have to earn at least $4.166

Read more on earnings here:https://brainly.com/question/28920245

#SPJ1

Answer:

3 squares

Step-by-step explanation:

Firstly, you have to count the number of squares in the shape. As it can been seen from the diagram, there are a total 18 squares (i.e 6 squares on each row × 3 squares on each column).

Secondly you have to find 1/6 of the total number of the squares in the shape. 1/6 of the total number of the square in the shape = 1/6 × 18 = 3 squares

Therefore 3 squares would have to be shaded so that 1/6 of the shape is shaded

Answer:

1

Step-by-step explanation:

1 part

i m sorry my small brother wrote it

Answer:

15πcm

Step-by-step explanation:

2πr = circumference

radius = 0.075m = 7.5cm

Circumference = 7.5X2π

15π cm

Answer:

218.57

Step-by-step explanation:

Since it is an isoceles triangle, the sides are 32, 32, and 14.

Using Heron's Formula, which is Area = sqrt(s(s-a)(s-b)(s-c)) when s = a+b+c/2,  we can calculate the area.

(A+B+C)/2  = (32+32+14)/2=39.

A = sqrt(39(39-32)(39-32)(39-14) = sqrt(39(7)(7)(25)) =sqrt(47775)= 218.57.

Hope this helps have a great day :)

Check the picture below.

so let's find the height "h" of the triangle with base of 14.

\(\begin{array}{llll} \textit{using the pythagorean theorem} \\\\ a^2+o^2=c^2\implies o=\sqrt{c^2 - a^2} \end{array} \qquad \begin{cases} c=\stackrel{hypotenuse}{32}\\ a=\stackrel{adjacent}{7}\\ o=\stackrel{opposite}{h} \end{cases} \\\\\\ h=\sqrt{ 32^2 - 7^2}\implies h=\sqrt{ 1024 - 49 } \implies h=\sqrt{ 975 }\implies h=5\sqrt{39} \\\\[-0.35em] ~\dotfill\)

\(\stackrel{\textit{area of the triangle}}{\cfrac{1}{2}(\underset{b}{14})(\underset{h}{5\sqrt{39}})}\implies 35\sqrt{39} ~~ \approx ~~ \text{\LARGE 218.57}\)

For the trapezoid to be proven to be an isosceles trapezoid, the additional information needed is: A. DE ≅ GF

An isosceles trapezoid is a type of trapezoid whose opposite non-parallel sides have the same side length and base angles that are congruent.

In essence, for trapezoid DEFG to be proven to be an isosceles trapezoid, DE must be congruent to GF.

The additional information needed is therefore: A. DE ≅ GF

Learn more about isosceles trapezium on:

https://brainly.com/question/4758162

#SPJ1

As per unitary method the recipe makes 20.5 servings of lemonade.

The unitary method is a method used to find the number of servings in a recipe by dividing the total amount of ingredients by the serving size.

Let's say a serving size of lemonade is 1 cup. To find the number of servings, we need to divide the total amount of lemonade by the serving size.

In this case, the total amount of lemonade is

=> 2 cups of lemon juice + 16 cups of water + 2.5 cups of agave nectar

=> 20.5 cups.

So, the number of servings can be found by dividing 20.5 cups by 1 cup per serving, which equals 20.5.

In conclusion, the unitary method is a simple way to find the number of servings in a recipe by dividing the total amount of ingredients by the serving size

To know more about unitary method here.

https://brainly.com/question/28276953

#SPJ4

The correct answer is (5,-7) Hope that helps!

Answer:

it would be (-5,6)

Step-by-step explanation:

since it is just reflected and not moving anywhere it would just be the same coordinates but flipped values. if its positive then when its reflected it would be negative.

The average rates of change for f(x)=0.1x squared, g(x)=0.3x squared is 0.5 and 1.3 over the interval [1,4].

In order to calculate the average rate of change of a function f(x) over an interval [a,b] we need to implement the formula

A(x) = {f(b) - f(a)] / (b – a)}

Here,

A(x)= average rate of change,

f(a) = value of function,

f(b) = value of function

given, from the question

f(x) = 0.1x^2

g(x) = 0.3x^2

The calculated interval is 1 ≤ x ≤ 4.

Therefore,

for f(x), we have staged the values as

A(x) = {f(4) - f(1)] / (4 - 1)}

= {(0.1 * 4^2) - (0.1 * 1^2)] / (4 - 1)}

= (1.6 - 0.1) / 3

= 0.5

for g(x), we have staged the values as

A(x) = {g(4) - g(1)] / (4 - 1)}

= {(0.3 * 4^2) - (0.3 * 1^2)] / (4 - 1)}

= (4.2 - 0.3) / 3

= 1.3

The average rates of change for f(x)=0. 1x squared, g(x)=0. 3x squared is 0.5 and 1.3 over the interval [1,4].

To learn more about average rates of change,

https://brainly.com/question/24313700

#SPJ4

Known as circular forts or Trelleborgs, Scandinavian architecture was unique in this regard.

Modernism, practicality, minimalism, and simplicity have been defining characteristics of Scandinavian design since the 1950s. It accepts the idea that everyone ought to be able to afford lovely and practical houses and everyday necessities.

Other Scandinavian constructions were taller than two stories and had both exterior and interior embellishment.

But the Nordic region's bitter, fleeting winters and the need for glowing, warm interiors also had a big influence on the period's Scandinavian architecture. These practical factors led to a new level of subtle elegance as well as a predilection for lighter colors, simple designs, and open-plan spaces.

To learn more about Architecture here:

https://brainly.com/question/9760486

#SPJ4

Answer:

\(p=\frac{5}{6}\)

Step-by-step explanation:

Answer:

Exact Form:

             5

p=     ---------

             6

Decimal Form:

The simplest way to perform a division is long division and synthetic division.

What is division?

Division in mathematics is the process of dividing an amount into equal parts. For instance, we may split a group of 20 people into four groups of 5, five groups of 4, and so on.

There are two methods to perform division:

Long division: The mathematical procedure for splitting big numbers into more manageable groups or sections is known as long division. A difficulty can be solved by breaking it down into manageable parts. Dividends, divisors, quotients, and remainders all exist in long divisions.

Synthetic division: In algebra, synthetic division is a technique for manually dividing polynomials according to Euclid, requiring less writing and calculation than long division. Although the approach can be applied to division by any polynomial, it is often taught for division by linear monic polynomials.

To learn more about division, click on below link:

https://brainly.com/question/11781269

#SPJ4

Explanation:

Apply the square root to 1.44 to get 1.2

\(\sqrt{1.44} = 1.2\)

If the square has side lengths 1.2 yards, then,

area = side*side = 1.2*1.2 = 1.44 square yards

which helps us confirm the answer

Answer:

A and D

hope this helps :)

Step-by-step explanation:

In calculating the mean of this data set  Ashrita did the best job.

The  Mean of the data set is the most commonly used measures of central tendency.

It means the average value of the data set.

one doesn't have to arrange the data in order  for finding it.

The data set value  takes is to add them all together and divide that by the number of the data.

It can be written as

\(,(x_1 + x_2 + x_3 + ..... + x_n) / n\)

Where \(x_1 , x_2 , x_3 , ..... ,x_n\)are the values in the data set

Therefore we can conclude that Ashrita did the best job in calculating the mean of this data set.

To learn more about the mean visit:

https://brainly.com/question/968894

Answer:

$204

Step-by-step explanation:

The question is at what price x will the company maximize revenue.

The revenue function is:

\(R(x) = 4,080x-10x^2\)

The price for which the derivate of the revenue function is zero is the price the maximizes revenue:

\(R(x) = 4,080x-10x^2\\\frac{dR(x)}{dx}=0=4,080-20x\\x=\frac{4,080}{20}\\ x=\$204\)

The company will maximize its revenue when the price is $204.

The probability of having 7 boys in a family with 7 children is 1 out of 128, as there is only one favorable outcome out of 128 total possible outcomes.

To find the probability, we need to calculate n(E) and n(S).

In this case, event E represents the scenario where all 7 children are boys. The sample space S consists of all possible permutations of boys and girls for the 7 children, which is 2^7 = 128.

This is because each child has 2 possibilities (boy or girl), and we multiply these possibilities for all 7 children.

Since event E includes only one specific outcome (all boys), n(E) is equal to 1. Therefore, both n(E) and n(S) are 1 and 128, respectively. The probability of having 7 boys is given by n(E)/n(S) = 1/128.

Learn more about Probability click here : brainly.com/question/30034780

#SPJ11

Answer: y = 3x+1

Step-by-step explanation: If (4,1) is a solution of y = 3x+1, that means if we plugin the respective values of (4,1), we should have an EQUALITY:

1 = 3(4) + 1

1 = 13 , which is wrong, then the point (4,1) is NOT a solution of y = 3x+1.

Answer:

m <E = 134

Step-by-step explanation:

Triangle DEF looks like an isosceles triangle to the base angles are the same measure.

6x+11 = 10x+3

Subtract 11 from both sides

6x = 10x-8

Subtract 10x from both sides

-4x = -8

Divide -4 from both sides

x = 2

Substitute 2 into both equations to make sure it works

6 (2) + 11

12+11

23

10 (2) +3

20+3

23

Both angles equal 23 degrees.

Now subtract both angles from the total angle measure of 180.

180-23-23=134

Answer:

HI = 10

Step-by-step explanation:

HI + IJ = HJ , substitute values

2x + 3x - 1 = 24 , that is

5x - 1 = 24 ( add 1 to both sides )

5x = 25 ( divide both sides by 5 )

x = 5

Thus

HI = 2x = 2 × 5 = 10

The maximum clearance of the underpass ahead is 12 feet and 6 inches.

Based on the information provided, the sign indicates that there is an underpass ahead with a clearance of 12 feet and 6 inches. The sign further mentions that the train in question is also 12 feet and 6 inches long, and it highlights the presence of a narrow median, which is only 6-12 inches wide.

In this context, the sign serves as a warning to drivers approaching the underpass. The clearance measurement of 12 feet and 6 inches informs drivers of the maximum height of vehicles that can safely pass through the underpass without any risk of collision. Since the train length matches the clearance, it implies that vehicles longer than the underpass clearance may not be able to pass through safely if the train is present.

The mention of a narrow median emphasizes the limited space available between the opposing lanes of traffic. With a width of only 6-12 inches, the median may not provide sufficient room for larger vehicles to maneuver, particularly when encountering oncoming traffic or passing through the underpass while the train is present.

Overall, the sign conveys important information regarding the underpass clearance, the train length, and the narrow median, all of which should be considered by drivers to ensure safe passage through the upcoming area.

Learn more about median

brainly.com/question/11237736

#SPJ11

The sign indicates the clearance height of an underpass, warns of a narrow median, and mentions the length of a train.

The sign in question is indicating that there is an underpass ahead with a clearance of 12 feet and 6 inches. This means that any vehicle taller than that would not be able to pass through without hitting the underpass ceiling. Additionally, the sign mentions that the train itself is also 12 feet and 6 inches long, so it is important for drivers to be cautious and aware of the height restrictions. The narrow median mentioned refers to the strip of land or barrier between lanes, which in this case is only 6-12 inches wide.

https://brainly.com/question/35343010

#SPJ6

f(x) = x - 4

g(x) = 2x

We need to find g(f(-2)), which means

Find f(-2) at first by substitute x by -2 in f

f(-2) = (-2) - 4 = -2 - 4 = -6

Replace f(-2) by -6

Now we need to find g(-6)

Substitute x in g by -6

g(-6) = 2(-6) = -12

g(f(-2)) = -12

By using linear equation, it is obtained that 218 minutes of phone call cost $100

What is linear equation?

At first it is important to know about 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.

Here linear equation is used

A long-distance telephone call from Center City to Smithville costs $3.25 for the first 3 minutes and $0.45 for each additional minute

Let the total time for the telephone call be t minutes

So total cost for t minutes telephone talk = $(3.25 + 0.45(t - 3))

By the problem,

3.25 + 0.45(t - 3) = 100

3.25 + 0.45 t - 1.35 = 100

1.9 + 0.45 t = 100

0.45 t = 100 - 1.9

0.45 t = 98.1

t = 218 minutes

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

https://brainly.com/question/2030026

#SPJ1