4-56 Determine the magnitude of the moments of the force F about the x. y, and z axes Solve the problem (a) using a Cartesian vector approach and (b) using a scalar approach

Answer:

[tex]a^{12} b^{4}[/tex]

Step-by-step explanation:

To simplify we will have to use the negative exponent rule and the power rule along with some algebra.

Negative Exponent Rule

[tex]a^{-b} =\frac{1}{a^b}[/tex]

Power Rule

[tex](a^b)^{c} =a^{bc}[/tex]

Given

[tex](a^{-4}b^{-1}c )^{2} (a^2bc)^{2}[/tex]

Rewrite [tex]a^{-4}[/tex] using negative exponent rule.

[tex](\frac{1}{a^{4}}* b^{-1}c )^{2} (a^2bc)^{2}[/tex]

Rewrite [tex]b^{-1}[/tex] using negative exponent rule.

[tex](\frac{1}{a^{4}}* \frac{1}{b}*c )^{2} (a^2bc)^{2}[/tex]

Simplify

[tex](\frac{c}{a^4b} )^{2} (a^2bc)^{2}[/tex]

Rewrite the base as its reciprocal.

[tex](\frac{a^4b}{c} )^{2} (a^2bc)^{2}[/tex]

Apply the power rule.

[tex]\frac{a^8b^2}{c^2} *(a^2bc)^{2}[/tex]

Apply the power rule.

[tex]\frac{a^8b^2}{c^2} *a^4b^2c^2[/tex]

Cancel the common factor of [tex]c^2[/tex].

[tex]a^8b^2 a^4b^2[/tex]

Apply the power rule.

[tex]a^{12} b^{4}[/tex]

Answer:

[tex]a^{12}\:b^{4}[/tex]

Step-by-step explanation:

Given expression:

[tex]\left(a^{-4}\:b^{-1}\:c\right)^{-2}\left(a^2\:b\:c\right)^2[/tex]

[tex]\textsf{Apply exponent rule} \quad (a^b)^c=a^{bc}:[/tex]

[tex]\implies a^{(-4 \times -2)}\:b^{(-1 \times -2)}\:c^{-2}\:a^{(2 \times 2)}\:b^2\:c^2[/tex]

Simplify:

[tex]\implies a^{8}\:b^{2}\:c^{-2}\:a^{4}\:b^2\:c^2[/tex]

Collect like terms:

[tex]\implies a^{8}a^{4}\:b^{2}b^2\:c^{-2}c^2[/tex]

[tex]\textsf{Apply exponent rule} \quad a^b \cdot a^c=a^{b+c}:[/tex]

[tex]\implies a^{(8+4)}\:b^{(2+2)}\:c^{(-2+2)}[/tex]

Simplify:

[tex]\implies a^{12}\:b^{4}\:c^{0}[/tex]

[tex]\textsf{Apply exponent rule} \quad a^0=1:[/tex]

[tex]\implies a^{12}\:b^{4}(1)[/tex]

[tex]\implies a^{12}\:b^{4}[/tex]

answer: -3 lmk if you want an explanation!

Answer: it is 90,000 i believe

Answer: 90,000

Step-by-step explanation: I think it is 90,000 because if the number was for an example 95,000 it would be 100,000 so the number after the 9 is deciding either it goes up or down

(sorry for the grammar and stuff because I'm from Germany so its not very easy to explain, thanks for understanding)

Answer:

11

Step-by-step explanation:

Based on the given conditions, formulate: 25 - 14

Calculate the sum or difference: 11

get the result: 11

Answer:

The answer will be 1.53 after dividing and rounding to the nearest tenth 3.5 divided by 2.29.

The total length needed in inches will be 490.5 inches.

A fraction simply means a piece of a whole. In this situation, the number is represented as a quotient such that the numerator and denominator are split. In this situation, in a simple fraction, the numerator as well as the denominator are both integers.

Since the machinist must cut 12 strips of metal that are each 3 ft 4 7/8 in. long The total length needed in inches will be:

= (3 ft 4 7/8 inch × 12)

Note that 1 feet = 12 inches

= (12 × 3) + (4 7/8) × 12

= (36 + 4.875) × 12

= 490.5 inches

Learn more about fractions on:

brainly.com/question/78672

#SPJ1

First, we assume that this conclusion is false. In other words, we assume that the contrary statement "none of the two angles has measure [tex]90^{\circ}[/tex] or greater" is true.

The assumption is equivalent to the following two statements:

(1) [tex]m\angle A\text{ } \boxed{ < 90^{\circ}}[/tex]

(2) [tex]m\angle B\text{ } \boxed{ < 90^{\circ}}[/tex]

Using (1) and (2) and the addition properties of inequalities, we conclude that [tex]m\angle A+m\angle B \text{ } \boxed{ < } \text{ } 180^{\circ}[/tex].

On the other hand, two adjacent angles form a linear pair. Thus, the last statement contradicts the Linear Pair Property, which states that for a linear pair of angles [tex]\angle A[/tex] and [tex]\angle B[/tex], [tex]m\angle A+m\angle B \text{ } \boxed{=} \text{ } 180^{\circ}[/tex].

Therefore, the assumption made is false, and the statement "at least one of the angles [tex]\angle A[/tex] and [tex]\angle B[/tex] has measure [tex]90^{\circ}[/tex] or greater" is true.

Answer: y = -150x + 1800

Step-by-step explanation:

1. Find the linear slope of the line between two points.

(Change in Y)/(Change in X)

2. Write out an equation in point slope form.

(y-y1) = m(x-x1)

y-1800 = -150(x-0)

3. Simplify the equation and turn it into slope-intercept form.

y = -150x + 1800

The function f(g) is 8/(8+9x) and the function g(f) is -8x/(x-9).

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.

The given functions are f(x)=x/(x-9) and g(x)= -8/x.

1) f(g)

Here, f(-8/x)= -8/x ÷ (-8/x -9)

= -8/x ÷ (-8-9x)/x

= -8/x × x/(-8-9x)

= 8/(8+9x)

2) g(f)

Now, -8/x/(x-9)

-8x/(x-9)

3) f(f)

Here, f(f) = x/(x-9) ÷ (x/(x-9) -9)

= x/(x-9) ÷ ((x-9x+81)/(x-9))

= x/(x-9) × (x-9)/(-8x+81)

= x/(-8x+81)

4) g(g)

Now, -8/(-8/x)

= 64/x

Therefore, the function f(g) is 8/(8+9x).

To learn more about the function visit:

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

#SPJ1

Answer:

x=4, y =5

Step-by-step explanation:

there's no factorization involved, just elimination and substitution. First subtract equation 1 and 2. The x's cancel out and you get y by itself and can solve for it. Then plug the value of y into equation 2 and solve for x and you get it. (In my picture I put value of y in equation 1 but your question asks for putting it in equation 2 so do that instead)

The area is 8.84 sq. units

Area is defined as the total space taken up by a flat (2-D) surface or shape of an object.

To find the area we will find the product of 3.4 x 2.6, we can break each length into its base-ten units,

3.4 = 3+0.4

2.6 = 2+0.6

We can rewrite the product and solve it,

= (3+0.4) × (2+0.6)

= (3+0.4) × 2 + (3+0.4) × 0.6

= 3 × 2 + 0.4 × 2 + 3 × 0.6 + 0.4 × 0.6

This expression represents the partial product, each of the expression gives the area of sub rectangles (A, B, C and D). the sum of the partial product will give the area of the main rectangle.

Therefore,

3 × 2 + 0.4 × 2 + 3 × 0.6 + 0.4 × 0.6

= 6+0.8+1.8+0.24

= 8.84

Hence, the required area is 8.84 sq. units.

For more references on area, click;

https://brainly.com/question/27683633

#SPJ1

The final point on the number line will be at 2/3 from 0 point, which represents the value of the expression -2/6 + (5/6).

To correctly model the expression -2/6 + (5/6) on a number line, we can use the following steps:

So to model the expression -2/6 + (5/6) on a number line, we start at 0 and move 1/3 to the left, to represent -2/6, and then move 5/6 to the right to represent 5/6. The final point on the number line will be at 2/3 from 0 point, which represents the value of the expression -2/6 + (5/6).

Learn more on number line here: https://brainly.com/question/22046767

#SPJ1

Answer:

Each book cost 222 - 15 = 207 / 9 = 22.88 dollars.

Answer: line AB and RS are parallel because their lines do not interact anywhere on the model, because it is 3D. this is the only one i am sure of, you may have to ask another person to get the other two.

Answer:

A. Line AB and Line CG are parallel, C. Line CG and Line RS are perpendicular, and E. Line CG lies in plane X

Step-by-step explanation:

A. Line AB and Line CG are parallel is true because the arrows are pointing in the same directions and do intersect or cross each other.

B. Line AB and Line RS are parallel is false because although they do not intersect, they also do not go in the same direction. These are also not perpendicular lines because they do not intersect other, even though they make a right angle.

C. Line CG and Line RS are perpendicular is true because these lines intersect at exactly 90° angle (as shown by the square).

D. Line AB and Line RS must intersect is false because Line AB does not intersect Line CG (which is the line that does intersect Line RS).

E. Line CG lies in plane X is true because point C and point G are in plane X.

F. Line RS lies in plane X is false because point r and point 2 are in plane Y.

On solving the provided question, we can say that -  here in the function, every element has an unique image

The topic of numbers, formulae and associated structures, forms and the areas where they exist, quantities and their variations, and spaces where they exist are all included in the field of mathematics. An association between a collection of inputs, each of which has an output, is known as a function. A function is, to put it simply, a relationship between inputs and outputs, where each input has a single, specific outcome. A domain and a codomain, or scope, are assigned to each function. Typically, f is used to represent functions (x). input is x. Four different sorts of functions are available. Based on the following items: One-to-one functions, many-to-one functions, on functions, one-to-one functions, and within functions.

every element has an unique image and,

this relation, is not a function, since it is not one-one and onto.

To know more about function visit:

https://brainly.com/question/28193995

#SPJ1

1)Triangle : s = 6cm ; P= 18 cm

2.) Square : s = 7 cm ; P = 28 cm

3.) Rectangle = W = 4cm , L = 8 cm ; P = 24cm

4.) Regular Heptagon : s = 3cm ; P = 21 cm

5.) Circle : r = 12cm ; C = 24∏ cm.

What is circumference?

The circumference of a circle or ellipse in geometry is its perimeter. That is, if the circle were opened up and straightened out to a line segment, the circumference would be the length of the arc. The curve length around any closed figure is more often referred to as the perimeter.

Given that the length of each side of a triangle is 6 cm.

The perimeter of an equilateral triangle is 3a, where a is the length of the side of the equilateral triangle.

The perimeter of the triangle is 3 × 6 = 18 cm

The length of side of a square is 7 cm.

The perimeter of a square is 4a, where a is the length of the side of the square.

The perimeter of the square is 4 × 7 = 28 cm.

The length and breadth of a rectangle is W = 4 cm and L = 8 cm.

The perimeter of a rectangle is 2(L+ W)

The perimeter of the rectangle is = 2(8 + 4) = 2 × 12 =24 cm

The perimeter of Regular Heptagon is 7a, where a is the length of the side of the Regular Heptagon.

The perimeter of a Regular Heptagon is (7  × 3) = 21 cm

The perimeter of a circle with a radius r is 2∏r.

The perimeter of the circle is 2∏ × 12 = 24∏ cm.

To learn more about perimeter, click on the below link:

https://brainly.com/question/27148391

#SPJ1

Area and circumference of the circle are 78.5 m² and 31.4 m respectively.

A circle is a shape consisting of all points in a plane that are at a given distance from a given point, the centre.

Given that, a circle have a radius 5 m

Area of a circle = π × radius²

Circumference = 2π×radius

Area = 3.14 × 5² = 3.14 × 25 = 78.5 m²

Circumference = 3,14 × 2 × 5 = 31.4 m

Hence, area and circumference of the circle are 78.5 m² and 31.4 m respectively.

Learn more about circle, click;

https://brainly.com/question/29142813

#SPJ1

The science of statistics focuses on creating and researching strategies for gathering, analysing, interpreting, and presenting empirical data.

Research in statistics finds application in almost all scientific domains, and research concerns in the various scientific fields inspire the creation of new statistical methods and theories. Statistics is a very interdisciplinary field. Statisticians use a range of mathematical and computational techniques while creating new approaches and researching the theory that supports such methods. Uncertainty and variation are two key concepts in the study of statistics. In science, as well as more generally in life, there are numerous circumstances where the result is unknown. Sometimes the uncertainty is caused by the fact that the result is still up in the air. Probability is a mathematical language that is used to talk about uncertain events, and it is crucial to statistics. There are numerous causes of variance that can affect any measurement or data collection attempt. By this, we indicate that the result would probably alter if the same measurement was repeated. The goal of statisticians is to comprehend and, whenever feasible, manage the sources of variation.

To know about statistics on

https://brainly.com/question/28494851?referrer=searchResults

Answer: simplified to the tens digit would be 93.4 simplified overall would just be 93.

Step-by-step explanation: Hope this helps, please mark brainliest, and give thanks!

On solving the provided question, we can say that - As a result, Orthocenter triangle is the answer to the given triangle issue (0, - 5 ).

Three sides and three vertices make up a triangle, which is a polygon. It is among the fundamental forms in geometry. Triangle ABC is the name given to a triangle with vertices A, B, and C. When the three points are not collinear, a unique plane and triangle in Euclidean geometry are found. A triangle is a polygon that has three sides and three corners. The spots where the three sides join end to end make up the triangle's corners. Three triangle angles added together equal 180 degrees.

determine LN's slope.

[tex]m = (y2 - y1)/ (x2- x1) = 1-5/8-0 = 2[/tex]

formula for altitude

[tex]y - 1 = 2(x - 3) (x - 3)\\y - 1 = 2x - 6\\[/tex]

y = 2x - 5

Altitude of N and LM

[tex]m = (y2 - y1)/ (x2- x1) = 1-5/3-0 ⇒ -3/4\\y - 1 = (x - 8) (x - 8)\\y - 1 = x - 6\\[/tex]

y = x - 5

[tex]8x - 20 = 3x - 20\\5x - 20 = - 20 \\5x = 0 = > x = 0\\[/tex]

y =0 - 5 = - 5

It is the orthocenter (0, - 5 )

To know more about triangle visit:

https://brainly.com/question/2773823

#SPJ1

When calculating the surface area of a 3D shape, it is important to remember to include the area of all the components that make up the shape.

To learn more about the surface area of a of the prism refer to:

https://brainly.com/question/1297098

#SPJ1

On solving the provided question, we can say that - here in equation 10x + =4 = 2

An equation is a formula in mathematics that joins two statements with the equal symbol = to represent equality. The definition of an equation in algebra is a mathematical statement proving the equality of two mathematical expressions. In the equation 3x + 5 = 14, for instance, the terms 3x + 5 and 14 are separated by an equal sign. The link between two phrases on either side of a letter is expressed mathematically. There is often only one variable, which is also the symbol. instance: 2x - 4 Equals 2.

here,

the equation we have is  = 10x + =4 = 2

10x = -2

x = -1/5

To know more about equation visit:

https://brainly.com/question/649785

#SPJ1

The volume of the solid is 104 cubic centimeters.

A cuboid is a solid in three dimensions with six rectangular faces, eight vertices, and twelve edges. Three dimensions, including length, breadth, and height, define a cuboid. A cuboid with integer edges is referred described as being perfect.

Given:

We have the cuboid.

And the height of the cuboid is 2 centimeters.

Length = 9 centimeters.

Width = 8 centimeters.
The volume of a cuboid is,

=  Length × Width × Height Cubic units.

= 9 x 8 x 2

= 144 cubic centimeters.

And we have missing part of the cuboid.

And the height of the missing cuboid is 2 centimeters.

Length = 9-4 = 5 centimeters.

Width = 8 - 4 = 4 centimeters.

The volume of the missing cuboid is,

=  Length × Width × Height Cubic units.

= 5 x 4 x 2

= 40 cubic centimeters.

So, the required volume,

= Total volume - missing volume

= 144 - 40

= 104 cubic centimeters.

Therefore, the required volume is 104 cubic centimeters.

To learn more about the cuboid;

https://brainly.com/question/29568631

#SPJ1

1) The equation is:

y = -29/x

And when we evaluate in x = 2, we get y = -14.5

2)  The equation is:

y = 88/x

And when we evaluate in x = 2, we get y = 44

We know that the variables x and y vary inversely, then the equation between these variables will be something like:

y = k/x

Where k is a constant.

1) First we know that when x = -1, y = 29, replacing these values we will get:

29 = k/-1

-1*29 = k

-29 = k

Then the equation is:

y = -29/x

If now we evaluate in x = 2, we will get:

y = -29/2

y = -14.5

2) Now we know that x = 8 and y = 11, replacing these we get:

11 = k/8

11*8 = k

88 = k

So the equation is:

y = 88/x

If now we replace x by 2, we will get:

y = 88/2 = 44

Learn more about inverse relations:

https://brainly.com/question/1266676

#SPJ1

Answer:

[tex]\displaystyle \frac{7}{12}[/tex]

Step-by-step explanation:

When we are subtracting fractions with different denominators, we find the least common denominator of each one. In the case of 6 and 4, they both share 12 as the least common denominator, so we can rewrite each fraction as equivalents with denominators of 12:

[tex]\displaystyle \frac{5}{6}-\frac{1}{4}=\frac{5*2}{6*2}-\frac{1*3}{4*3}=\frac{10}{12}-\frac{3}{12}=\frac{7}{12}[/tex]

Step-by-step explanation:

This calculator subtracts two fractions. First, convert all fractions to a common denominator when fractions have different denominators

Answer:

See below

Step-by-step explanation:

Because it's an inequality, the upside-down parabola has dashed lines instead of a sold line. Additionally, only one side of that parabola will contain the solution set, which we can easily figure out by testing a point like (0,0):

[tex]0\stackrel{?}{ > }-3(0)^2-30(0)-48\\0\stackrel{?}{ > }-48\\\\0 > -48 \text{ is true}[/tex]

Hence, the side that contains (0,0) gets shaded. See the graph below.

The length x is found to be 10 yards and is calculated using Polygon Triangulation.

What is Polygon Triangulation?

The polygonal triangulation is a method in which the area of polygon is divided into triangles to simplify calculation.

From the attached figure, we can find a using Pythagorus Theorem

a = [tex]\sqrt{6^{2} - 4.8^{2} }[/tex] = 3.6

cos θ = [tex]\frac{4.8}{6}[/tex] = 0.8

In ΔXYZ

cos θ = [tex]\frac{8 + 4.8 }{x+ 6} \\\\[/tex]

0.8 =       [tex]\frac{12.8}{x + 6}[/tex]

Solving for x,

x = 10 yards

Therefore the length of x found using polygonal triangulation method is 10 yards.

To learn more about polygonal triangulation, follow the link.

https://brainly.com/question/15243897

#SPJ1

Answer:

In the quadratic function "y = -x^2q - 2x + 10", the term "-x^2q" is the coefficient of the quadratic term and is represented by the letter "A". The term "-2x" is the coefficient of the linear term and is represented by the letter "B". The constant term "10" is the coefficient of the constant term and is represented by the letter "C".

The axis of symmetry of the graph of this quadratic function is the line that divides the graph into two congruent halves. It can be found by using the formula "x = -B / 2A". In this case, the axis of symmetry is "x = -(-2) / 2(-x^2q) = x^2q / x".

So in the function "y = -x^2q - 2x + 10", the coefficient of the quadratic term is "A = -x^2q", the coefficient of the linear term is "B = -2x", the coefficient of the constant term is "C = 10", and the axis of symmetry is "x = x^2q / x".

Answer:

k = [tex]\frac{3}{4}[/tex]

Step-by-step explanation:

given variation equation

y = kx

to find k substitute y = 3 and x = 4 into the equation and solve for k

3 = 4k ( isolate k by dividing both sides by 4 )

[tex]\frac{3}{4}[/tex] = k