Resolve F2 into components along the u and v axes determine the magnitudes of these components.

Answers

Answer 1

Resolving F2 into components along the u and v axes, the magnitudes of the components are determined as 150 N and 77.6 N.

According to the sine law, the side length of a triangle should be divided by the sine of the opposite angle. That is, when we divide side a by the sine of angle A, we get the same result as side b divided by angle B and side c divided by angle C.

For the given diagram, first, draw the vector components. Then, by sine law, we get,

[tex]\begin{aligned}\frac{F_u}{\sin 75^{\circ}}=\frac{F_2}{\sin 75^{\circ}}=\frac{F_v}{\sin 30^{\circ}}\end{aligned}[/tex]

Now, substitute the value of F₂, and we get,

[tex]F_u=F_2=\mathrm{150\;N}[/tex]

Now, solve for [tex]F_v[/tex], we get,

[tex]\begin{aligned}F_v&=\frac{F_2\sin 30^{\circ}}{\sin75^{\circ}}\\&=\mathrm{\frac{150\;N\times 0.5}{0.966}}\\&=\mathrm{77.64\;N}\end{aligned}[/tex]

The required answers are 150 N and 77.64 N.

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Resolve F2 Into Components Along The U And V Axes Determine The Magnitudes Of These Components.

Related Questions

Jakobe runs a coffee cart where he sells coffee for $1.50 tea for $2 , and donuts for $0.75 . On Monday, he sold 320 items and made $415 . He sold 3 times as much coffee as tea. How many donuts did he sell?

Answers

Jakobe sold 150 coffee, 50 tea and 120 donuts at the coffee cart on Monday.

What is an equation?

An equation is an expression that shows the relationship between two or more numbers and variables.

Let x represent the amount of coffee, y represent the amount of tea and z represent the amount of donuts, hence:

x + y + z = 320 (1)

Also:

1.5x + 2y + 0.75z = 415 (2)

And:

x = 3y (3)

From the equations:

x = 150, y= 50 and z = 120

Jakobe sold 150 coffee, 50 tea and 120 donuts at the coffee cart on Monday.

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Find the slope of the line passing through the points (-4, -9) and (5, -9).

Answers

The slope of the line passing through the points (-4, -9) and (5, -9) is 0

How to determine the slope?

The points are (-4, -9) and (5, -9).

The slope is calculated using:

Slope = (y2 - y1)/(x2 - x1)

So, we have:

Slope = (-9 + 9)/(5 + 4)

Evaluate

Slope = 0

Hence, the slope of the line passing through the points (-4, -9) and (5, -9) is 0

Answers

Step-by-step explanation:

1) if m(∠A)∈[0;90°), then

[tex]cos(A)=\sqrt{1-sin^2A} =\frac{3}{5};[/tex]

[tex]sin2A=2sinAcosA=2*\frac{3}{5} *\frac{4}{5}=\frac{24}{25};[/tex]

[tex]cos2A=cos^2A-sin^2A=\frac{9}{25}-\frac{16}{25}=-\frac{7}{25};[/tex]

[tex]tan2A=\frac{sin2A}{cos2A}=-\frac{\frac{24}{25}}{\frac{7}{25}}=-\frac{24}{7}.[/tex]

2) if m∠A∈[90°;180°), then

cos(A)=-0.6;

sin2A=-0.96;

cos2A=-0.28;

tan2A=-24/7.

Mal works at a photo gallery. He charges $50 for a large photo and $40 for a large frame. Sales tax is 5%. How much total tax will a customer pay on both?Answer the questions to show how to write and simplify expressions that represent the problem.

2. Use the distributive property to expand 0.05(50 + 40). (2 points)

Answers

Answer:

$4.50

Step-by-step explanation:

We can use the distributive property to solve this problem. 0.05(50+40) is the total sales tax. 0.05 being the percentage and 50 and 40 being the things we need to distribute 0.05 to. This becomes 2.5+2. This is 4.5.

Answer:

$0.45

Step-by-step explanation:

0.05(50 + 40) = 50 x 0.05 + 40 x 0.05 = 0.25 + 0.20 = 0.45

To graph the inequality t>3, you would put an open circle on 3 and shade to the left

Answers

Answer:

It is an open circle and you would shade to the right on a number line.

Step-by-step explanation:

The circle is open because you are not including 3. Put numbers in for t and you will see that the numbers greater than 3 are all on the right side of the number line.

what is the ration between 28000 and 14?

Answers

The ratio between 28,000 and 14 is 2000 : 1

How to determine the ratio?

The numbers are given as:

28,000 and 14

Express as ratio

Ratio = 28000 : 14

Divide each number by 14

Ratio = 2000 : 1

Hence, the ratio between 28,000 and 14 is 2000 : 1

Answers

The largest y-value from the solution set of the nonlinear system is 3.78. (Correct choice: C)

What is the solution of a non-linear system

In this question we have a system of non-linear equation formed by a radical equation and a quadratic equation, which can be solved both analytically and graphically. By equalizing the two formulas we have the following equation:

√(2 · x + 4) = x² - 5 · x + 3

√(2 · x + 4) + 13 / 4 = x² - 2 · (5 / 2) · x + 25 / 4

√(2 · x + 4) + 13 / 4 = (x - 5 / 2) ²

√(2 · x + 4) = (x - 5 / 2) ² - 13 / 4

Then, we square both sides to eliminate the radical sign:

2 · x + 4 = (x - 5 / 2)⁴ - (13 / 2) · (x - 5 / 2)² + 169 / 16

2 · x + 4 = x⁴ + 4 · x³ · (- 5 / 2) + 6 · x² · (- 5 / 2)² + 4 · x · (- 5 / 2)³ + (- 5 / 2)⁴ - (13 / 2) · [x² + 2 · (- 5 / 2) · x + ( - 5 / 2)²] + 169 / 16

2 · x + 4 = x⁴ - 10 · x³ + (75 / 2) · x² - (125 / 2) · x + 625 /16 - (13 / 2) · x² + (65 / 2) · x - 325 / 8 + 169 / 16

2 · x + 4 = x⁴ - 10 · x³ + 31 · x² - 30 · x + 9

x⁴ - 10 · x³ + 31 · x² - 32 · x + 5 = 0

The real roots of this polynomial are:

x₁ ≈ 5.152, x₂ ≈ 2.862, x₃ ≈ 1.797, x₄ ≈ 0.189

Now we evaluate f(x) at each root:

y₁ ≈ 3.782, y₂ ≈ 3.118, y₃ ≈ 2.756, y₄ ≈ 2.092

The largest y-value from the solution set of the nonlinear system is 3.78. (Correct choice: C)

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Which of the following inequalities matches the graph?
-8 -0
O x>4
O x<4
O y> 4
O y<4
1

Answers

Answer:

it matches with equation c

I need help to this it would be awesome if you could help.

Answers

In the given diagram, the value of JI is 6

Solving equations

From the question, we are to determine JI

From the given diagram, we can write that

JI + IH = x + 22

Also,

JI = 2x + 28

and

IH = 5

Then, we can write that

2x + 28 + 5 = x + 22

Collect like terms

2x - x = 22 -28 -5

x = -11

Now, substitute the value of x into the equation

JI = 2x + 28

JI = 2(-11) + 28

JI = -22 +28

JI = 6

Hence, the value of JI is 6

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What is the area of an equilateral triangle having side 'a' units?

Answers

Answer:

[tex]A=\frac{\sqrt{3}}{4}a^2[/tex]

Step-by-step explanation:

Since an equilateral has all of the sides equal, we can find the height of triangle using: [tex]a^2+b^2=c^2[/tex]. I attached a diagram which should explain how I got the dimensions of the three sides. Using the information from the diagram we get the equation:

[tex]h^2+(\frac{a}{2})^2=a^2[/tex]

Subtract a^2 from both sides

[tex]h^2=a^2-(\frac{a}{2})^2[/tex]

Take the square root of both sides

[tex]h = \sqrt{a^2-(\frac{a}{2})^2}[/tex]

If you know the area of a triangle, it's: [tex]\frac{1}{2}bh[/tex]. In this case the base=a, and the height is what we defined above. Using this we get:

[tex]A = \frac{a}{2}*\sqrt{a^2-(\frac{a}{2})^2}[/tex]

We can distribute the exponent over the division to get:
[tex]A = \frac{a}{2}*\sqrt{a^2-(\frac{a^2}{4})[/tex]

Now we can rewrite a^2 as 4a^2/4

[tex]A = \frac{a}{2}*\sqrt{\frac{4a^2}{4}-(\frac{a^2}{4})[/tex]

Now add the two fractions:

[tex]A = \frac{a}{2}*\sqrt{\frac{3a^2}{4}[/tex]

We can distribute the square root the division just like how we distributed the exponent 2, since the square root can be expressed as an exponent (1/2)

[tex]A = \frac{a}{2}*\frac{\sqrt{3a^2}}{\sqrt{4}}[/tex]

There's a radical identity that states: [tex]\sqrt[n]{a} * \sqrt[n]{b} = \sqrt[n]{a*b}[/tex]. We can use this to rewrite one radical as multiple radicals to simplify it:

[tex]A = \frac{a}{2}*\frac{\sqrt{a^2}*\sqrt{3}}{2}[/tex]

Simplify:

[tex]A = \frac{a}{2}*\frac{a*\sqrt{3}}{2}[/tex]

Now multiply the two fractions

[tex]A = \frac{a^2*\sqrt{3}}{4}[/tex]

This is the formula for the area of an equilateral triangle, but it is also often written as:
[tex]A=\frac{\sqrt{3}}{4}a^2[/tex]

Suppose f′(6)=5 and g′(6)=7.
Find h′(6) where h(x)=4f(x)+5g(x)+1.

Answers

The value of the derivative of functions h'(6) as requested in the task content is; 55.

What is the value of h'(6)?

Since it follows from the task content that the function h(x)=4f(x)+5g(x)+1.

Hence, the derivative of h(x) can be evaluated as;

h'(x)=4f'(x)+5g'(x)

On this note, by substitution, it follows that;

h'(6)=4(5)+5(7)

h'(6) = 55.

Answers

The cube can contain 1000 cm^3 of water

How to determine the amount of water?

The side length is given as:

L = 10 cm

The amount of water it can contain is calculated as;

V =L^3

So, we have:

V = 10^3

Evaluate

V = 1000

Hence, the cube can contain 1000 cm^3 of water

Answers

Using the simple interest formula, it is found that the APR for the loan is of 4.472%.

What is the simple interest formula and when it is used?

Simple interest is used when there is a single compounding per time period.

The amount of money after t years in is modeled by:

[tex]A(t) = A(0)(1 + rt)[/tex]

In which:

A(0) is the initial amount.r is the interest rate, as a decimal.

The parameters for this problem are:

A(t) = 6 x 511.18 = 3067.08, A(0) = 3000, t = 0.5.

We solve the equation for r to find the APR.

[tex]A(t) = A(0)(1 + rt)[/tex]

[tex]3067.08 = 3000(1 + 0.5r)[/tex]

[tex]1 + 0.5r = \frac{3067.08}{3000}[/tex]

1 + 0.5r = 1.02236

r = (1.02236 - 1)/0.5

r = 0.04472.

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Question 1 of 10
If f(x)=x-1, which of the following is the inverse of f(x)?
O A. f¹(x) = x
OB. f¹(x)=x+1
O C. f¹(x)=x-1
O D. f¹(x) = 1 - x
SUBMIT

Answers

Question 1 of 10
If f(x)=x-1, which of the following is the inverse of f(x)?

Correct Options is A

In science class, the average score on a lab report is 87 points, with all students scoring within 1.8 points of the average. If x represents a student's score, write an equation that represents the
minimum and maximum scores.

Answers

The equations which represents the minimum and maximum scores of the students is; x = 87 ± 1.8.

Which equations represents the minimum and maximum possible scores of each student?

According to the task content, the

Average score of the students in the science class is; 87 points

All students are within 1.8 points of the average,

it therefore follows from the task content that the

minimum score is;

= 87 -1.8

= 85.2

maximum score is;

= 87+1.8

= 88.8 points.

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Answer:

Step-by-step explanation:

A. |x − 87| = 1.8

-hope this helps.

What is the angle of rotation of the following figure?

Answers

This snow flake-like figure can be generated by rotating an end 60° five times around the center of the hexagon. There are two forms: (i) clockwise, (ii) counterclockwise.

What is the angle of rotation of a snow flake?

Geometrically speaking, snow flakes represent regular hexagons. Regular hexagons can divided into six concentric regular triangles, whose central angles have a measure of 60°. This fractal figure can be generated by rotating 60° five times around the center.

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Choose the algebraic description that maps the image ΔABC onto ΔA′B′C′.

Answers

The algebraic description that maps the image ΔABC onto ΔA′B′C′ is (x, y) ⇒ (x + 7, y - 4)

What is transformation?

Transformation is the movement of a point from its initial location to a new location. Types of transformations are reflection, rotation, translation and dilation.

Translation is the movement of a point either up, left, right or down in the coordinate plane.

The algebraic description that maps the image ΔABC onto ΔA′B′C′ is (x, y) ⇒ (x + 7, y - 4)

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the cowboys football team started at the zero yard line.throughout the course of the first quarter the team gained 7 yards, lost 8 yards and then lost 7 more yard. what is the total of these three plays? how many yards did the team gain or lose?

Answers

The net number of yards lost by the cowboys football team is; 8 yards.

How many yards did the team gain or lose?

It follows from the task content that the number of yards gained or lost by the football team during each of the three plays is; gained 7 yards, lost 8 yards and then lost 7 more yard.

Hence, by polarising yard gain as positive and yard loss as negative; we have;

Net total = 7 - 8 -7 = -8

Hence, the team lost 8 yards in the total game.

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23 gram put into milligrams

Answers

Answer:

Step-by-step explanation: 23000 milligrams

23000 milligrams. just multiply by 1000

Match each function with the corresponding function formula when h(x) = 5 - 3x and g(x) = -3x + 5.

Answers

Answer: -5=x

Step-by-step explanation:

kmbtvonpvnp4tnv

Choose the correct simplification of (4x − 3)(3x2 − 4x − 3).

Answers

the expression simplified is:

[tex]12x^3 - 25x^2 + 9[/tex]

How to simplify the given expression?

Here we have the expression:

[tex](4x - 3)*(3x^2 - 4x - 3)[/tex]

We just need to distribute the product, we will get:

[tex](4x - 3)*(3x^2 - 4x - 3)\\\\(4x)*(3x^2 - 4x - 3) - 3*(3x^2 - 4x - 3)\\\\12x^3 - 16x^2 - 12x - 9x^2 + 12x + 9[/tex]

Now we just need to group terms with the same exponent of x:

[tex]12x^3 - 16x^2 - 12x - 9x^2 + 12x + 9\\\\12x^3 + (-16 - 9)x^2 + (-12 + 12)x + 9\\\\12x^3 - 25x^2 + 9[/tex]

That is the expression simplified

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What is the domain of the rational function f of x is equal to the quantity x squared minus x minus 12 end quantity over the quantity x cubed minus 4 times x squared minus 4 times x plus 16 end quantity question mark

{x ∈ ℝ| x ≠ –2, 2, 4}
{x ∈ ℝ| x ≠ –2, 2}
{x ∈ ℝ| x ≠ –3, 4}
{x ∈ ℝ| x ≠ –3, –2, 2, 4}

Answers

The domain of the rational function is:

{x ∈ ℝ| x ≠ –2, 2}

What is the domain of the rational function?

Here we have the rational function:

[tex]f(x) = \frac{x^2 - x - 12}{x^3 - 4x^2 - 4x + 16}[/tex]

We want to get the domain of that function. First, we can rewrite the numerator and denominator as:

[tex]x^2 -x - 12 = (x + 3)*(x - 4)[/tex]

[tex]x^3 - 4x^2 - 4x + 16 = (x - 4)*(x + 2)*(x - 2)[/tex]

Then we can rewrite the rational function as:

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

This can be simplified to:

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

Now, the domain will be the set of all real numbers, minus the values of x that generate problems.

In this case, the values:

x = -2 and x = 2 make the denominator to be zero, and we can't divide by zero, so we conclue that the domain is:

{x ∈ ℝ| x ≠ –2, 2}

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solve this pleas i need urgent answer

Answers

Answer:

f(n)={n/2 = if n is even= n={2/2

{3n+1 {3(2)+1 =7

Step-by-step explanation:

if n is even u can put any even no in that place and u can get odd no or even no.(i think)

a two digit number has twice as many ones as tens twice the original number is 9 more than the reversed number find the original number

Answers

Answer: 36

Step-by-step explanation:

As this is a two-digit number, it will have a digit in its 10's place and a digit in its 1's place. We can represent the 10's digit using x and the 1's digit using y.

Since the ones is twice the number of tens, this means that y is equal to 2*x. Let's put this into an equation.

[tex]y=2x[/tex]

If the 10's digit is x and the 1's digit is y, the original number would be [tex]10x + y[/tex], as x must be multiplied by 10 to get it to the 10's place. Similarly, the reversed number would be [tex]10y + x[/tex], as y must be multiplied by 10 to get it to the 10's place.

Twice the original number (10x+y) is equal to 9 more than (i.e. 9 plus) the reversed number. We can put this into an equation to help us answer the question.

[tex]2(10x+y)=9+10y+x\\20x+2y=9+10y+x\\19x+2y=9+10y\\19x=9+8y[/tex]

Now we have a system of two equations.

[tex]y=2x\\19x=9+8y[/tex]

We can solve this system by substituting y for 2x in the second equation. Then, we can isolate and get the value of x.

[tex]19x=9+8(2x)\\19x=9+16x\\3x=9\\x=3[/tex]

Now that we have the value of x, let's put it back into the first equation and solve for y.

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

Remember that x is the 10's digit and y is the one's digit of our answer. Since x is 3 and y is 6, our answer is 36.

Checking

We can quickly check if our answer is right by making sure both conditions in the question are met.

6 (the one's digit) is twice the value of 3 (the ten's digit), making the first condition true. Twice of 36 is 72, which is 9 more than the reversed number, which is 63.

A company determines that the revenue, in dollars, for selling a particular model of lamp is given by R(x)=x(−20x+1200), where x is the price of each lamp. At which of the following prices will the company’s revenue be $10,000?

Answers

The price that will maximize company’s revenue of $10,000 is $50.

How to calculate the price?

From the information, the company determines 50that the revenue, in dollars, for selling a particular model of lamp is given by R(x)=x(−20x+1200),

Therefore, this will be:

R(x) = -20x² + 1200x

10000 = -20x² + 1200x

-20x² + 1200x - 10000 = 0

x² - 60x + 500

x² - 50x - 10x + 500

x(x - 50) - 10(x - 50)

(x - 50)(x - 10)

Therefore, x - 50 = 0

x = 0 + 50 = 50

The price is 50.

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1. Determine the measure of angle B.
B
30
A
64
51

Answers

Answer: 51.4°

Step-by-step explanation:

Use law of cosines:

(because you are trying to find angle B, you need to use Cos B)

Cos B = c² + a²-b²/ 2ca

Then, plug in your numbers:

Cos B = 30²+64²-51²/ 2(30)(64)

Simplify:

Cos B = 0.6237

Next, to get rid of Cos B, so that we have just B, you need to do the Arccosine or 0.6237:

B = arccosine (0.6237)

Which gets you: 51.4°

The measure of angle B is 51.41 degrees after applying the cos law of the triangle.

What is the triangle?

In terms of geometry, the triangle is a three-sided polygon with three edges and three vertices. The triangle's interior angles add up to 180°.

We have given a triangle in the figure:

To find the measure of the angle B

We can apply cos law:

c² = a² + b² - 2ab cosB

The a, b, and c represents the side lengths of the triangle and the measures are:

a = 30

b = 64

c = 51

51² = 30² + 64² - 2(30)(64) cosB

3840CosB = 4996 - 2601

3840CosB = 2395

CosB = 2395/3840

CosB = 0.623

B = Cos⁻¹(0.623)

B = 51.41 degrees

Thus, the measure of angle B is 51.41 degrees after applying the cos law of the triangle.

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What is the value of x
83
58
50
70.5

Answers

Answer:

Step-by-step explanation:

[tex]x = \frac{141 - 25}{2} = 58[/tex]

-4
-2
4
-2-
0
3
On which interval are both functions increasing?
2
-8
p
0
-X
-2
g(x) = -x - 3| +4
(,0)

Answers

Answer: [tex](3, \infty)[/tex]

Step-by-step explanation:

q(x) is increasing for [tex]x > 3[/tex].

p(x) is increasing for [tex]x \geq -2[/tex].

So, both functions are increasing for [tex](3, \infty)[/tex].

Write the positive or negative number that best
represents the given information.
12 ft above sea level

Answers

Answer:

Step-by-step explanation:

Usually, above sea level is represented by a positive number and below sea level by a negative number.

12 ft above sea level = 12

1. In a class of 60 students, a survey was conducted, 30 students had applied for Addis Ababa University, 25 students applied for Bahir Dar University and 24 students applied for Wachemo University. 11 students applied for both Addis Ababa and Bahir Dar Universities, 6 applied for both Addis Ababa and Wachemo Universities, 9 applied for both Wachemo and Bahir Dar Universities while 4 applied neither of the aforementioned universities. Find 1.. number of students that applied for all the universities. 2 number of students that applied for at least two of the universities. 3 number of students that applied at most two universities. 4 number of students that applied for Addis Ababa but not Bahir Dar University? Please I need your help?

Answers

1. Consult the linked question. [tex]n(A\cap B\cap W) = \boxed{3}[/tex].

2. We have

[tex]n(A\cap B) = n(A\cap B \cap W) + n(A\cap B \cap W') \\\\ \implies 11 = 3 + n(A\cap B \cap W') \\\\ \implies n(A\cap B\cap W') = 8[/tex]

Similarly we can find

[tex]n(A\cap B' \cap W) = 3[/tex]

[tex]n(A'\cap B\cap W) = 6[/tex]

[tex]n(A\cap B'\cap W') = 16[/tex]

[tex]n(A'\cap B\cap W') = 8[/tex]

[tex]n(A'\cap B'\cap W) = 12[/tex]

Then the total number of students that applied to at least two of the universities is

[tex]\underbrace{n(A\cap B\cap W') + n(A\cap B'\cap W) + n(A'\cap B\cap W)}_{\text{only 2}} + \underbrace{n(A\cap B\cap W)}_{\text{all 3}} = \boxed{20}[/tex]

3. There's a small ambiguity here. Are we interested in students that applied to zero universities? If so, there are

[tex]\underbrace{n(U\setminus(A\cup B\cup W))}_{\text{none}} + \underbrace{n(A\cap B'\cap W') + n(A'\cap B\cap W') + n(A'\cap B'\cap W)}_{\text{only 1}} = \boxed{40}[/tex]

If we want students that applied to at least 1 school, we omit the first term and get a total of 36.

4. Split this set of students into those that also applied to Wachemo and those that did not.

[tex]n(A \cap B') = n(A\cap B' \cap W) + n(A\cap B'\cap W') = \boxed{19}[/tex]

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