Two forces with magnitudes of 25 and 30 pounds act on an object at angles of 10° and 100°, respectively. Find the direction and magnitude of the resultant force. Round to two decimal places in all intermediate steps and in your final answer.

Answers

Answer 1

The direction and magnitude can be found by summing the x- and y-components of each force.
It is best presented in the form of a table, where
x-component = Fcos(theta)
y-component = Fsin(theta)
For F=25 pounds, angle = 30
25cos(30)=21.65

Force angle x-component y-component
25 30 25cos(30)=21.65 25sin(30)=12.5
30 100 30cos(100)=-5.21 30sin(100)=29.54
Total Fx=16.44 Fy=42.04
Therefore angle = tan^(-1)(Fy/Fx)=tan^(-1)(42.04/16.44) = 68.64 °
magnitude = sqrt(Fx^2+Fy^2)=sqrt(16.44^2+42.04^2)=45.15 pounds

Related Questions

1/6 of 3 yards=______feet

I know I just ask one but u get 17 points so plz help I'm stuck

Answers

In this question, first we have to see how many feets are in 1 yard .

And there are 3 feets in 1 yard.

So in 3 yards, there are 9 feets

Therefore we will get

[tex] \frac{1}{6}*3 yards= \frac{1}{6} * 9 feet = 1.5 feet [/tex]

Therefore the answer of the given question is 1.5 feet.

Final answer:

To find the equivalent feet for 1/6 of 3 yards, multiply 1/6 by 3 feet per yard to get 1.5 feet.

Explanation:

1/6 of 3 yards=_____feet

Step 1: 1 yard is equal to 3 feet.

Step 2: To find the equivalent feet for 1/6 of 3 yards, calculate 1/6 x 3 = 0.5 x 3 = 1.5 feet.

Elijah is going to spin a spinner that goes to 4 180 times.He predicts that 60 of those spins will result in the spinner landing on the section labeled 3. Based on the theoretical probability, which best describes Elijah’s prediction?

Answers

The spinner will probably land on 3

Answer:

A. Elijah’s prediction is exact because 180 divided by 3 = 60.

Step-by-step explanation:

A rectangular prism has a length of 4 1/2 millimeters, a width of 4 1/2 millimeters, and a height of 6 millimeters.

Sally has a storage container for the prism that has a volume of 143 cubic millimeters.

What is the difference between the volume of the prism and the volume of the storage container?

Help Please?

Answers

Volume of a rectangular prism is found by multiplying the length by the width by the height. The volume of our given prism would be
V = (4 1/2)(4 1/2)(6)
Converting the fractions to mixed numbers we have
V = (9/2)(9/2)(6/1) = 486/4 = 121.5

The storage container has a volume of 143, so the difference is 143 - 121.5 = 21.5 cubic mm.

Answer:

21 1/2

Step-by-step explanation:

Patrick ate 2/3 of a fruit bar write an equivalent fraction for the amount of fruit bar Patrick ate

Answers

To get an equivalent fraction, multiply the fraction by a whole number. For example, you can do 2/3 times 2 to both sides which is 4/6.

which is equivalent to (9y2 – 4x)(9y2 + 4x), and what type of special product is it?
81y4 – 16x2, a perfect square trinomial
81y4 – 16x2, the difference of squares
81y4 – 72xy2 – 16x2, a perfect square trinomial
81y4 – 72xy2 – 16x2, the difference of squares

Answers

81y4 -16x, the difference of squares.

Final answer:

The expression (9y2 – 4x)(9y2 + 4x) is equivalent to 81y4 – 16x2, a difference of squares in mathematical terms.

Explanation:

The expression you are asking about is equivalent to

81y4 – 16x2

, which is a special product known as

the difference of squares

. In mathematics, a difference of squares is a term that describes an expression of the form a^2 - b^2. It can be factored into the multiplication of two binomials: (a+b)(a-b). In your example, (9y2)^2 is 81y4 and (-2x)^2 is 16x2, so the final expression is 81y4 – 16x2.

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△ABC is reflected to form △A′B′C′ . The vertices of △ABC are A(3, 1) , B(1, 5) , and C(6, 9) . The vertices of △A′B′C′ are A′(−1, −3) , B′(−5, −1) , and C′(−9, −6) . Which reflection results in the transformation of △ABC to △A′B′C′ ?

Answers

The reflection of the triangle across y = -x is the new triangle.

Answer:

that would be a reflection across the y axis resulting in a -x

Step-by-step explanation:

Rearrange the formula A = P + Prt for t.

Answers

Given that:
A=P+Prt
Solving for t.
Factor out P from the right side of the equation.
A=P(1+rt)
Divide both sides by P.
A/P= 1+rt
Subtract 1 from both sides
A/P-1=rt
Divide both sides by r.
(A/P) / r - 1/r= t
or
t= (A/P) / r - 1/r
t= A/Pr - 1/r
t= (A-P)/r

Answer: t= (A-P)/rP

Divide both side by p+pr . And T should be t= A over p+pr

how to solve -2x+y=7, 3y=6x+4

Answers

Consider, pls, this option.
To the additional, see the attached graph for this system.

Which expression represents the sixth term in the binomial expansion of (5y+3)^10

Answers

[tex]\bf \textit{the coefficient and values of an expanded term}\\\\ (5y-3)^{10} \qquad \qquad \begin{array}{llll} expansion\\ for\\ 6^{th}~term \end{array} \quad \begin{cases} \stackrel{term}{k}=0..10\\ \stackrel{exponent}{10}\\ -----\\ k=\stackrel{6^{th}~term}{5}\\ n=10 \end{cases}[/tex]

[tex]\bf \stackrel{coefficient}{\left(\frac{n!}{k!(n-k)!}\right)} \qquad \stackrel{\stackrel{first~term}{factor}}{\left( a^{n-k} \right)} \qquad \stackrel{\stackrel{second~term}{factor}}{\left( b^k \right)}[/tex]

[tex]\bf \stackrel{coefficient}{\left(\frac{10!}{5!(10-5)!}\right)} \qquad \stackrel{\stackrel{first~term}{factor}}{\left( (5y)^{10-5} \right)} \qquad \stackrel{\stackrel{second~term}{factor}}{\left( (-3)^5 \right)} \\\\\\ 252(5y)^5(-3)^5\implies 252(5^5y^5)(-3)^5\implies -252(3125y^5)(243) \\\\\\ -191362500y^5[/tex]

Answer:

Step-by-step explanation:

The scale on a map is 1 cm for every 400 km. If Maine and Japan are 22 cm apart on the map, what is the distance between Maine and Japan?

Answers

Essentially, you must multiply 22 by 400. You get 8800 km apart for your answer.

a kittens heartbeat can be as fast as 240 beats per minute . to find the number of times a kittens heart beats in 30 seconds , Aiden says divide 240 ny 30 . do you agree with him why or why not

Answers

I do not agree. If you divide 240 by 30, it would be 8 heartbeats, which is absurd. It's impossible for something to survive with 8 heartbeats per 30 seconds.
In order to get the CORRECT answer, divide 240 by 60 seconds.
This would give you 4 heartbeats per second.
Then, multiply it by 30 seconds, which would give you 120 heartbeats.

CORRECT answer: 120

how many radians are in a semicircle? a.2π, b.π, c.π/2, d.3π/2

Answers

Final answer:

A semicircle, which is half of a full circle, consists of half the total amount of radians in a full circle. Since a full circle has 2π radians, a semicircle contains π radians. Therefore, the correct answer is b.π.

Explanation:

To answer your question, let's review the structure of a circle.It is divided by its radius into 360 degrees or by its diameter into a full rotation of 2π radians. Therefore, a semicircle, which is half of a circle, must consist of half the total amount of radians in a full circle.

In a full circle, there are 2π radians. Hence, in a semicircle, which is exactly half of the full circle, there would be 2π/2. This simplifies to π radians.

So, the correct answer to your question 'How many radians are in a semicircle?' is b.π.

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what is the solution to -9×<63

Answers

Hey there! :D

I'm assuming that the multiplication sign is x.

When you are multiply something by x, you divide -9 on both sides. When you divide a negative number in an equality, you switch the signs.

x>-7 <== solution

I hope this helps!
~kaikers

Find the sum of the geometric series with a1 = 7, r = 2, And n = 14

Answers

Final answer:

The sum of the geometric series with a1 = 7, r = 2, and n = 14 is -327661.

Explanation:

The question is asking for the sum of a geometric series. In mathematics, the sum (S) of a geometric series is determined using the formula S = a1 * (1 - r^n) / (1 - r), where a1 is the first term, r is the common ratio, and n is the number of terms.

In the provided geometric series, a1 = 7, r = 2, and n = 14. Substituting these values into the formula gives us S = 7 * (1 - 2^14) / (1 - 2). After performing the calculations, the sum of the geometric series is -327661.

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Final answer:

The sum of the first 14 terms of the geometric series with the first term (a1) = 7, common ratio (r) = 2, is 114,691.

Explanation:

Given the first term of the geometric series (a1) = 7, the common ratio (r) = 2, and the number of terms (n) = 14, we would like to find the sum of this series. Using the formula for the sum of a geometric series, S = a1 * (1 - r^n) / (1 - r), substituting the given values, we get:

S = 7 * (1 - 2^14) / (1 - 2)

This simplifies to S = 7 * ( -16383) / -1, which results in S = 114,691. So, the sum of the first 14 terms of this geometric series is 114,691.

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Which statement best compares -1/2 and -2 1/2

Answers

From the Iready New York CCLS Question 18, The answer is B. If you count the spaces between -1 1/2 and -2 1/2 you get -2.

The Comparison between -1/2 and -2 1/2 is -1/2 is -2 more than -5/2.

What are fraction?

The fractional bar is a horizontal bar that divides the numerator and denominator of every fraction into these two halves.

The number of parts into which the whole has been divided is shown by the denominator. It is positioned in the fraction's lower portion, below the fractional bar.How many sections of the fraction are displayed or chosen is shown in the numerator. It is positioned above the fractional bar in the upper portion of the fraction.

Given:

-1/2 and -2 1/2

So, -1/2 and -5/2.

So, the quantity -1/2 > -5/2

Also, -1/2 is -2 more than -5/2.

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What is 1/4 as a whole number?

Answers

the answer is 1÷4=0.25

i think the answer is = .25

Identify the type of correlation shown in the scatter plot
A. Positive Correlation
B. Negative Correlation
C. No correlation.

Answers

I think it is no correlation because we can't exactly draw a line through this scatter plot

what is the square root of 4 multiplied by 16

Answers

it is 32, 2x2 is 4 so 2x16 is 32

the square root of 4 is 2, 2 x 16 is 32.

the answer is 32.

HELP ME PLEASE! How is the graph of mc027-1.jpg related to its parent function, mc027-2.jpg?

Answers

We will try to approach it generally. If we have a function y=f(x) and we have then y=f(2x), then the graph of the function will be horizontally compressed. If we take f(x/2), the graph of the function will be dilated. (To get horizontal shifts, we need f(x+a), which is not the case here; for example [tex] \sqrt{x+4} [/tex] is horizontally shifted relative to its parent function). If we consider -y=f(x), then the graph of this new function is the graph of the parent function flipped along the x-axis. If we consider y=f(-x) (which is the case here, since [tex] \sqrt{-x} = \sqrt{(-x)} [/tex]) we have that the graph of the new function is the same as the old graph, just flipped along the y-axis. Each of those transformations is independent; combining our observations we see that the last answer is the correct one.

The graph of [tex]y = \sqrt{-2x[/tex] relates to its parent function as a result of (d) horizontal compression by a factor of 2, and a reflection across the y-axis

What is a function transformation?

A function transformation involves changing the form or equation of a function to another through reflection, dilation, translation or rotation

How to determine the function transformation

The parent function is given as:

[tex]y = \sqrt x[/tex]

Compress the function horizontally by a factor of 2, using the following rule

[tex](x,y) \to (2x,y)[/tex]

So, we have:

[tex]y = \sqrt {2x[/tex]

Next, reflect the function over the y-axis, using the following rule

[tex](x,y) \to (-x,y)[/tex]

So, we have:

[tex]y = \sqrt {-2x[/tex]

Hence, the function transformation is (d)

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The measure of angle E, the angle of elevation from point A to point B, is 5(x-2). The measure of angle D, the angle of depression from point B to point A, is (x+14). Find the measure of each angle.

Answers

The angle of elevation and the angle of depression are the same. (They are alternate interior angles between the parallel lines of the ground and "horizontal.")
5(x -2) = x +14
5x -10 = x +14 . . . . . . . eliminate parentheses
4x = 24 . . . . . . . . . . . . add 10-x
x = 6

The angles of elevation and depression are both (6+14)° = 20°.

Answer:

measure of angle E equals 20 degrees, measure of angle D equals 20 degrees

In an office, the number of chairs, c , is equal to five more than twice the number of desks, d. Which equation matches the information?

Answers

c (unknown)
d (unknown)
chair is 5 more than twice the number of desks
So if I'm not wrong
The answer should be

c = 5+2d

Please correct me if I'm wrong :D

Final answer:

The algebraic equation that represents the relationship between the number of chairs, c, and the number of desks, d, in an office, where the number of chairs is five more than twice the number of desks, is c = 2d + 5.

Explanation:

The student's question pertains to creating an algebraic equation based on a given word problem describing the relationship between the number of chairs (c) and desks (d) in an office. The problem states that 'the number of chairs, c, is equal to five more than twice the number of desks, d'.

To formulate the equation that illustrates this relationship, we apply the information provided:

Identify the number of chairs as c.Determine that c is 'five more than' something, which suggests addition.Recognize that 'twice the number of desks' means 2 times d, or 2d.Combine the above to conclude that the 'five more than' is added to the 'twice the number of desks', which gives us the equation c = 2d + 5.

A radar gun used to determine the speed of passing cars must be within 7 mph of the actual speed of a selected car. If a highway patrol officer reads a speed of 59 mph for a car, does he have irrefutable evidence that the car was speeding in a 55 mph zone?

Answers

No. if it has a 7mph range the highest and lowest possible values would be 66mph to 52mph. The radar gun would have to measure 63 to cover the 14mph range for accuracy to claim the person was speeding.

Which is a disadvantage of withdrawing more money than is available in a checking account?

Answers

One disadvantage is most banks charge an overdraft fee once you take out more money than what is available.

A disadvantage of withdrawing more than you have in your account is you will be charged an overdraft fee.

What is an Overdraft Fee?

An overdraft fee can be described as the fee your bank charges you when you make a withdrawal from your account beyond what you have in it.

An overdraft fee is one of the disadvantages of withdrawing more money than you have in your account..

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amy is building a house. the basement floor is at -15 feet. the roof of the house is above the ground 25 feet. write an inequality to compare the heights. explain the meaning of the inequality.

BONUS: what is an inequality.

Answers

An inequation is a mathematical expression that is used to make constraints given a problem.
For example, this is a problem of heights.
There is a minimum height and a maximum height.
We can use the following inequation to describe the problem:
Let
x = height in feet.
The inequation is:
-15 <= x <= 25
answer:
-15 <= x <= 25

What is the total finance charge for a $4,250 loan at 13.25% interest compounded monthly for 24 months?
a. $25.47
b. $202.55
c. $611.20
d. $4,861.20

Answers

Answer: Option c. $ 611.20 will be correct.

Explanation:

Since, the total amount of finance charge is [tex]A=P\frac{r(1+r)^n}{(1+r)^n-1}[/tex]

Where P is the principle, r is the rate, n is the times of compound interest (monthly or quarterly etc.) .

Here P=$4250 r=13.25%, and n=24.

So according to the formula So, the finance charge= [tex]4250\frac{13.25(1+13.25)^{24}}{(1+13.25)^{24}-1}[/tex] = $ 611.20

The total finance charge for a $4,250 loan at 13.25% interest compounded monthly for 24 months is c) $611.20.

To calculate the total finance charge for a $4,250 loan at 13.25% interest compounded monthly for 24 months, we can use the following formula:

Total finance charge = Principal * (1 + Monthly interest rate)^Number of months - Principal

Where:

Principal is the amount of the loan ($4,250)

Monthly interest rate is the annual interest rate divided by 12 (13.25% / 12 = 1.1042%)

Number of months is the term of the loan in months (24)

Total finance charge = 4250 * (1 + 0.011042)^24 - 4250

Total finance charge = 611.20

Therefore, the answer is c. $611.20.

Note that this formula is for calculating the total finance charge over the entire term of the loan. If you want to calculate the monthly finance charge, you can simply divide the total finance charge by the number of months in the loan term. For example, the monthly finance charge for this loan would be $611.20 / 24 = $25.47.

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A bucket is put under a leaking ceiling. the amount of water in the bucket doubles every minute. after 8 minutes, the bucket is full. after how many minutes is the bucket half full? show work

Answers

This question is more of an Intelligence Question rather than a Mathematics Question.

The water in the bucket doubles every minute. After 8 minutes the bucket is full. This means a minute earlier (i.e. at 7th minute) the water in bucket was half as compared to water in bucket after 8 minute.

So, if after 8 minutes bucket is full, after 7 minutes bucket will be half full. So the answer is 7 minutes.

If f(x)=7+4x and g(x)=1/2x What is the value of (f/g)(5)?

Answers

If im not mistaken the answer is D 270

Answer:

[tex]\bigg(\displaystyle\frac{f}{g}\bigg)(5) = 270[/tex]

Step-by-step explanation:

We are given the following information in the question:

[tex]f(x) = 7 +4x\\\\g(x) = \displaystyle\frac{1}{2x}[/tex]

We have to find the values of [tex]\displaystyle\frac{f}{g}(x)[/tex]

[tex]\bigg(\displaystyle\frac{f}{g}\bigg)(x) = \frac{f(x)}{g(x)} = \frac{7 + 4x}{\frac{1}{2x}} = 2x(7+4x)[/tex]

Putting x = 5, we have:

[tex]\bigg(\displaystyle\frac{f}{g}\bigg)(x) = 2x(7+4x)\\\\\bigg(\displaystyle\frac{f}{g}\bigg)(5) = 2(5)(7+20)=270[/tex]

270 is the required value of [tex]\bigg(\displaystyle\frac{f}{g}\bigg)(5)[/tex].

Translated these questions to a equation:
6 more than 9 times a number x is -12
the quotient of a number t and 7, plus 2, is -4

Answers

6 more than 9 times a number x is -12...
6 + 9x = -12

the quotient of a number t and 7, plus 2, is -4 ...
(t/7)+ 2 = -4

Hope this helps :)

Suppose that with a budget of $100, Deborah spends $60 on sushi and $40 on bagels when sushi costs $2 per piece and bagels cost $2 per bagel. But then, the price of bagels falls to $1 per bagel.

Answers

60 divided by 2 = 30
40 divided by 2 =20
and thats all i got xD

60/2=30
40/2=20
with a new price of that bagel drop is 50%
(40/40+60=80
and 20$ is the money that Deborah income reducing

What is the solution to 2log9(x)=log^9(8)+log9(x-2)

Answers

2log9(x)=log^9(8)+log9(x-2)

Log₉x² = log₉8 + log₉(x-2)

Log₉x² = log₉(8×(x-2))

Log₉x² = log₉8x-16

Log₉x² - log₉8x-16 = 0

Log₉(x²/(8x-16)) = 0

x²/(8x-16) = 9°

x² = 1 × 8x-16

x²-8x+16 = 0

x²-4x-4x+16 = 0

x(x-4)-4(x-4) = 0

(x-4)(x-4) =0

Therefore x = 4.....

Answer:

C. x=4

Step-by-step explanation:

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