Answers
(a) v appears to have a fixed direction along the positive x-axis. If ||u|| = 150 N, ||v|| = 220 N, then when θ = 30°, you have
u = (150 N) (cos(30°) i + sin(30°) j ) ≈ (129.904 i + 75 j ) N
v = (220 N) (cos(0°) i + sin(0°) j ) = (220 i ) N
(i and j are the unit vectors in the positive x and y directions)
and their sum is
u + v ≈ (349.904 i + 75 j ) N
with magnitude
||u + v|| ≈ √((349.904)² + (75)²) N ≈ 357.851 N ≈ 357.9 N
and at angle φ made with the positive x-axis such that
tan(φ) ≈ (75 N) / (349.904 N) → φ ≈ 12.098° ≈ 12.1°
(b) Letting θ vary from 0° to 180° would make v a function of θ :
u = (150 N) (cos(θ) i + sin(θ) j ) = (150 cos(θ) i + 150 sin(θ) j ) N
Then
u + v = ((220 + 150 cos(θ)) i + (150 sin(θ)) j ) N
→ M = ||u + v|| = √((220 + 150 cos(θ))² + (150 sin(θ))²) N
M = √(48,400 + 66,000 cos(θ) + 22,500 cos²(θ) + 22,500 sin²(θ)) N
M = 10 √(709 + 660 cos(θ)) N
(c) As a function of θ, u + v makes an angle α with the positive x-axis such that
tan(α) = (150 sin(θ) / (220 + 150 cos(θ))
→ α = tan⁻¹((15 sin(θ) / (22 + 15 cos(θ)))
(d) Filling in the table is just a matter of evaluating M and α for each of the given angles θ. For example, when θ = 0°,
M = 10 √(709 + 660 cos(0°)) N = 370 N
α = tan⁻¹((15 sin(0°) / (22 + 15 cos(0°))) = 0°
When θ = 30°, you get the same result as in part (a).
When θ = 60°,
M = 10 √(709 + 660 cos(60°)) N ≈ 323.3 N
α = tan⁻¹((15 sin(60°) / (22 + 15 cos(60°))) = 23.8°
and so on.
Related Questions
∠1and ∠2 are complementary angles.
m∠1=52°
What is the measure of ∠2?
Answers
Answer: 38°
Step-by-step explanation:
Complementary angles are two angles that add up to 90°
Simce the first angle is 52°, subtract 90-52 to get 38°
x +y=5, 2x-3y=4
3x+4y=10, 2x-2y=2
by Multiplication method
correct answer will mark as brainiest
Answers
Find the value of x and then perimeter
Answers
Answer:
×= 4 and the perimeter is 18
Step-by-step explanation:
(x+3)(x-2)=14
x^2+x-6=14
x^2+x-20=0
(x+5)(x-4)=0
x=4
perimeter = 7(2)+2(2)=18
Lots of points and brainliest!!!
A system of inequalities can be used to determine the depth of a toy, in meters, in a pool depending on the time, in seconds, since it was dropped. Which constraint could be part of the scenario?
The pool is 1 meter deep.
The pool is 2 meters deep.
The toy falls at a rate of at least a Negative one-half meter per second.
The toy sinks at a rate of no more than a Negative one-half meter per second.
Answers
Answer:
The toy falls at a rate of at least a Negative one-half meter per second.
Step-by-step explanation:
Answer:
the awnser is a or the pool is 1 meter deep
Step-by-step explanation:
i am smart and i got it right when i did it
Helen bought metal rods that are each 4.2 centimeters long. If Helen lines up 7 of them end-to-end, how long will the line be? Must bein centimeters
Answers
Answer:
29.40 cm
Step-by-step explanation:
total length = length of each rod x number of rods
4.2 x 7 = 29.40cm
Help pls!! I need to pass
Answers
A cell phone company data about students texting skills.They collected the texting speed in words per minutes according to time in minutes.Identify the data's independent and dependent values
Answers
Answer:
independent variable = Time
Dependent variable = texting speed
Step-by-step explanation:
The Independent and dependent variables are used in regression analysis for making prediction. The Independent variable also called the predictor are the variables or data collected in other to influence or determine the outpjt obtained which is the dependent or predicted variable. Hence, the aim or prediction we wish to obtain, measure or determine is the dependent variable In the scenario above, the aim of the data collected is to determine the typing skill, here, the dependent variable is the typing skill. The data required to define the bthis is the data collected on typing speed which measures time taken to type.
Therefore, independent variable = Time
Dependent variable = texting speed
I will mark you brainiest if you an answer this
Answers
Answer:
the awnswer is a = 7 + c
Step-by-step explanation:
Use the Distributive Property to solve the equation. 4(x + 3) = 32 The solution of the equation is (Type the value of x)
Answers
Answer:
x = 5
Step-by-step explanation:
4(x + 3) = 32
Use Distributive Property
4x + 12 = 32
Subtract 12 on both sides
4x = 20
Divide 4 on both sides
x = 5
Hope this helps! ^^
Their is a rectangle that has measurements in inches. If the width is 7/8 of an inch and the height is 2/3 of an inch, what is the AREA of the rectangle?
Answers
Answer:
Area of a rectangle = 7/12 of an inch
Step-by-step explanation
Area of a rectangle = Length × width
In this case, the length is represented by height
Height = 2/3 of an inch
Width = 7/8 of an inch
Area of a rectangle = Length × width
= 2/3 × 7/8
= (2 * 7) / (3 * 8)
= 14 / 24
= 7 / 12
Area of a rectangle = 7/12 of an inch
3/5 of 3 1/4 is
( Thx for the answer :) )
Answers
Answer:
Step-by-step explanation:
1.95 is the correct answer
Pslss helpppp (any diffrent answer will be reported)
Answers
Pie multiply 6.5^2=132.7322896
Please please help me with this question
Profile: John John is a 35 year old, divorced man with one child (who lives with his mom). His take home pay is $4123 per month. He pays $1200 per month in child support to his ex-wife. He owns a 2-storey home and his monthly mortgage payments are $475 every 2 weeks. His car expenses total $145 monthly and his car insurance costs him $113 every month. His house insurance is $47.36 monthly. John also has an outstanding credit line of $8500. The only amount due on this account is the interest of about $55 monthly. However John is trying to pay off the credit line within the next 2 years, so he pays off as much of this loan as he can afford each month.
1.Use one highlighter to identify all sources of income. Total the income for each month.
2.Use a different highlighter to identify all sources of expense. Total the expenses for each month.
3. Subtract the Total Expenses from the Total Income for each
month. A Surplus is when your Income minus Expenses = a positive number.
A Shortage is when your Income minus Expenses = a negative number. Does he have a surplus or a shortage?
Answers
Answer:
1. Income highlight: $4123 of take home pay. That's it.
Total monthly income: $4123
------------------------------------
2. Expense highlight:
$1200 child support
$475 every 2 weeks
$145 car payment
$113 car insurance
$47.36 house insurance
$55 loan payment
Total monthly expense: $2510.36
(1200 + 2(475) + 145 + 113 + 47.36 + 55 = $2510.36
---------------------------------------------
3. $4123 - 2510.36 = 1612.64 surplus
--------------------------------------------
The only question remaining is what if they want him paying more on his credit line...it's kind of a variable expense at this point.
John also has an outstanding credit line of $8500. The only amount due on this account is the interest of about $55 monthly. However John is trying to pay off the credit line within the next 2 years, so he pays off as much of this loan as he can afford each month.
Spinning an odd number and flipping heads.
Answers
Answer:
what
Step-by-step explanation:
Help plsss no links!!! What is the measure of X in degrees?
Answers
Answer:
40⁰
Step-by-step explanation:
As triangle is isosceles,
Z = Y = 70⁰
Thus X = 40⁰, to corporate angle sum property
Which three lengths could be the lengths
of the sides of a triangle?
A. 4 cm, 8 cm, 13 cm
B. 13 cm, 11 cm, 23 cm
C. 5 cm, 18 cm, 12 cm
D. 25 cm, 8 cm, 16 cm
Answers
Given:
The three lengths in the options.
To find:
Which three lengths could be the lengths of the sides of a triangle?
Solution:
If the sum of two smaller sides is greater than the largest side, then the three sides can form a triangle otherwise the triangle is not possible.
In option A, the three sides are 4 cm, 8 cm, 13 cm. Here, the largest side is 13 cm.
Sum of two smaller sides is:
[tex]4+8=12[/tex]
[tex]4+8<13[/tex]
So, the triangle is not possible.
In option B, the three sides are 13 cm, 11 cm, 23 cm. Here, the largest side is 23 cm.
Sum of two smaller sides is:
[tex]13+11=24[/tex]
[tex]13+11>23[/tex]
So, the triangle is possible.
In option C, the three sides are 5 cm, 18 cm, 12 cm. Here, the largest side is 18 cm.
Sum of two smaller sides is:
[tex]5+12=17[/tex]
[tex]5+12<18[/tex]
So, the triangle is not possible.
In option D, the three sides are 25 cm, 8 cm, 16 cm. Here, the largest side is 25 cm.
Sum of two smaller sides is:
[tex]8+16=24[/tex]
[tex]8+16<25[/tex]
So, the triangle is not possible.
Therefore, the correct option is B. The three lengths 13 cm, 11 cm, 23 cm could be the lengths of the sides of a triangle.
Hi i need help identifying them
Answers
3.scalene triangle
5. Acute triangle
I’m a bit rough when it comes to triangles, so I hope this helped!
The circumference of a fire is 96 inches. Determine the radius of the tire. Use 3 for TT.
Answers
Answer:
radius is 16 inches
Step-by-step explanation:
C = 2πr
96 = 2(3) r
16 = r
X=? What’s is this one?
Answers
Answer:
x = 50°
y = 130°
z = 130°
Step-by-step explanation:
the central angle is equal to it's arc in degrees.
y = 180° - 50° = 130°
(a) Is the image of the dilation a reduction or an enlargement of the original figure? Explain.
(b) What is the scale factor? Explain.
Answers
Answer:
Hello it is a reduction because it is smaller then the original shape and the green shape is the dilation!
Its a scale factor of 1/2 Hope this helps!
Answer:
Step-by-step explanation:
It's a reduction (smaller) so the scale factor is less than 1.
In fact it is 1/2 as for example B (4, 4) maps to B' (2, 2).
Subtract line 2 from line 1 to find your taxable income
Answers
Answer:
is there a pic?
Step-by-step explanation:
Your taxable income for the year is $42,000.
What is your available pay in an expense estimation?Your taxable income is the amount on which you are taxed in a tax calculation. Start with your $50,000 annual income as your base for the calculation.
Then, at that point, take away the allowances, which diminish your available pay, from the all-out pay. The deductions in this instance total $8,000 As a result, your taxable income will be $42,000, or $50,000 divided by $8,000.
This indicates that you will pay tax on $42,000, which will determine your tax bracket and the amount you owe. Deductions like contributions and expenses lower taxable income, thereby lowering the yearly tax bill.
Deduct the total income from the deductions to determine the taxable income:
Available pay = Complete pay - Allowances
Available pay = $50,000 - $8,000
Available pay = $42,000.
Your taxable income for the year is $42,000.
Learn more about expenses here:
https://brainly.com/question/14697297
#SPJ2
The complete question:
What is your taxable income in an expense estimation on the off chance that your year's complete pay is $50,000 and you deduct $8,000?
4x^2=27x+40
Solve by factoring
Answers
Answer: hewo, there! your answer is below
x= -5/4
or x= 8
Step-by-step explanation:
step 1: Subtract 27x+40 from both sides.
4x2−(27x+40)=27x+40−(27x+40)
4x2−27x−40=0
Step 2: Factor left side of equation.
(4x+5)(x−8)=0
Step 3: Set factors equal to 0.
4x+5=0 or x−8=0
hope this helps you
have a great Day
Plz makr branilest
help pleasee::::::::::::::::::::
Answers
Step-by-step explanation:
simplify
log(x)/log(4) = 0
simplify
log(4x)/log(4) = 1
expand
2log(5)/log(4) + log(4x)/log(4) = log(100)/log(4)
factor
2log(5) + log (4x) / log(4) = log (100) / log (4)
then
x=1
which value is closest to 0 on a number line? A.12 B.|-12.5| C.-11.75 D.|12.1
Answers
Answer: -11.75
Step-by-step explanation: The distance is 11.75 units close to 0, compared to the 2nd closest which is A (12)
Which statements are correct about the following expression? Select TWO that apply.
2y + 1
Answers
Answer:
Step-by-step explanation:
2y + 1 is a binomial, in that it has two terms.
If we set 2y + 1 equal to x, then 2y = x - 1, or
x - 1
y = -----------
2
You fill cone-shaped pastry bags with icing to a height to 1 foot and a diameter of 3.5 inches. You use about 1.35 cubic inches of icing per cupcake. About how many cupcakes can you decorate with 2 bags of icing?
Answers
Answer:
about 57
Step-by-step explanation:
a basket contains 6 white socks 4 blue socks and 2 black socks
what is the probability of choosing one blue sock and then a white socks with replacement
Answers
Answer:
Tha answers is
1/6
Step-by-step explanation:
Hope this help
A cylinder has a radius of 5 cm and a height of 8 cm. What is the volume of the cylinder in terms of π?
Answers
Answer:
The answer to the question is 80π
Helps are really appreciated!!
Answers
Answer:
a) 58.24 square centimeters
b) 5cm
Step-by-step explanation:
a) Area of a parallelogram
The formula for the Area of a parallelogram = Base × Height
Height : 5.2cm
Base : 11.2cm
Area = 5.2 cm × 11.2cm
= 58.24 square centimeters
b) Volume of a cuboid
The formula for the Volume of a cuboid = Length × Width × Height
7cm = Width
3cm = Length
y = Height
Volume = 105cm³
We are to find y
Hence,
105cm³ = 7cm × 3cm × y
y = 105cm³/7cm × 3cm
y = 5cm
if x=4 what is the value of 3x-2
Answers
Answer:
10
Step-by-step explanation:
Because x=4 you have to plug it into the equation
3(4)-2=
12-2=
=10