The magnitude and the direction of the resultant are approximately 57.871 and 198.676°.
How to determine the magnitude and the direction of a resultantVectors are elements with two given characteristics: Magnitude and direction. A resultant is derived from the sum of vectors, the magnitude is the norm of a vector and the direction is the orientation of a vector. The resultant and its characteristics are described below:
Resultant[tex]\vec r = \left(\sum\limits_{i=1}^{n}x_{i}, \sum\limits_{i=1}^{n}y_{i}\right)[/tex] (1)
Magnitude[tex]\|\vec r\| = \sqrt{\left(\sum\limits_{i=1}^{n} x_{i}\right)^{2}+\left(\sum\limits_{i=1}^{n} y_{i}\right)^{2}}[/tex] (2)
Direction[tex]\theta = \tan^{-1}\frac{\sum\limits_{i=1}^{n}y_{i}}{\sum\limits_{i=1}^{n}x_{i}}[/tex] (3)
Where [tex]\theta[/tex] is resultant angle, measured in degrees.
If we know that [tex]\|\vec u\| = 90[/tex], [tex]\theta_{u} = 40^{\circ}[/tex], [tex]\|\vec v\| = 60[/tex], [tex]\theta_{v} = 20^{\circ}[/tex], [tex]\|\vec w\| = 40[/tex] and [tex]\theta_{w} = 30^{\circ}[/tex], then the resultant, its magnitude and its direction:
Resultant[tex]\vec r = (-90\cdot \cos 40^{\circ}-60\cdot \sin 20^{\circ}+40\cdot \cos 30^{\circ}, 40\cdot \sin 30^{\circ}+60\cdot \cos 20^{\circ}-90\cdot \sin 40^{\circ})[/tex]
[tex]\vec r = (-54.824, 18.531)[/tex]
Magnitude[tex]\|\vec r\| = \sqrt{(-54.824)^{2}+18.531^{2}}[/tex]
[tex]\|\vec r\| \approx 57.871[/tex]
Direction[tex]\theta = \tan^{-1} \left(\frac{18.531}{-54.824}\right)[/tex]
[tex]\theta \approx 198.676^{\circ}[/tex]
The magnitude and the direction of the resultant are approximately 57.871 and 198.676°. [tex]\blacksquare[/tex]
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Can someone help me?
True or False. The volume formula for a general prism is dependent on the shape of the base.
answer: FALSE
Step-by-step explanation:
V=Bh
The formula for the volume of a prism is V=Bh , where B is the base area and h is the height. The base of the prism is a rectangle. The length of the rectangle is 9 cm and the width is 7 cm. The area A of a rectangle with length l and width w is A=lw .
A small bottle of shampoo can hold 35 milliliters of shampoo, whereas a large bottle can hold 500 milliliters of shampoo. Jasmine wants to buy the minimum number of small bottles necessary to completely fill a large bottle. How many bottles must she buy
Answer:
15
Step-by-step explanation:
500/35 approx 14.28
Always round up otherwise there won’t be enough
14.28 rounded up = 15
Could someone help me
Answer:
D) 3^9
Step-by-step explanation:
3^4 3^8 / 3^3
3^4 / 3^3 = 3
= 3 * 3^8
= 3^9
Answer:
(x+2)(x+3)
√2x
3
−3
−4+i
Step-by-step explanation:
A local hamburger shop sold a combined total of 394 hamburgers and cheeseburgers on Wednesday. There were 56 fewer cheeseburgers sold than hamburgers. How many hamburgers were sold on Wednesday?
Answer:
Step-by-step explanation:
Total number of Hamburgers and Cheeseburgers = 394
Let the number of hamburgers = x
x + x - 56 = 394 Combine the left
2x - 56 = 394 Add 56 to both sides
2x - 56 + 56 = 394 + 56 Combine
2x = 450 Divide both sides by 2
2x/2 = 450/2
x = 225
Answer
225 hamburgers were sold169 Cheeseburgers soldGive me full working and explanation! And I give you stars and I mark you as brainliest for sure. Best deal here.
1st clock timing
1 : 152nd clock timing
2 : 003rd clock timing
3 : 304th clock timing
4 : 4530.
formula for discount: original price - final price
discount: $700 - $505.75 = $194.25In percentage:
[tex]\rightarrow \sf \dfrac{194.25}{700} *100[/tex]
[tex]\rightarrow \sf 27.75\%[/tex]
ii)
3($194.25) = $582.75 discount
In percentage: same. 27.75%
Which medical professional or service treats severe medical needs?
emergency room
pregnancy center
medical specialist
general practitioner
Answer:
emergency room
Step-by-step explanation:
well the most severe medical cases come from immediate accidents and for that you go to the emergency room
(correct me if I'm wrong)
Emergency room treats severe medical needs.
Given,
Treatment of severe medical needs.
Now,
Emergency room treats the person having critical illness which requires instant medication .
For example :
If a person met with an accident then the medication must be provided instantly so that the person can survive . Instant medication will be provided under emergency rooms .
Therefore option A is correct .
Know more about emergency needs,
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A soda company made 1,040,000 bottles of soda. The manufacturer tested 200 bottles and found that 32 have cracks. About how many of the bottles that were manufactured are likely to have cracks?
WHich answer is correct
A. 32
B. 163
C. 166,368
D. 166,400
I don't know if this is correct but this is what I thought of:
Answer:
D 166,400
Step-by-step explanation:
200÷32 = 6.25
1040000 ÷ 6.25 = 166,400
A rectangular prism is 20 meters long, 13 meters wide, and 5 meters high. What is the surface area of the rectangular prism?
Answer:
850m^2
Step-by-step explanation:
Look at the formula SA=L*W*H. And plug in the numbers pertaining the question! hints on to what to add is stuff like "long" for length, "wide" for width, and "high" for height! And use a calculator, or scetch it out to find your total answer!
Hope this helps!
HELPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPP
Answer:
76 in²
Step-by-step explanation:
Area of the figure
Area (top rectangle) + 2 x Area (bottom rectangle)12 x (7 - 2) + 2 x 2 x 412 x 5 + 1660 + 1676 in²help help help help help help help
please help me with this slope intercept form
Answer:
5x+3=8
Step-by-step explanation:
this is the answer
Which of the following points is a solution to the system of inequalities?
6x-2y<10
6x+3y>/=15(greater than or equal to)
A. (1,2)
B. (3,3)
C. (0,5)
D. (2,1)
Answer: C (0,5)
Step-by-step explanation:
So firstly you're going to try to solve the inequality, so what I did first is used the second equation because if I divide both sides by 3, I'm able to get the y by itself:
6x+3y>/=15, 6/3=2, 3/3=1, 15/3= 5
So now its: 2x+y>/=5
now I should get the y by itself by subtracting 2x from both sides to get
y>/=15-2x, now if we wanted to plug it in to the top equation, we could make it as, y=15-2x because the it is GREATER THAN OR EQUAL TO.
so to plug it in to the first equation we get:
6x-2(15-2x)<10,
x<4, to find y we just plug it in to any equation now we have x, so I did
6(3)-2y<10
18-2y<10
-18 -18
-2y<10
divide both sides by -2 (flips the equation sign)
y>4,
So take consider both X and Y values, C would be correct because X is less than four and 0 is less than four, and 5 is greater than four.
6. Hadila is 2 years younger than Kai Yee. Kai Yee's father's age is the square of Hadila's age. If Kai Yee is p years old, calculate the total age of the three of them. Express your answer in the form of algebraic expression.
ANSWER: p^2 - 2p + 2
Step-by-step explanation:
Total age of three = p + p-2 + (p-2)^2
= 2p-2 + p^2-4p+4
= p^2 - 2p + 2
Yo I need to bring up my math grade bad so
4x-5y>20
(please show it graphed already, and step by step, NO LINKS
Answer:
Graphed verison:
See screenshot below! :^)
Solution version:
[tex]x > \frac{5}{4}y+5[/tex]
Step-by-step explanation:
For graphed verison:
See screenshot below.
For solution version:
[tex]4x-5y > 20[/tex]
Step 1: Add 5y on each side:
[tex]4x-5y+5y > 20+5y[/tex]
[tex]= 4x > 5y+20[/tex]
Step 2: Divide both sides by 4:
[tex]\frac{4x}{4} > \frac{5y+20}{4}[/tex]
[tex]= x > \frac{5}{4}y + 5[/tex]
Therefore, your answer is [tex]x > \frac{5}{4}y + 5.[/tex]
Hope this helped! :^)
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Submitted on 4/15/2022 at 10:43 PM
(To avoid plagarism, by users whom decide to copy.)
The box plots summarize the attendance for the spring musical and fall musical. Each musical was performed for six evenings. Which statement best describes the data represented in the box plots? (6.13A)
Answer:
B
Step-by-step explanation:
The 1st quartile is 135. The 3rd quartile is 195. To find the interquartile, you would subtract the 3rd quartile from the 1st quartile. 195-135=60. The interquartile range for the spring musical is 60
The zeroes of a 3rd degree polynomial are 1 and (5 –
i).
Find the remaining zeroes.
-1
:)
-5 + i
no other zeros
5 + i
5+ i
?
Answer:
5 + i
Step-by-step explanation:
the Fundamental theorem of Algebra states that a polynomial of gegree n has n zeros , some of which may be complex.
A polynomial of degree 3 will therefore have 3 zeros
given x = 1 and 5 - i are two of the zeros
Complex zeros occur as conjugate pairs , then
5 - i is a zero then 5 + 1 is also a zero
the 3 zeros are x = 1 , x = 5 - i and x = 5 + i
I need help solving this
Answer:
x = 46 :)
Step-by-step explanation:
First we subtract :)
180 - 88 = 92
Now we divide :)
92/2 = 46
Now you know how to solve this type of problem!!
Have an amazing day!!
Please rate and mark brainliest!!
A radioactive compound with mass of 260 grams decays at a rate of 3.8% per hour. Which equation represents how many grams of the compound will remain after 8 hours?
A: C=260(1.038)^8C=260(1.038)^8
B: C=260(0.962)^8C=260(0.962)^8
C: C=260(0.038)^8C=260(0.038)^8
D: C=260(1-0.38)^8C=260(1−0.38)^8
The exponential equation that represents how many grams of the compound will remain after 8 hours is:
B: C=260(0.962)^8
What is an exponential function?A decaying exponential function is modeled by:
[tex]A(t) = A(0)(1 - r)^t[/tex]
In which:
A(0) is the initial value.r is the decay rate, as a decimal.A radioactive compound with mass of 260 grams decays at a rate of 3.8% per hour, hence the equation for the mass after t hours is given by:
[tex]A(t) = 260(1 - 0.038)^t[/tex]
[tex]A(t) = 260(0.962)^t[/tex]
After 8 hours, the amount is given by:
[tex]A(t) = 260(0.962)^8[/tex]
Hence option B is correct.
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PLEASE HELPPPP WILL MARK BRAINLIEST
Answer:
2×5÷4=2.5
Step-by-step explanation:
2 boxes × 5 cards ÷ white cards
2 m
6 m
Volume = Base x height
Find the volume of this cylinder.
A traffic cone has a volume of 150 cubic inches. The height of the cone is 18 inches. What is the diameter of the traffic cone?
A.
3 inches
B.
5 inches
C.
10 inches
D.
50 inches
WILL GIVE BRAINLIEST!!
Help with this please and thank you.
Answer:
the first
Step-by-step explanation:
the first and the second set both multiply out correctly to the original expression, but -2x² is of greater dimension than -2x.
What does s equal? (Write your answer like this: s = __)
Answer:
S= -15/5
the slashes are supposed to be fractions.
Step-by-step explanation:
What is the value of b:
-8-b=-6
1) b=-2
2) b=2
Answer:
b = -2
Step-by-step explanation:
Add 8 to both sides: -8 - b + 8 = -6 + 8
-b = 2
Divide both sides by -1: -b/-1 = 2/-1
b = -2
find the value of a and b in parallelogram WXYZ
opposit side of parallelogram are equal and opposit angles are also equal
Alberto’s monthly income is $3,200. Part of Alberto’s monthly budget is shown in the table.
Monthly Budget
Category Amount of Money
Rent $896
Groceries $384
Savings $165
Car payment $428
Utilities $120
What percentage of Alberto’s income is used to pay for his rent and groceries?
Using the percentage concept, it is found that 40% of Alberto’s income is used to pay for his rent and groceries.
What is a percentage?The percentage of an amount a over a total amount b is given by a multiplied by 100% and divided by b, that is:
[tex]P = \frac{a}{b} \times 100\%[/tex]
In this problem:
Alberto’s monthly income is $3,200, hence b = 3200.He spends 896 + 384 = $1280 in rent and groceries, hence a = 1280.Then, the percentage is given by:
[tex]P = \frac{1280}{3200} \times 100\% = 40\%[/tex]
More can be learned about the percentage concept at https://brainly.com/question/10491646
Al vender una computadora, un vendedor descuenta el 15%, y aun así gana el 35%, del costo. ¿qué %del costo es el precio de venta?
Veremos que el precio de venta es el 158% del costo.
¿Que porcentaje del costo es el precio de venta?
Sabemos que con el descuento del 15%, el vendedor gana 35% del costo.
Es decir, si el costo es C, entonces el precio al que se vende la computadora es:
P' = (1 + 0.35)*C = 1.35*C
Pero, esto es con un 15% de descuento. Entonces si el precio de venta es P, tendremos:
P' = (1 - 0.15)*P = (0.85)*P
Reemplazando esto arriba tenemos:
(0.85)*P = 1.35*C
Resolviendo para P:
P = 1.35*C/0.85 = 1.58*C
Para obtener el porcentaje, multiplicamos el coeficiente por 100%.
1.58*100% = 158%.
Es decir, el precio de venta es el 158% del costo.
Sí quieres aprender más sobre porcentajes puedes leer:
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which ordered pair represents
(fg)(3) on the graph of the combined function?
A. (9,-3)
B. (3,25)
C. (3,5)
D. (9,25)
If the point (-4,b) is on the line what is the value of b
Answer: if you are talking about a grid than the answer is 0.
Step-by-step explanation: this is becasuse the y coordinate is the elevation of the x coordinate. B is 0 because it is on the line meaning it has no elevation
Class A has 25 pupils and class B has 28 pupils.
Both classes sit the same maths test.
The mean score for class A is 69.
The mean score for both classes is 41.
What is the mean score in the maths test for class B?
Please helppp
Answer:
I think it will be less than 69 because the tozal mean is 41 while of A is 69 mean the values has decreased