Answer:
i. a = -6 ii. b = 12 iii. 100 iv. 26.6°
Step-by-step explanation:
Since the weight of the object is 20 N and directed downwards, its vector is -20j. Now, since the particle is in suspension, AP + BP = -20j
So, since AP = ai + 8j and BP = 6i + bj,
AP + BP = -20j
ai + 8j + 6i + bj = -20j
ai + 6i + 8j + bj = -20j
(a + 6)i + (8 + b)j = -20j
(a + 6)i + (8 + b)j = 0i - 20j
equating the components on both sids,
a + 6 = 0 and 8 + b = 20
a = -6 and b = 20 - 8 = 12
i. The value of a is -6
ii. The value of b is 12
iii. The magnitude of the tension in string AP is?
since AP = ai + 8j = -6i + 8j
magnitude of AP = √[-6² + 8²] = √[36 + 64] = √100 = 10
iv. The angle that string BP makes with the vertical is?
Since BP = 6i + bj = 6i + 12j, the angle it makes with the horizontal is Ф = tan⁻¹(12/6) = tan⁻¹(2) = 63.44°.
Thus, the angle it makes with the vertical is thus 90° - 63.44° = 26.56° (complementary angles) ≅ 26.6° to 3 s.f
1) The values of a and b of the given vectors are respectively; -6 and 12
2) The magnitude of the tension in string AP is; 10
3) The angle that string BP makes with the vertical is; 26.6°
What is the magnitude of the tension?
We are told that the weight of the particle P is 20 N. Since the particle is suspended by two strings, then its' direction is downwards and as such its vector is -20j.
By equilibrium;
AP + BP = -20j
1) We are given the tension vectors;
AP = ai + 8j and BP = 6i + bj,
Thus;
ai + 8j + 6i + bj = -20j
(ai + 6i) + (8j + bj) = -20j
(a + 6)i + (8 + b)j = -20j
(a + 6)i + (8 + b)j = 0i - 20j
Equating the components of both sides gives;
a + 6 = 0 and 8 + b = 20
Solving gives;
a = -6 and b = 20 - 8 = 12
Thus, the values of a and b are -6 and 12
2) The magnitude of the tension in string AP is gotten from resolution of the tension vector AP;
AP = ai + 8j = -6i + 8j
Thus, magnitude of AP = √(-6² + 8²) = √(36 + 64) = √100 = 10
3) The angle that string BP makes with the vertical is gotten from;
BP = 6i + bj = 6i + 12j
Thus, the angle it makes with the horizontal;
θ = tan⁻¹(12/6) = tan⁻¹(2) = 63.44°.
Angle it makes with the vertical = 90° - 63.44° = 26.56° ≈ 26.6°
Read more about Magnitude of Tension at; https://brainly.com/question/13370981
Can someone help me with this question? Explanations would be nice. Question: Right ΔKLM with m∠J= 45°, leg JK= 4√3
(Question was resubmitted because of misspelling.)
Answer:
Step-by-step explanation:
Find the value of x for the pic
What is the volume of a square prism that is 4 centimeters by 4 centimeters by 8 centimeters
Answer:
138 is the answer
Step-by-step explanation:
128 square
Yaritza and eddy race to school on their bikes. Yaritza bikes 2 miles in 12 minutes, eddy bikes 3 miles in 15 minutes. Who is going faster?
How much air can the basketball
hold? With a radius of 3 inches. Round to the nearest hundredth.
Answer:
113.10 if you use the pi button
113.04 if you use 3.14
Step-by-step explanation:
We want to find the volume
V = 4/3 pi r^3
The radius is 3
V = 4/3 pi (3)^3
Using the pi button for pi
V = 113.09734
Rounding to the nearest hundredth
V = 113.10
If you use 3.14 for pi
V = 113.04
Simplify
x(2x + 3) + (x - 3)(x - 4)
Answer:
3x^2-4x+12
Step-by-step explanation:
x(2x+3)+(x-3)(x-4)
2x^2+3x+x^2-3x-4x+12
2x^2+x^2+3x-3x-4x+12
3x^2-4x+12
Answer:
3x² -4x + 12
Step-by-step explanation:
x(2x + 3) + (x - 3)(x - 4)
= 2x² + 3x + x² - 4x -3x + 12
= 3x² -4x + 12
I didn't pay attention in class for a few days and now I'm lost. if somebody could at least explain proportions I would be very thankful.
Answer:
A proportion is a comparison of two numbers that each represent the parts of a whole. Essentially, a proportion says that two fractions are the same, even if the amount is different. For example, 1/2 of 10 marbles is the same proportion as 1/2 of 50 marbles.
Step-by-step explanation:
Find the Surface Of a rectangular prism with base of 4m by 5m and height 8m.
Answer:
184
Step-by-step explanation:
SA = 2LW + 2LH + 2WH
SA = 2(5 × 4) + 2(5 × 8) + 2(4 × 8)
SA = 2(20) + 2(40) + 2(32)
SA = 40 + 80 + 64
SA = 184
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YW
Please I will give brainliest
Answer:
The answer is 91 bags.
Step-by-step explanation:
You divide 45.5 by 0.5
Can yall help
Thank you im really confused correct answer gets brainliest
The functions q and r are defined as follows.
q(x)=2x + 2
r(x)=-2x²-2
Find the value of r(q(2)).
Answer:
Step-by-step explanation:
[tex]r(x)=-2x^2-2\\ \\ q(x)=2x+2\\ \\ r(q(x))=-2(2x+2)^2-2\\ \\ r(q(2))=-2(2(2)+2)^2-2\\ \\ r(q(2))=-2(6^2)-2\\ \\ r(q(2))=-2(36)-2\\ \\ r(q(2))=-72-2\\ \\ r(q(2))=-74[/tex]
Graph this equation :
y= 3/2 x + 2
An insect is standing next to a flower. The insect is 1 cm tall and makes a shadow of 0.5 cm. If the flower makes a 15-cm shadow, how tall is the flower?
Answer:
30 cm
Step-by-step explanation:
set up a proportion of insect height over its shadow equals flower height over its shadow, then cross-multiply
1/.5 = x/15
.5x = 15
x = 30
HELP NO ONE IS HELPING AND I REALLY NEED THE ANSWERS PLEASE!!!!
How much NaBr solute is saturated at 70 degrees?
A.
110
B.
B.120
C.
130
D.
140
Answer:
120
Step-by-step explanation:
2 · y - 8 ÷ 4 when y = 7
Answer:
12
Step-by-step explanation:
Answer:
Step-by-step explanation:
Plugin y = 7 in the expression
y - 8 ÷ 4 = 7 - 8÷ 4 { here division has to be done first as per PEDMAS}
= 7 - 2
= 5
Gabriel wants to solve the equation 5 eights M equals 25 what steps should he do to get him by itself on one side of the equation
Answer:
Kindly check explanation
Step-by-step explanation:
Given the Equation :
(5/8)m = 25
The first step to take with this kind of equation is to multiply both sides by the denominator, 8
5m/8 * 8 = 25 *8
5m = 200
Then, we can divide both sides by 5 in other to isolate m
5m / 5 = 200 / 5
m = 40
Answer: m+40
Step-by-step explanation:
Given the Equation :
(5/8)m = 25
The first step to take with this kind of equation is to multiply both sides by the denominator, 8
5m/8 * 8 = 25 *8
5m = 200
Then, we can divide both sides by 5 in other to isolate m
5m / 5 = 200 / 5
m = 40
A construction company can remove 3/3/4 metric tons of dirt from a construction site in 1/1/8 hours what is the unit rate in metric tons per hour write your answer as a fraction or a mixed number in simplest form
Answer:
3 1/3 metric tons per hour
Step-by-step explanation:
To find the unit rate, divide 3 3/4 metric tons by 1 1/8 hours (notice that the correct format is 3 3/4, not 3/3/4).
3 3/4 metric tons 3.75 metric tons
---------------------------- = --------------------------
1 1/8 hours 1.125 hours
It's easier to deal with decimal fractions here than with proper fractions.
The unit rate then comes out to be 3.75/1.125 metric tons per hour, or
3.33333 metric tons per hour, or 3 1/3 metric tons per hour
Choose the solids with approximately equal volumes.
9 cm:
5 cm
6 cm
9 cm
11 cm
cm
14
9 cm
9 cm
13 cm
-cm
14
Answer:
Adding 12 to the circle area is equal to the square area.
Or
s2 = 12 + A
Where
s = side of square
A = area of circle
So
s2 = 12 + 36
s2 = 48
Solve this for s to get the side length
Answer: It's the first cone (9cm, 9cm), the cylinder at the bottom (9cm, 3cm), and the sphere at the bottom (9/3sqrt4cm).
Step-by-step explanation: I got this right on Edmentum.
I need the answer for the question -4(x-10)+8 for my homework please.
Answer:
i think the answer is
-4x+48
What is another way to write 46?
4×4×4×4×4×4
6×6×6×6
6+6+6+6
4+4+4+4+4+4
If you mean 4x6, then it would be C and D.
A would be 4^6 and B would be 6^4, both of which we don't want.
---
hope it helps
Answer:
None of the answers match your question.
Arianna invests $2,000 into an ETE which earns 2% per year. In 10 years, how much will Arianna's investment be worth if interest is compounded monthly? Round to the nearest dollar. Workspace V 3 < TI
Answer:
$2040
Step-by-step explanation:
HELP ME GUYS MY TEACHER IS WACHING I NEED HELP GUYS PLZZZZ
Answer:
Step-by-step explanation:
Volume=LxWxH
So, we would have 1/4*1/4*1/2=1/32
1/32
what's the answer to
375 = 15c
Step-by-step explanation:
Given
375 = 15 c
c = 375 / 15
c = 25
Hope it will help :)❤
HELP ASAP ME PLS I GIVE BRAINLY
i think D all equivalent I'm not sure but I hope that helped you.
glencoe geometry unit 9: whoever can answer the page gets 100 points and brainliest
Step-by-step explanation:
14. K' = x + a, y + b
= -1 + 2, 6 + 3
K' = 1, 9
K" = (x, y) → (-x, y)
= (1, 9) → (-1, 9)
K" = -1, 9
15. D. Octagon
Since it has 8 angles, of 360 ° is divided by 8 angles, then each corner has an angle of 45 °
16. P' = x + a, y + b
= -2 + 6, 4 + 5
P' = 4, 9
17. H' = x + a, y + b
= 5 + 10, 4 + (-11)
= 15, -7
18. A (6, -1)
A' = (x, y) → (x, -y)
= (6, -1) → (6, -(-1)
= 6, 1
19. J' = x + a, y + b
= -2 + (-3), 1 + (-3)
= -5, -2
J" = (x, y) → (x, -y)
= (-5, -2) → (-5, -(2))
= -5, -2
#CMIIW
5 points A farmhouse shelters 10 animals. Some are goats and some are ducks. Altogether there are 36 legs. How many ducks and goats are there?
Answer:
2 ducks and 8 goats
Step-by-step explanation:
let goat be g
let duck be d
d + g = 10
ducks have 2 legs, 2d
goats have 4 legs, 4g
2d + 4g = 36
making d the subject in the first equation;
d = 10 - g
put in second equation
2(10 - g) + 4g = 36
20 -2g + 4g = 36
2g = 36 - 20
2g = 16
g = 8
if g is 8
d = 10 - 8
d = 2
Helppppppppp please
Answer:
b : 1/4
Step-by-step explanation:
Tell whether the angles are adjacent or vertical. Then find the value of x.
to
128°
The angles are
vertical
X=
Answer:
x = 128
Step-by-step explanation:
Adjacent angles - Angles right next to each other. They share a common vertex
Vertical angles - angles that are vertically aligned with each other.
The angle that has a measure of 128 degrees and x are vertical angles
If you didn't know vertical angles are congruent so because one angle equals 128 degrees the other equals 128 degrees
x = 128
The given angle are the vertical angles and the measure of the angle x is 128°.
Given that,
To specify whether the angles are adjacent or vertical. Then find the value of x.
orientation of one line with respect to the horizontal or other respective line is known as a measure of orientation and this measure is known as the angle.
Here,
By the observation, angle x and 128° are the vertical angles and by the property of the intersection of the line both are equal angles so the measure of angle x is also equal to 128°.
Thus, the given angle is the vertical angle and the measure of the angle x is 128°.
Learn more about Angles here:
https://brainly.com/question/13954458
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how do you do: -x-x-3x+2-5 ?
Answer:
=−5x−3
Step-by-step explanation:
Let's simplify step-by-step.
−x−x−3x+2−5
=−x+−x+−3x+2+−5
Combine Like Terms:
=−x+−x+−3x+2+−5
=(−x+−x+−3x)+(2+−5)
=−5x+−3
brainliest please?
3 times the difference of a number and 4 equals 12. Find the number.
Answer:
Step-by-step explanation:
9