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
increase £196 by 9%
old old working out need asap
Answer:
£213.64
Step-by-step explanation:
You do 196(0.09)
That's 17.64
The you add the two
196+17.64
The way I got 9 was from 9%.
To make it in decimal form you have to move the decimal over two places.
Hope this helps
is 17/5 rational or irrational
Answer:
rational
Step-by-step explanation:
Answer:
rational
Step-by-step explanation:
The total bill for drinks and a pizza for three people is $14.90 before tax. The group wants to leave a 15% tip on the cost of the food, not including tax. What will be the amount of the tip?
Answer:
$2.24
Step-by-step explanation:
Since we are trying to find a percentage of something, we can multiply whatever we're trying to find a percentage from by 0.X where X is equal to the number of the percentage. So in this case it's 15%. We can multiply $14.90 by 0.15 and we get 2.23500. Since we cannot have 2.235 dollars, we must round up decimal places.
The tip would be 2 dollars and 24 cents. ($2.24).
Which number is in the solution set of this equation? 7x − 9 = 40
Answer: the answer is 7
Step-by-step explanation: add 9 to both sides, eliminating -9 so now you have 7x=49 divide both by 7 and you get x= 7 check it by inputing 7 for x, 7(7)-9=40
7(7)=49 next 49-9= 40
it checks out, so x= 7
help please!!!!!!!!!!
Answer:
3125
Step-by-step explanation:
cubed root of 125 = 5
5^5 = 3125
Hope this helps!!
La ultima alternativa es la correcta: 3 125
Help Me, Now! B. What is the value of each funtion at x = 1?
Answer:
Step-by-step explanation:
Use the course calculator to solve this problem:
8 + 17 × 26
Answer:
450
Step-by-step explanation:
8+17=25
25x26=450
Answer: 500
Step-by-step explanation:
You have to do multiplication first according to PEMDAS so you do 17 times 26 and you get 442 add 8 you get 500.
Write an equation to show how many times greater the value of a 5 in the tens place is than a 5 in the tenths place
What is the mass of 1.50 moles of Cl ?
Answer
:Assuming you are talking about odium chloride,NaCl your answer would be
87.7 g
we discover the answer because 1 x 22.99 + 1 x 35.99= 58.4 g/mol
1.50 Moles:
We need to multiply our initial value by 1.50.
1.50 x 58.44/1= 87.66 = 87.7 g
Hope this helps
-Tobie the dog <3
I need help with fractions
Answer: 3 1/2 represents G and 2 3/4 represents point K
Step-by-step explanation: If you look at the first on it is 3 1/2 because it is in the middle and the second one is divided in fourths so K is 2 3/4.
solve all of these ?
21 Answer:
[tex] \frac{3}{a} [/tex]
22 Answer:
[tex] \frac{1}{ {b}^{3} } [/tex]
23 Answer:
[tex] \frac{ {4a}^{2}c^{3} }{ {b}^{2} } [/tex]
24 Answer:
[tex]9c ^{4} [/tex]
25 Answer:
[tex] - \frac{1}{ {a}^{2} } [/tex]
26 Answer:
[tex] \frac{1}{ {c}^{2} } [/tex]
consider the image that shows a tower anchored by a guy with the guy wire is attached at point b on the tower 119 feet above the ground and then anchored to the ground at point a 120 feet from the base of the tower.
Options are: A) sin0= 119/120, B) sin0= 120/119, C) sin0= 119/169, and D) sin0= 120/169
Answer:
Step-by-step explanation:
[tex]sin\theta=\frac{opposite}{hypotenuse}\\ \\ sin\theta=\frac{119}{169}\ (answer\ C)[/tex]
PLS HELP 10 POINTS
QUESTION IN PIC
Answer:
Some integers are irrational
Step-by-step explanation:
An integer must be a whole number so it will always be rational.
In your own words, explain the steps you would need to take to find a slope from data in a table.
Answer:
Pick two points on the line and determine their coordinates. Determine the difference in y-coordinates of these two points (rise). Determine the difference in x-coordinates for these two points (run). Divide the difference in y-coordinates by the difference in x-coordinates (rise/run or slope).
Step-by-step explanation:
Answer:
To Find the slope of a data table, you first need to plot two points on the line. It is easiest if the points are on a coordinate with whole numbers (i.e. (3,6 and (4,8)). Once you have plotted two pints, you then need to take the value of the point with the largest x value, and subtract the other points from it (i.e. (4,8)-(3,6)=(1,2). Then, take the new y value, and divide it by the new y-value (i.e. (2/1), and you have your slope.
Step-by-step explanation:
plot points (3,6), (4,8)
subtract points (4,8)-(3,6)=(1,2)
divide new points 2/1
m=2/1, or 2
Abdul deposited $460 into a savings account that has a simple interest rate of 3.5%. Isaac deposited $550 into a savings account that has a simple interest rate of 2.8%. Who earned more interest in one year?
Answer:
Adbul earned more interest
Step-by-step explanation:
3.5% of 460 = 16.1
2.8% of 550 = 15.4
Adbul earned more interest
How to graph absolute value functions?
Answer:
DJthresh
ugh yet the wasn't Hagel
Please Help!!!! need it just right now
Answer:
A. y = x² + 12x - 8Step-by-step explanation:
The u-shaped function should have:
positive leading coefficienteven degreeThe only function with mentioned parameters is:
y = x² + 12x - 8Correct option is A
The other options don't fit:
B. Even degree with negative leading coefficientC. Odd degreeD. Odd degreeA mountain climber found that the relationship between his altitude and the surrounding air
temperature is linear. The function f (a) = - -100 a + 75 represents this relationship, where a
is the altitude in meters and f(a) is the temperature in degrees Fahrenheit. According to this
function, by how much is the temperature decreasing for every meter that the mountain climber's
altitude increases?
IF
100
O IF
100
75 F
-75F
Answer:- 1/100 degrees Fahrenheit
Step-by-step explanation:
The directions say decreasing so it has to be negative, and the slope is showing how much it is decreasing every meter. y=mx+b. The mx is the slope which is where the answer is located.
what’s the answer to this question
Step-by-step explanation:
I can't see the question. please resend picture
What is the slope between the points (1,5) and (3, 15)
Which scatterplot shows a nonlinear association?
Answer:
B
Step-by-step explanation:
B shows a parabola, which is a quadratic equation, not a linear one.
The association between two numerical variables measured for the same individuals is displayed in a scatterplot. One variable's values are displayed on the horizontal axis, and the other variable's values are displayed on the vertical axis. On the graph, each individual in the data is represented by a point.
What is scatter plot?A scatter plot is a type of plot or mathematical diagram using Cartesian coordinates to display values for typically two variables for a set of data. If the points are coded, one additional variable can be displayed.
here, we have,
we know that,
The relationship between two economic phenomena, such as employment and output, inflation and retail sales, and taxes and economic growth, can be visually illustrated using scatter plots.
Spread Plots. Points on a scatter (XY) plot depict how two sets of data relate to one another. Each dot in this illustration represents a person's weight in relation to their height. (The information is displayed as "Cartesian (x, y) Coordinates")
Display a connection between the data and a trend. Display all data points, including outliers, minimum, and maximum values. can draw attention to relationships. the sample size and exact data values are retained.
To learn more about scatterplots refer to:
brainly.com/question/6592115
#SPJ7
A rectangle has a perimeter of 18. The height of the rectangle is 4 cm. What is the area of the rectangle?
Answer:
20
Step-by-step explanation:
Perimeter of rectangle= 2l+2h so 2l+2(4)=18. SO 2l=10. l=5
Area=bh
(5)(4)=20cm
What is the measure of n?
6
24
n
m
n =
[?]
Answer:
n = 12
Step-by-step explanation:
By applying geometric mean theorem in the given right angle triangle,
[tex]\frac{AD}{BD}=\frac{BD}{DC}[/tex]
BD² = AD × DC
Now substitute the values of each side given,
n² = 6 × 24
n² = 144
n = 12
A baseball player gets a hit 20% of the times he is at bat. Out of the next 15 times at bat, how many hits can you expect the player to get?
Answer:
...
Step-by-step explanation:
The batsman will hit =20% of 15
= 15/5
= 3
Answer:
3
Step-by-step explanation:
15 x 0.20
i need help ASAP please
Answer:
umm so i belive you will mulltiply all of thoes together
Step-by-step explanation:
chicken nuggies are good :0
Answer:
number 3
Step-by-step explanation:
p represents amount of tickets sold at the pre-sale and d represents the amount of tickets sold at the door. If you add p + d, that equals the total amount of tickets sold which is 345 tickets.
So:
p + d = 345
Pre-sale tickets (p) cost $7 while tickets at the door (d) cost $10, and the total amount of money mad is $2550.
So:
7p + 10d = 2550
Answer should be the equations in number 3.
6n blocks of clay are shared among 14 students. Write and algebraic expression for the number of blocks of clay that each student will get
Answer:
6n ÷ 14
Step-by-step explanation:
the blocks are shared among the people.
Use a net to find the surface area of the prism.
7 cm
10 cm
5 cm
Answer:
10 cm i think
Step-by-step explanation:
but i dont know.
Wanna be the Brainiest
Answer:
156cm^3
Step-by-step explanation:
V= 1/2 a*c*h
a=3
c=8
h=13
3*8*13=312
312/2=156
Someone help please and please make sure the answer is right
Answer:
the answer is 7
Step-by-step explanation:
Consider a system of two linear equations in two variables. If the graphs of the equations are not the same line, is it possible for the system to have infinitely many solutions. Explain.
Answer:
No
Step-by-step explanation:
Solutions to systems of equations are points at which the lines of the equations intersect. Knowing this, only equations representing the same line would have infinitely many solutions because they would intersect at every one of each other's points - they're the exact same line. Therefore, if they are not the same line, they would not intersect at each and every point, and would not have infinitely many solutions.