Answer:
The magnitude of the resultant force is:
[tex]R=100.3 \:pound[/tex]
The direction is:
[tex]\theta=1.2^{\circ}[/tex]
Step-by-step explanation:
Let's find the components of each vector is x and y-directions first.
Sum of x-component vector forces.
[tex]F_{tot-x}=F_{1}cos(45)+F_{2}cos(30)[/tex]
[tex]F_{tot-x}=50cos(45)+75cos(30)[/tex]
[tex]F_{tot-x}=100.3 \: pound[/tex]
Sum of y-component vector forces.
[tex]F_{tot-y}=-F_{1}sin(45)+F_{2}sin(30)[/tex]
[tex]F_{tot-y}=-50sin(45)+75sin(30)[/tex]
[tex]F_{tot-y}=2.1 \: pound[/tex]
The magnitude of the resultant force is:
[tex]R=\sqrt{100.3^{2}+2.1^{2}}[/tex]
[tex]R=100.3 \:pound[/tex]
The direction is:
[tex]tan(\theta)=\frac{2.1}{100.3}[/tex]
[tex]\theta=arctan(\frac{2.1}{100.3})[/tex]
[tex]\theta=1.2^{\circ}[/tex]
I hope it helps you!
For a rock concert a rectangular field of size 100 m by 50 m was reserved for the
audience.
The concert was completely sold out and the field was full with all the fans standing.
Which one of the following is likely to be the best estimate of the total number of people
attending the concert?
2000
5000
20000
50000
100000
Answer:
5000
Step-by-step explanation:
but this depends upon how much room each person needs
Find the distance between a point (–7, –19) and a horizontal line at y = 3.
Work out the lengths of sides a and b.
Give your answers to 1 decimal place.
17 cm
a
a
b
8 cm
12 cm
5 cm
Answer:
No solution is possible since you failed to provide the necessary information
Step-by-step explanation:
The length of a rectangle is six times its width.
If the perimeter of the rectangle is 84 in, find its area.
Answer:
6yd=W The width of the rectangle is 6 yards. L=6W=6(6yd)=36 yards The length is 36 yards. A=36yd*6yd=216 sq yd ANSWER: The area is 216 square yards...The area of a given rectangle is 216 square inches.
Given that, the perimeter of the rectangle is 84 inches.
We need to find the area of a rectangle.
What is the perimeter of a rectangle?The perimeter of a rectangle is the total distance of its outer boundary. It is twice the sum of its length and width and it is calculated with the help of the formula: Perimeter = 2(length + width).
Let the width of a rectangle be x.
Given, that the length of a rectangle is six times its width. So, length=6x.
Now, 84=2(6x+x)
⇒14x=84
⇒x=6 inches
Then, length=6x=36 inches.
Area of a rectangle= Length×width=36×6=216 square inches
Therefore, the area of a given rectangle is 216 square inches.
To learn more about the area of a rectangle visit:
https://brainly.com/question/20693059.
#SPJ2
Michael and Sondra are mixing lemonade. In Michael’s lemonade, the ratio of lemons to water is 1:4. In Sondra’s lemonade, the ratio of lemons to water is 2:6. Several equivalent ratios for each mixture are shown in the ratio tables.
Michael
Lemons
Cups of Water
1 4
3 12
4 16
Sondra
Lemons
Cups of Water
2 6
4 12
6 18
Imagine that you want to compare Michael’s ratio to Sondra’s ratio. Which two ratios in the tables shown have a common denominator you could use to compare?
Answer:
1/4= 3/12 & 2/6 = 4/12
Step-by-step explanation:
Answer:
Its simply B
Step-by-step explanation:
If we are to express both ratios in their simplest form, we will have the ratio of Michael’s lemonade is 1:4 and that of Sondra is 1:3. The denominator that can be used in order to compare the ratios is that which can be divided by both ratios. For example, we have 12 as a denominator. The ratios can be expressed as 3/12 and 4/12. Also, the denominator can be 24 such that the ratios can be expressed as 6/24 and 8/24.
To mix a pastel orange paint, 5ml of yellow pigment and 3 ml of red pigment are added to 1litre of white paint. How much yellow pigment and red pigment are added to 6litre of white paint to reproduce the same colour
Answer:
30ml of yellow
18ml of red
Step-by-step explanation:
5x6=30
3×6=18
Answer:
Step-by-step explanation:
a color
Xavier shoots a basketball in which the height, in feet, is modeled by the equation,h(t) = -4t2 + 10 + 18, where t is time, in
seconds. What is the maximum height of the basketball?
Answer:
The maximum height of the basketball is of 24.25 feet.
Step-by-step explanation:
Vertex of a quadratic function:
Suppose we have a quadratic function in the following format:
[tex]f(x) = ax^{2} + bx + c[/tex]
It's vertex is the point [tex](x_{v}, y_{v})[/tex]
In which
[tex]x_{v} = -\frac{b}{2a}[/tex]
[tex]y_{v} = -\frac{\Delta}{4a}[/tex]
Where
[tex]\Delta = b^2-4ac[/tex]
If a<0, the vertex is a maximum point, that is, the maximum value happens at [tex]x_{v}[/tex], and it's value is [tex]y_{v}[/tex].
Height of the basketball:
Given by the following function:
[tex]h(t) = -4t^2 + 10t + 18[/tex]
Which is a quadratic function with [tex]a = -4, b = 10, c = 18[/tex]
What is the maximum height of the basketball?
y(in this case h) of the vertex. So
[tex]\Delta = b^2-4ac = 10^2 - 4(-4)(18) = 388[/tex]
[tex]y_{v} = -\frac{388}{4(-4)} = 24.25[/tex]
The maximum height of the basketball is of 24.25 feet.
A ramp is in the shape of a triangle
Answer:
Step-by-step explanation:
x+y=13
2x-y=5
solve using any method
Answer:
x = 6 , y = 7
Step-by-step explanation:
solving by substitution method
x + y = 13
x = 13 - y equation (i)
2x - y = 5
substitute the value of x
2(13 - y) - y = 5
26 - 2y - y = 5
26 - 3y = 5
26 - 5 = 3y
21/3 = y
7 = y
substitute the value of y in equation (i)
x = 13 - y
x = 13 - 7
x = 6
A vault contains 3000 worth of nickels.
How many nickels are in the vault
Answer:
600 nickels
Step-by-step explanation:
Answer to the question?
Answer:
35
Step-by-step explanation:
AEC and AEB form a straight angle(180°)
180-40=140
AEV and AED are equal
140 divided by 4 = 35
convert 122f to Celsius
Answer:
50°C
Step-by-step explanation:
(122°F − 32) × 5/9 = 50°C
explanation would be appreciated, last word is indicated.
Answer:
AC = 28
Step-by-step explanation:
Ok, we know that:
Points A, B, and C are collinear.
Point B is between A and C.
We want to find the length AC (distance between A and C), if we know that:
AB = 16
BC = 12
Ok, knowing that B is between the other points, we know that:
AB + BC
defines the total length of the segment that connects the 3 points.
Thus, if we define this segment as a length, we only use the endpoints, A and C.
Then we have that:
AB + BC = AC
now we can solve this:
16 + 12 = AC
28 = AC
Find the x-intercept and the y-intercept of the graph equation 7x +3y =21 type a integer
Answer:
7(y intercept)
Step-by-step explanation:
y = mx +c form
y = 21-7x/3
c = 21/3 = 7(y intercept)
x i have no idea
To find x-intercept ,put y= 0 in the given eqn
So, 7x+3(0) = 21
=> 7x =21
=> x= 21/7 = 3
x-intercept = 3
Similarly, to find y-intercept put x=0 in the given eqn
So ,7(0)+3y=21
=> 3y=21
=> y= 21/3 = 7
y-intercept = 7
What is the product?
(-282 +8)(502-65)
Answer:
option c is the answer for pic
and for question the answer is
(-274)*(437)
-119738
Answer:
the first one
Step-by-step explanation:
In 42 - 15 = 27, the number 42 is called the
the number 15 is called the
and the number 27 is called
Answer:
The Answer to the Ultimate Question of Life, the Universe, and Everything is 42
Step-by-step explanation:
In this equation, the number 42 is called a minuend.
15 is a subtrahend because it is being subtracted from another number.
The number 27 would be called the difference.
help
Sadie needs 3.1 yards to make one costume for each choir member in the play. How much fabric will she need if she has to make 5 costumes?
A.
15.5 yards
B.
10.5 yards
C.
18.6 yards
D.
16.5 yards
Answer:
A. 15.5 yards
Step-by-step explanation:
3.1 ×5=15.5
Could anyone help me please?
9514 1404 393
Answer:
4
Step-by-step explanation:
In order to evaluate f(g(-1)), you first need to find g(-1).
The graph of g(x) crosses the line x = -1 at y = 1, so g(-1) = 1.
The second step is evaluating f(1). The graph of f(x) crosses the line x=1 at y=4, so f(1) = 4.
f(g(-1)) = f(1) = 4
you and your friend start biking to opposite directions from the same point. You travel 108 feet every 8 seconds. Your friend travels 63 feet every 6 seconds. a) how far apart are you and your friend after 15 minutes? b) after 20 minutes you take a 5- minutes rest, but your friend does not. How far apart are you and your friend after 40 minutes? Explain your reasoning.
Answer:
To find your distance apart, you can convert 15 minutes to seconds because that is what the rate is given in.
15 mins x 60 seconds = 900 seconds.
Step-by-step explanation:
In 900 seconds, there are 900/8=112.5 groups of 8 seconds. This means there are 112.5 groups of 108 feet.
112.5 x 108 = 12150 feet
12150 feet/5280 feet is approximately 2.3 miles.
For your friend you take 900/6 = 150 groups of 6 seconds.
150 x 63 = 9540 feet
9540 feet/5280 feet = 1.79 miles
1.79 miles + 2.3 miles = 2.09 miles
You and your friend are about 2.09 miles apart after 15 minutes.
B). If you go 2.3 miles every 15 minutes, that means you travel about 0.77 miles every 5 minutes. If you travel 20 more minutes (40-15-5) that would be 0.77x 4=3.07 miles more
3.07 + 2.3 = 5.37 miles after 40 minutes (you).
Your friend travels 1.79 in 15 minutes, so 1.79/3 = 0.6 miles every 5 minutes
0.6 x 5 (5 x 5 = 25 minutes)= 3 miles
1.79 + 3 miles= 4.79 miles (friend)
4.79 + 5.37 = 10.16 miles
You and your friend are about 10.16 miles apart after 40 minutes.
There is a bag with only red marbles and blue marbles.
The probability of randomly choosing a blue marble is
7
8
.
There are 56 marbles in total in the bag and each is equally likely to be chosen.
Work out how many red marbles there must be.
Answer:
7
Step-by-step explanation:
The probability of choosing a blue marble is 7/8, or 49/56, which means that out of 56 marbles, 49 are blue. 56-49=7, so there are 7 red marbles. Hope this helps! :)
PLEASE HELPPPPP!!! WILL MARK BRAINLIEST!!
X = -1
This is because when you multiply 2 to the -1 power, it is negative because a positive times a negative is always negative. And 1/2 by the same -1 is -1/2
is the point (2,5) a solution to the equation y=3x-5?
Answer and Step-by-step explanation:
To figure out, we plug in the x-value into the equation and see if it is equal to the y-value.
y = 3(2) - 5
y = 6 - 5
y = 1
5 ≠ 1
The point (2, 5) is not a solution.
#teamtrees #PAW (Plant And Water)
if someone can explain this it would really help.
Answer:
6
Step-by-step explanation:
KL = 26-(11+9) = 26-20 =6
Answer:
KL is 6
Step-by-step explanation:
IL is 26, IJ = 9 JK= 11
IL= IJ + JK + KL
26= 9 + 11 + KL
Rearrange
KL= 9 + 11 - 26
= 6
what is the mean mark of 847 ÷ 30?
Answer:
Step-by-step explanation:
Rounding in the calculation of monthly interest rates is discouraged. Such rounding can lead to answers different from those presented here. For long-term loans, the differences may be pronounced.
Assume that you take out a $2000 loan for 48 months at 3.5% APR. How much total interest will you have paid at the end of the 48 months? (Round your answer to the nearest cent.)
$
Step-by-step explanation:
Are you using a particular calculator for the class? For this class, is the payment expected to be compounded monthly?
There is a function in Microsoft Excel that will calculate the payment for you, but the answer is going to be slightly different for a business math class than a calculus-based statistics class.
The excel formula to calculate a payment is
=PMT(0.04/12,60,25000,0)
.04/12 is the interest APR on a monthly basis
60 is the number of months
25000 is the current amount owed
0 is the future balance after 60 payments
The answer from Excel is $460.41 -- ignore the negative sign for these purposes.
Multiply that number by the 60 months you pay and you get a total paid of $27,624.78
Remove the initial 25K and $2,624.78 is your interest amount.
By the way, I used the simplifying assumptions that the problem meant "interest rate" when it said "APR", and that the rate would compound monthly. In the actual loan industry, the interest rate is only part of the calculation for APR, a
146.08
Step-by-step explanation:
Let's start by figuring out the payment
effective rate: .035/12= .002916667
\begin{gathered}2000=x\frac{1-(1+.002916667)^{-48}}{.002916667}\\x=44.71\end{gathered}
2000=x
.002916667
1−(1+.002916667)
−48
x=44.71
then it's just
44.71*48-2000=146.08
Answer:
146.08
Step-by-step explanation:
Let's start by figuring out the payment
effective rate: .035/12= .002916667
[tex]2000=x\frac{1-(1+.002916667)^{-48}}{.002916667}\\x=44.71[/tex]
then it's just
44.71*48-2000=146.08
Two trains leave a train station at the same time. One travels north at 12 miles per hour. The other train travels south at 9 miles per hour. In
how many hours will the two trains be 88.2 miles apart?
O 4.7 hours
O 4.2 hours
O 2.1 hours
O 8.4 hours
Answer:
4.2 hours
Step-by-step explanation:
400 is 100 times as much as
please help! (listing BRAINLIST and giving points) :D
Answer:
x = 50 + 95 = 145
.........
Answer:
x = 145°
Step-by-step explanation:
Given,
Measure of the first angle = 50°
Measure of the second angle = 95°
We know,
Sum of 3 angles of a triangle is equals to 180°
∴ The third angle = 180° - (50+95)°
= 180° - 145°
= 35°
Again,
Straight angle = 180°
∴ x = 180° - 35°
= 145°
∴x = 145°
calculate 3ab + b for a=2 and b=-3
`Please help me with this 4/5v = - 8/7
