Answer:
56. In the Vector Addition Lab, Anna starts at the classroom door and walks:
2.0 meters, West
12.0 meters, North,
31.0 meters, West,
8.0 meters, South
3.0 meters, East
Using either a scaled diagram or a calculator, determine the magnitude and direction of Anna's resulting displacement.
Answer: 30.3 meters, 172 degrees
To insure the most accurate solution, this problem is best solved using a calculator and trigonometric principles. The first step is to determine the sum of all the horizontal (east-west) displacements and the sum of all the vertical (north-south) displacements.
Horizontal: 2.0 meters, West + 31.0 meters, West + 3.0 meters, East = 30.0 meters, West
Vertical: 12.0 meters, North + 8.0 meters, South = 4.0 meters, North
The series of five displacements is equivalent to two displacements of 30 meters, West and 4 meters, North. The resultant of these two displacements can be found using the Pythagorean theorem (for the magnitude) and the tangent function (for the direction). A non-scaled sketch is useful for visualizing the situation.
Applying the Pythagorean theorem leads to the magnitude of the resultant (R).
R2 = (30.0 m)2 + (4.0 m)2 = 916 m2
R = Sqrt(916 m2)
R = 30.3 meters
The angle theta in the diagram above can be found using the tangent function.
tangent(theta) = opposite/adjacent = (4.0 m) / (30.0 m)
tangent(theta) = 0.1333
theta = invtan(0.1333)
theta = 7.59 degrees
This angle theta is the angle between west and the resultant. Directions of vectors are expressed as the counterclockwise angle of rotation relative to east. So the direction is 7.59 degrees short of 180 degrees. That is, the direction is ~172 degrees.
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57. In a grocery store, a shopper walks 36.7 feet down an aisle. She then turns left and walks 17.0 feet straight ahead. Finally, she turns right and walks 8.2 feet to a final destination. (a) Determine the magnitude of the overall displacement. (b) Determine the direction of the displacement vector relative to the original line of motion.
Answer: (a) 48.0 feet; (b) 21 degrees from the original line of motion
This problem is best approached using a diagram of the physical situation. The three displacements are shown in the diagram below on the left. Since the three displacements could be done in any order without effecting the resulting displacement, these three legs of the trip are conveniently rearranged in the diagram below on the right.
Now it is obvious from the diagram on the right that the three displacement vectors are equivalent to two perpendicular displacement vectors of 44.9 feet and 17 feet. These two vectors can be added together and the resultant can be drawn from the starting location to the final location. A sketch is shown below.
Since these displacement vectors are at right angles to each other, the magnitude of the resultant can be determined using the Pythagorean theorem. The work is shown below.
R2 = (44.9 ft)2 + (17.0 ft)2 = 2305 ft2
R = Sqrt(2305 ft2)
R = 48.0 feet
The angle theta in the diagram above can be found using the tangent function.
tangent(theta) = opposite/adjacent = (17.0 ft) / (44.9 ft)
tangent(theta) = 0.3786
theta = invtan(0.3786)
theta = 20.7 degrees
This is the angle which the resultant makes with the original line of motion (the 36.7 ft displacement vector).
Useful Web Links
Vector Addition || Vector Components || Vector Resolution
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58. A hiker hikes 12.4 km, south. The hiker then makes a turn towards the southeast and finishes at the final destination. The overall displacement of the two-legged trip is 19.7 km at 309 degrees . Determine the magnitude and direction of the second leg of the trip.
Answer: 12.7 km, 347 degrees
Like the previous problem (and most other problems in physics), this problem is best approached using a diagram. The first displacement is due South and the resulting displacement (at 309 degrees) is somewhere in the fourth quadrant. (It is in the fourth quadrant because 309 degrees lies between 270 degrees or due South and 360 degrees or due East.) For communication sake, we will refer to the first displacement as A and the second displacement as B. Note that A + B = R. Since the magnitude and direction of the resultant is known, the x- and y-components can be determined using trigonometric functions. Since the angle of 309 degrees is expressed as a counterclockwise angle of rotation with due East, it can be used as the Theta in the equation.
Rx = R•cos(theta) = 19.7 km • cos(309 deg) = 12.398 km
Ry = R•sin(theta) = 19.7 km • sin(309 deg) = -15.310 km (the "-" means South)
Whatever the magnitude and direction of B is, it must add on to vector A in order to give a southward displacement of 15.310 km and a eastward displacement of 12.398 km. This could be expressed by mathematical equations as
Ty earns a base rate of $12 an hour and receives a weekly attendance award of $20. He works 40 hours this week. What would be his total compensation for the week
Ty total compensation for the week where he earns a base rate of $12 per hour and receive a weekly attendance award of $20 is $500.
What is rate ?Rate is the ratio between two related quantities in different units.
Therefore, he earn a base rate of $12 per hour and receives a weekly attendance award of $20.
If he works 40 hours a week, his compensation will be as follows:
let
y = total compensation
x = number of hours worked
Hence,
y = 12x + 20
y = 12(40) + 20
y = 480 + 20
y = $500
Therefore, Ty total compensation is $500.
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Please help!! Will give brainliest! I need the steps too
Answer:
Day 44
Step-by-step explanation:
Given function:
[tex]f(t)=500t^2[/tex]
where:
f = number of daily hitst = times (in days)To find the day on which the number of daily hits reaches 1,000,000, set the function to 1,000,000 and solve for t:
[tex]\begin{aligned}f(t) & =1000000\\ \implies 500t^2 & = 1000000\\ t^2&=\dfrac{1000000}{500}\\ t^2 & = 2000\\ t & = \pm \sqrt{2000}\\ t & = \pm 44.72135955...\end{aligned}[/tex]
As time in positive, t = 44.72135955 only.
This tells us that the number of daily hits reaches 1,000,000 during the 44th day.
Please
Solve!
For the Perimeter and Area
I can see if the answer is correct or not by putting the answer in the box.
The user that is correct will get brainliest! If someone else answers!
Urgent !!!
What does the absolute value of the correlation coefficient say about the predictions in part B? How do you know? Write an explanation of about one to two sentences
Part B attached
The line of best fit shows that Luther can expect the speed to be 51 miles/hour when he throws 80 pitches and 64 miles/hour when he throws 54 pitches.
How to calculate the speed?The average speed of Luther's pitches when he throws 80 pitches will be:
y = -0.511x + 91.636
= -0.511(80) + 91.636
= 50.756
= 51
Also, the number of pitches that Luther can throw when the speed is 64 miles per hour will be:
y = -0.511x + 91.638
64 = -0.511x + 91.638
0.511x = 91.638 - 64
0.511x = 27.636
x = 54
Therefore, the number of pitches will be 54.
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A rectangular prism is 30 yards long, 29 yards wide, and 33 yards high. What is the surface
area of the rectangular prism?
square yards
Calculate the cost (omit commission) of buying the 500 shares of Delta Air at $50.61.
Multiplication is the process of multiplying, therefore, adding a number to itself for the number of times stated. The cost of 500 shares of Delta Air is $25,305.
What is multiplication?Multiplication is the process of multiplying, therefore, adding a number to itself for the number of times stated. For example, 3 × 4 means 3 is added to itself 4 times, and vice versa for the other number.
The cost of a single share is $50.61, therefore, the cost of 500 shares will be,
Cost of 500 shares = 500 × cost of single share
= 500 × $50.61
= $25,305
Hence, the cost of 500 shares of Delta Air is $25,305.
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Anna ordered a large pizza with 2 toppings. What was the total cost of her pizza? Show your equation and the total cost.
Answer: $15.49.
Step-by-step explanation: So far, her pizza already costs $13.99 because she chose large. However, she also ordered two toppings for $0.75 each, which is $1.50. We need to add $13.99 and $1.50 to find out the total cost of her custom pizza.
$13.99 + $1.50 = $15.49.
Therefore, the total cost of her pizza is $15.49.
Have a great day! :)
If 2 dozens of eggs cost #300. How much will 5 eggs cost?
answer:62.5
a dozen=12 eggs
12× 2 eggs=300
5 eggs=x
cross multiply
24x=1500
thus x=62.5
help me please ,this is my school work and i need help .
Answer:
2-5f ≤ 52, so -5f ≤ 50
f≥-10, because we flip the sign when multiplying or dividing by a neg number for inequalities.
Draw a closed circle on -10 and in the direction all the way towards the right arrow.
PLEASE HELP!!!! I’LL GIVE BRAINLIEST!
use vertical angles to find the value of x.
Answer:240
Step-by-step explanation: ×/6 =40
Multiply both sides by 6
× is 240
The top of the table can be modeled with a cylinder, and the legs can be modeled with rectangular prisms. Estimate the amount of paint needed to cover all parts of the table, to the nearest square inch.
Answer:
A. 3,703 inches squared
Step-by-step explanation:
I took the test and got it right. #platofam
in a sale the normal price of a boat is 15%, the sale price of the boat is £272000, work out the normal price of the boat
Step-by-step explanation:
normal 100 part sale 15 part saple price 85 part
85/100 = 272000/normal price
normal price = 272000 × 100/85
= 320000
Answer:
312800
Step-by-step explanation:
You could do 272000 times 15% then add the discount price
which is 272000 + 40800 = 312800
The cutoff point for the p-value area is called the:.
Answer:
It is called the test statistic
Step-by-step explanation:
Hope this helps:)...if not then sorry for wastign your time and may God bless you:)
solve: 3/5x +30 is ≥ 150
Answer: x>=200
Step-by-step explanation:
After a heavy rainstorm, Barbara's dog left muddy paw prints all over her back patio. She decided to rent an electric
pressure washer to clean up the mess. The piecewise function below shows the rental charges for the pressure
washer, dependent upon how many hours she rents it. Due to high demand, you cannot rent the washer for more
than 24 hours at a time. Barbara's brother asked to use the washer and agreed to pay Barbara for any additional
monies owed.
(26,0
y= {26 + 5% - 4),4
60,8
If Barbara used the washer for 3 hours and her brother returned it to the store 7 hours after she rented it, how much
does her brother owe her?
$15.00
O $41.00
$60.00
$61.00
Answer:
$15.00
Step-by-step explanation:
Just did the quiz
By evaluating the piecewise function, we will see that the brother owes $15.
How much does her brother owe her?
The piecewise function is:
y = 26, if 0 < h < 4
y = 26 + 5*(h - 4), if 4 < h < 8
y = 60, if 8 < h
Barbara uses it for 3 hours, so we only need to use the first part for her, so she needs to pay $26.
Then the brother uses it for 4 hours (and we need to add the 3 hours that Barbara used it, so we have h = 7).
Then for the 7 hours the two brothers need to pay:
y = $26 + $5*(7 - 4) = $41
If we subtract the part that Barbara needs to pay we get.
$41 - $26 = $15
This means that the correct option is $15.
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is √16 rational or unrational?
Answer:
Rational number
Step-by-step explanation:
√16 is Rational number simply because its value is 4, which can be expressed as a Ratio of Two Numbers
kindly answer it....
Answer:
1. 360 km
2. 2 seconds
Step-by-step explanation:
Question 1Formula
distance = speed × time
Given:
speed = 120 km/htime = 3 hours⇒ distance = 120 × 3 = 360 km
----------------------------------------------------------------------------------
Question 2Given:
initial velocity (u) = 0 m/sfinal velocity (v) = 20 m/sacceleration (a) = 10 m/s²To find time (t), use the SUVAT equation: v = u + at
⇒ 20 = 0 + 10t
⇒ 20 = 10t
⇒ t = 20/10
⇒ t = 2 s
What percent of the time did Mountain View get at least 4,000 visitors?
Kyle competes in 100 m wheelchair races. Hel
calculates the information below using his last 4
race times.
His minimum race time was 19.8 s.
The range of his race times was 5.6 s.
The median of his race times was 23.8 s.
The mode of his race times was 25.4 s.
If Kyle includes a new race time of 25.7 s in his
calculations, how much will the mean change
by?
Answer:
0.5s
Step-by-step explanation:
His initial mean would be calculated by:
His minimum race time = 19.8s
The maximum race time = 19.8 + 5.6 = 25.4s
Since the mode is also 25.4, there are 2 25.4s races.
Since the median is 23.8s and the number of race times is even, the final race time can be calculated by:
25.4- 23.8s = 1.6s
23.8-1.6 = 22.2s
So the race times are 19.8s, 22.2s, 25.4s and 25.4s.
This means that his initial mean was (19.8+22.2+25.4+25.4)/4 = (42+50.8)/4= 92.8 /4 = 23.2s
With the new race time, the equation will change to (92.8+25.7)/(4+1)= 118.5/5= 23.7s
So the mean change would be 23.7 - 23.2 = 0.5 s.
Hope this helps!
A cube of side 14 cm is surmounted by a hemisphere. What is the greatest diameter the hemisphere can have? Find the surface area of the solid?
Answer:
Greatest diameter of hemisphere = 14 cm
Surface area of solid = 1330 cm²
Step-by-step explanation:
Side of the cube (a) = 14 cm
If a cube is surmounted (placed right over its top) by a hemisphere, then that means that the greatest diameter of the hemisphere will be equal to the measure of the edge of the cube (a cube has equal sides). Hence, the greatest diameter of the hemisphere is 14 cm & the radius (r) will be 14/2 = 7 cm (radius = ½ diameter)
Now, we need to find the surface area of the solid.
Here, the solid comprises of a cube & a hemisphere sharing a same circular base area. Hence,
Surface area of the solid
= Surface area of cube + Curved surface of hemisphere - Circular base area
= 6a² + 2πr² - πr²
= 6a² + πr²
= 6(14)² + 22/7×(7)² [π = 22/7]
= 1176 + 154
= 1330 cm²
[tex]\rule{150pt}{2pt}[/tex]
NOTE:
Refer to the attached picture to see how a hemisphere is surmounted on top of a cube.
[tex]\rule{150pt}{2pt}[/tex]
Please find attached herewith the solution of your question.
If you have any doubt, feel free to ask.
Solve the equation (x-2)(3x-1)=0
x=2
_______
x= [tex]\frac{1}{3}[/tex]
The table below shows the gender and type of movies they prefer to watch.
What is the approximate probability that a person will be a female and prefer suspense movies?
Probability helps us to know the chances of an event occurring. The probability that a person will be a female and prefer suspense movies is 0.047.
What is Probability?Probability helps us to know the chances of an event occurring.
[tex]\rm Probability=\dfrac{Desired\ Outcomes}{Total\ Number\ of\ outcomes\ possible}[/tex]
The total number of people who were surveyed are:
Total Number of people = 82 + 94 +18 + 46 + 48 + 91 = 379
Also, it is mentioned in the table that the number of females who prefers suspense movies is 18. Therefore, the probability that a person will be a female and prefer suspense movies will be,
[tex]\rm Probability = \dfrac{\text{Number of females who prefers suspense movies}}{\text{Total Number of people}}\\\\Probability = \dfrac{18}{379} = 0.047[/tex]
Hence, the probability that a person will be a female and prefer suspense movies is 0.047.
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[tex]f(x) = 2^{x + 1} - 2^{x - 1} [/tex]
please help, we need to find the derivative, explain step by step
Note the derivative rule
[tex]\\ \boxed{\star\bf \dfrac{d}{dx}(x^n)=nx^{n-1}}[/tex]
Let's see
[tex]\\ \rm\Rrightarrow \dfrac{d}{dx}(2^{x+1}-2^{x-1})[/tex]
[tex]\\ \rm\Rrightarrow \dfrac{d}{dx}2^{x+1}-\dfrac{d}{dx}2^{x-1}[/tex]
[tex]\\ \rm\Rrightarrow (x+1)2^{x+1-1}-(x-1)2^{x-1-1}[/tex]
[tex]\\ \rm\Rrightarrow (x+1)2^x-(x-1)2^{x-2}[/tex]
[tex]\\ \rm\Rrightarrow (x+1)2^x-(x-1)2^x/2^2[/tex]
[tex]\\ \rm\Rrightarrow (x+1)2^x-(x-1)2^x2^{-2}[/tex]
[tex]\\ \rm\Rrightarrow 2^x(x+1-(x-1)2^{-2})[/tex]
[tex]\\ \rm\Rrightarrow 2^x(x+1-x/4-1/4)[/tex]
2. Cordasha is making her morning Starbucks run before school. She is buying
several coffees for her teachers. An Espresso costs $5.50 and a latte costs
$7.25. In total she spent $45.50 and bought a total of 7 types of coffees.
Write a system of equations that finds the amount of Espresso's and latte's
that Cordasha bought.
Answer:
x*5.5 + y* 7.25 = 45.5
x + y = 7
Step-by-step explanation:
every Espresso cost 5.5 => x*5.5
And the total cost is 45.5 so the sum should be 45.5
there are 7 coffees. means that the number of Espresso and latte is 7
which equation represents the line through (4, -6) (0, 2)
Answer:
[tex]y=-2x+2[/tex]
Step-by-step explanation:
Firstly we need to find the gradientWe can do this with [tex]\frac{\triangle y}{\triangle x}[/tex] ([tex]\frac{change\ in\ y}{change\ in\ x}[/tex])[tex]\frac{2--6}{0-4}[/tex][tex]\frac{8}{-4}=-2[/tex]So far we have [tex]y=-2x+c[/tex]Choose one of the pairs of coordinatesI’ll choose (0,2)[tex]2=c[/tex]So your equation is [tex]y=-2x+2[/tex]Answer:
y = -2x +2 I think
Step-by-step explanation:
HELP PLEASEEEEEEEE
Ashley's bus ride to school is 7/10 of a mile and Gavin's bus ride is 1/5 of a mile. How much longer is Ashley's bus ride than Gavin's?
How many different ways can 1 committee of 5 students be selected from a class of
25?
Answer:
125 ways
Step-by-step explanation:
5 x 25 = 125
Hope this helps!
In the coordinate plane, what is the distance between the points (- 2, 3) and (4, 0) HELP
Answer:
Exact Form:
3√5
Decimal Form:
6.70820393
Step-by-step explanation:
Answer:
Distance = 3√5 or 6.708203932,,,
Step-by-step explanation:
Find the distance between the y-values and x-values which in this case would be 6 and 3. Use the Pythagorean theorem.
[tex]3^2 + 6^2 = 45[/tex]
Simplify.
[tex]\sqrt{45} = 3\sqrt{5}[/tex]
(4 questions) Is 8km greater than 8000mm? Is 50km greater than 5000m? Is 10m greater than 100cm? (last one) Is 4mm greater than 40cm?
Answer:
1. 8000mm is the same as 8 metres. So 8km is greater than 8000mm
2. 5000m is the same as 5 km. So 50 km is greater than 5000m
3. 100cm is the same as 1 m. So 10m is greater than 100cm
4. 40 cm is the same as 400mm. So 4mm is less than 40cm.
b) Work out (7 x 10^5) x(9x 10^7)
Give your answer in standard form.
Answer:
3,500
Step-by-step explanation:
700,000/200
7,000/2
3,500