Using vector concepts, it is found that the components of the velocity are given as follows:
North: 205.21 mi/h.East: 563.82 mi/h.How can a vector be represented in i and j notation?Given a magnitude M and angle [tex]\theta[/tex], the a vector V can be represented as follows:
[tex]V = M\sin{\theta}i + M\cos{\theta}j[/tex]
In which:
i is the horizontal(east/west) component.j is the vertical(north/south) component.In this problem, we have that the magnitude and the angle are given as follows:
[tex]M = 600, \theta = 70^{\circ}[/tex]
Hence the north component is:
[tex]600\cos{70^{\circ}} = 205.21[/tex]
And the east component is:
[tex]600\sin{70^{\circ}} = 563.82[/tex]
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A pennant flag that is 2 inches high with a base of 1.5 inches has an area of 1.5 square inches. The
area of a triangle varies jointly with the base and height. Find the area of a flag whose base
measures 2 inches and height is 2.5 inches.
Answer:
2.5 sq. inches
Step-by-step explanation:
Explanation is given in the pic attached.
Area of triangle= 1/2* base* height
Hope this helps!
The area of the flag when the base is 2 inches and the height is 2.5 inches is 2.5 square inches
From the question, we understand that the area (A) of the flag varies jointly with the base (B) and the height (H)
This variation is represented as:
[tex]\mathbf{A\ \alpha\ B \times H}[/tex]
So, we have:
[tex]\mathbf{A\ \alpha\ BH}[/tex]
Express as an equation
[tex]\mathbf{A\ =k BH}[/tex]
When the area is 1.5 square inches, the base is 1.5 inches and the height is 2 inches, we have:
[tex]\mathbf{A\ =k BH}[/tex]
This gives
[tex]\mathbf{1.5\ =k \times 1.5 \times 2}[/tex]
[tex]\mathbf{1.5\ =k \times 3}[/tex]
Divide both sides by 3
[tex]\mathbf{\frac 12 =k }[/tex]
Rewrite as:
[tex]\mathbf{k = \frac 12}[/tex]
When the base is 2 inches and the height is 2.5 inches, we have:
[tex]\mathbf{A\ =k BH}[/tex]
This gives
[tex]\mathbf{A = \frac 12 \times 2 \times 2.5}[/tex]
[tex]\mathbf{A = 2.5}[/tex]
Hence, the area of the flag is 2.5 square inches
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calculate the interquartile range of 45 47 48 49 50 51 52 53 60
Answer:
48
I hope it helps.
Which mixed number is represented by the shaded
area?
0 1 1/4
0 1 3/4
0 2 1/4
0 2 3/4
Hurry up plz I’m being timed
the answer to the question is 11/4
- Alto and Sheryl both worked hard over the summer. Together they earned a total of $475. Sheryl earned $25 more than Alto. (a) Write a system of equations for the situation. Use s for the amount Sheryl earned and a for the amount Alto earned. a (b) Graph the equations of the system on the graph provided on the next page. a. Note: Insert->Shape will allow you to add lines, draw dots, and otherwise insert shapes in both Microsoft Word and LibreOffice. The graph should be big enough for you to easily plot points using this method. b. If you do not want to graph using the drawing tools built into Microsoft Word or LibreOffice you may also print out, graph by hand, and scan the page. Please note it's perfectly okay to upload multiple files. (c) Use Elimination or Substitution to solve the system. (d) Use your graph to estimate how much each person earned, check your work with part C, and explain your results in complete sentences. Answer:
pls hurry its due tomorrow
Answer:
s = 250
a = 225
Step-by-step explanation:
Because they both earned a total of 475 dollars, the total amount of the two is 475. Because a represents Alto's earnings, and s represents Sheryl's earnings, we have [tex]a+s=475[/tex]
Sheryl also earned 25 more dollars than Alto, so the value of s is 25 larger than a: [tex]s=a+25[/tex]
By graphing, we can let s = y and a = x, so we have the following equations:
[tex]x + y=475\\y=x+25[/tex]
Plugging this into Desmos, we have this: (look at screenshot uploaded)
We see that y, or Sheryl's amount is around 250, and x, or Alto's amount is in the middle of 200 and 250, roughly about 225.
Now, we can solve for a and s. Because the value of s is equal to a + 25, we can represent s as a + 25 in the first equation: [tex]a + (a + 25) = 475[/tex]. Combining like terms, we have [tex]2a+25=475[/tex], and [tex]2a = 450[/tex]. Dividing, we have [tex]a = 225[/tex], and since s is 25 more than 225, we have [tex]s = 250[/tex]
The amount we estimated was around what we solved for. We found that the solution, or the value where both cases are true is around 250 and 225 for Sheryl and Alto's earnings.
Pls brainlest ASAP and add extra points for correct answer
Answer:
glucose, sunlight and oxygen on the left (they go in the cell)
water and carbon dioxide on the right (they go out of the cell)
A bag of marbles consists of 14 blue marbles and 7 red marbles. If you reach into the bag and choose 2 marbles,
what is the probability that they are both blue? Assume the first marble is not replaced.
Answer:
chances are 10.5
Step-by-step explanation:
What is the sum of 4 of the interior angles of a regular octagon?
Answer:
540°
Step-by-step explanation:
inter angle vertex = 135°
135 + 135 + 135 + 135 = 540°
For BOTH Bruce and Felicia, graph a line to represent y, the area each person covered using x tiles.
The tiles that Bruce used were each 1/4 of a square foot in area. The table shows the area covered by Felicia’s tiles in terms of the number of tiles used.
Number of tiles Area covered
6 1
12 2
18 3
Bruce and Felicia want to know whose tiles cover the most area per tile.
If the area each person covered using x tiles. Bruce's tiles cover the most area per tile.
What is the equation?An equation is a statement that two expressions, which include variables and/or numbers, are equal. In essence, equations are questions, and efforts to systematically find solutions to these questions have been the driving forces behind the creation of mathematics.
It is given that, the tiles that Bruce used were each 1/4 of a square foot in the area and a table shows as,
Number of tiles(y) 6 12 18
Area covered (x) 1 2 3
Felicia tile's relationship between the number of tiles and the area covered is,
(1/6) =(12/2)=(18/3)
y=(1/6)x
The equation of a line to represent y, the area each person covered using x tiles for Bruce is,
y =(1/4)x.
Thus, if the area each person covered using x tiles. Bruce's tiles cover the most area per tile.
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NO LINKS!!!!
Consider the following sequence 4, 8, . . .
a. Assuming the sequence is arithmetic:
i. Write the next four terms
ii. What is the generator?
iii. Write a formula for t(n).
iv. Create a table and graph your sequence.
b. Assuming the sequence is geometric:
i. Write the next four terms
ii. What is the generator?
iii. Write a formula for t(n).
iv. Create a table and graph your sequence
9514 1404 393
Answer:
a. 12, 16, 20, 24; t(n)=4n
b. 16, 32, 64, 128; t(n)=2·2^n
Step-by-step explanation:
a. The difference of the given terms is 8-4=4, so the arithmetic sequence has a first term of 4 and a common difference of 4. The general term has the formula ...
t(n) = t(1) +d(n -1)
t(n) = 4 +4(n -1) . . . . . with t(1) and d filled in
t(n) = 4n . . . . . . . . . . simplified
This formula can be considered to be the generator of the sequence. For values of n from 3 to 6, the next four terms are ...
t(3) = 12; t(4) =16; t(5) = 20, t(6) = 24
A table and graph are shown in the first attachment.
__
b. The ratio of the given terms is 8/4 = 2, so the geometric sequence has a first term of 4 and a common ratio of 2. The general term has the formula ...
t(n) = t(1)·r^(n-1)
t(n) = 4·2^(n-1) . . . . . . . with t(1) and r filled in
t(n) = 2·2^n . . . . . . . . simplified
This formula can be considered to be the generator of the sequence. For values of n from 3 to 6, the next four terms are ...
t(3) = 16; t(4) = 32; t(5) = 64; t(6) = 128
A table and graph are shown in the second attachment.
A restaurant has total of 60 tables . Of those tables , 38 are round and 13 are located by the window . There are 6 round tables by the window . If tables are randomly assigned to customers , what is the probability that a customer will be seated at a round table or by the window
Answer:
The probability that a costumer will be seated at a round table are 44/60 and the probability that he will be seated by the window is 13/60
The probability that a customer will be seated at a round table is [tex]\frac{19}{30}[/tex] and by the window is [tex]\frac{13}{60}[/tex].
What is Probability ?Probability is a ratio of the number of favorable outcomes to the number of possible outcomes of the experiment.
Probability [tex]=\frac{Number \ of\ outcomes}{Number\ of\ possible\ outcome}[/tex]
We have,
Total number of tables [tex]=60[/tex]
Number of round tables [tex]=38[/tex]
Number of tables located by the window [tex]=13[/tex]
Number of round tables located by the window [tex]=6[/tex]
Now,
Number of possible outcomes customer will be seated at a round table [tex]=38[/tex]
So,
Probability of seated at a round table [tex]=\frac{Number \ of\ outcomes}{Number\ of\ possible\ outcome}[/tex]
[tex]=\frac{38}{60}=\frac{19}{30}[/tex]
Now,
Number of possible outcomes customer will be seated by the window [tex]=13[/tex]
Probability of seated by the window[tex]=\frac{Number \ of\ outcomes}{Number\ of\ possible\ outcome}[/tex]
[tex]=\frac{13}{60}[/tex]
So, probability that a customer will be seated at a round table is [tex]\frac{19}{30}[/tex] and by the window is [tex]\frac{13}{60}[/tex].
Hence, we can say that the probability that a customer will be seated at a round table is [tex]\frac{19}{30}[/tex] and by the window is [tex]\frac{13}{60}[/tex].
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On a family trip to Oman, Tarek drove 300 km in 5 hours. This is an example of a unit rate or a rate? Please tell the correct answer.
Answer:
300 km in 5 hours is the rate
unit rate is how much in one unit
in this case the unit is one hour
60km / hour
HELP ME OUT PLEASE!!!!!!!
Which equation could represent the relationship shown in the scatter plot?
A) y = -3x - 2
B) y = 9x - 1/2
C) y = -3/4x + 10
D) y = -2/3x + 1
Answer:
option C is correct.
according to me..
hope it helpful for you.
ITS 100 POINTS!!!! AND DO IT IN A STEP BY STEP EXPLAINATION.
A proportional relationship between the number of pounds of cabbage (x) and the price in dollars (y) is graphed, and the ordered pair (5, 2) is on the graphed line.
Part A: What is the price of 1 pound of cabbage? Show your work. (8 points)
Part B: What does the ordered pair (10, 4) on the graph represent? Explain in words. (2 points)
Answer:
part a: If x represents the number of pounds of cabbage and y represents the price in dollars, then (5, 2) means that 5 pounds of cabbage costs $2.00. If that is true, then 1 pound of cabbage will cost $0.40. (divide both values by 5)
The ordered pair (10, 4) means that 10 pounds of cabbage cost $4.00.
explanation: sorry its late but hope it helps
The perimeter of a rectangle is represented by the expression 12x-2812x−28. The length of the rectangle is represented by the expression 2x+102x+10. Which expression represents the width of the rectangle?
Answer:
339,006 that's the answer
Ernie deposits $9,800 into a pension fund. The fund pays a simple interest rate of 7%. What will the balance be after four years?
Answer:
$12,845.80
Step-by-step explanation:
take the first number and go +7%. repeat four times
hope this helps :-)
The picture below shows the graph of which inequality?
Answer A is correct.
Step-by-step explanation:
Negative one is less than one.
On a cold February morning, the temperature of the radiator fluid in Stanley’s car is Negative 18 degrees Fahrenheit. When the engine is running, the temperature of the fluid goes up 5.4 degrees Fahrenheit per minute. Approximately how long will it take before the radiator fluid temperature reaches 60 degrees Fahrenheit? (HELPP)
It takes 14.4 minutes for the radiator fluid temperature to reach 60 degrees Fahrenheit
A function is said to be linear if it is a straight line graph and it can be represented by the equation:
y = mx + b
where y, x are variables, m is the rate of change and b is the initial value of y.
Let y represent the temperature in Fahrenheit of the radiator after t minutes.
Stanley’s car is Negative 18 degrees Fahrenheit. Hence b = -18. The temperature of the fluid goes up 5.4 degrees Fahrenheit per minute. hence m = 5.4. The equation becomes:
y = 5.4x - 18
For the radiator fluid temperature to reach 60 degrees Fahrenheit:
60 = 5.4x - 18
5.4x = 78
x = 14.4 minutes
It takes 14.4 minutes for the radiator fluid temperature to reach 60 degrees Fahrenheit
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Simplify the expression, ((p^(-2)+1/p)^1 )^p, when p=3/4, in both radical and rational exponents forms.
Radical form: Rational exponent form:
this question requires two answers please
Answer:
(1/27)252^(3/4)(1/27)fourth root(252^3)Step-by-step explanation:
The exponent of 1 can be ignored. This means we're simplifying ...
[tex]\left(\left(\dfrac{3}{4}\right)^{-2}+\dfrac{1}{\left(\dfrac{3}{4}\right)}\right)^{3/4}=\left(\dfrac{16}{9}+\dfrac{4}{3}\right)^{3/4}=\left(\dfrac{28}{9}\right)^{3/4}\\\\=\left(\dfrac{28\cdot9}{3^4}\right)^{3/4}=\boxed{\dfrac{252^{3/4}}{27}}\qquad\text{rational exponent form}\\\\=\boxed{\dfrac{\sqrt[4]{252^3}}{27}=\dfrac{\sqrt[4]{16003008}}{27}}\qquad\text{radical form}[/tex]
Two consecutive odd integers have sum of 44. Find the integers
Answer:
21, and 23
Step-by-step explanation:
divide 44 by 2 to find the integer that spits it up perfectly into two. Then just add 1 to one 22 and minus 1 to the other. Then its 21 and 23.
HELP ME OUT PLEASE!!!
Which equation matches the function described in the table?
A) y = 4x
B) y = x + 1
C) y = x + 5
D) y = 4x - 1
Answer:
D) y= 4x - 1
Step-by-step explanation:
We are basically trying to see which of the equations provided are true on both sides of the equal sign when you plug in the x and y values.
Let's start!
Choice A:
plug in 0 for x and -1 for y
-1 = 4(0)
And you are left with...
-1 = 0
This equation is false! Therefore it does not match the function in the table
Choice B:
plug in the values again
-1 = 0 + 1
-1 = 1
False!
Choice C:
-1 = 0 + 5
-1 = 5
False!
Lastly...Choice D:
-1 = 4(0) -1
Multiply 4 and 0 which is 0, so you are left with...
-1 = -1
This equation is true!!
So your answer is D
Hope this helps :D
Your parents decide to build a rectangular pool in your backyard. They determine that the length of the pool should be 15 feet longer than the width.
The area of the pool is the amount of space it occupies
The expression for the area and the perimeter are [tex]\mathbf{A = 15x + x^2}[/tex] and [tex]\mathbf{P = 4x +30}[/tex], respectively
Let the dimension of the pool be x and y, where x represents width and y represents length.
So, the relationship between the width and the length is given as:
[tex]\mathbf{y = 15 + x}[/tex]
The area of the pool would be:
[tex]\mathbf{A = xy}[/tex]
Substitute 15 + x for y
[tex]\mathbf{A = x(15 + x)}[/tex]
Open bracket
[tex]\mathbf{A = 15x + x^2}[/tex]
And the perimeter of the pool would be
[tex]\mathbf{P = 2(x + y)}[/tex]
Substitute 15 + x for y
[tex]\mathbf{P = 2(x +15 + x)}[/tex]
[tex]\mathbf{P = 2(2x +15)}[/tex]
Open brackets
[tex]\mathbf{P = 4x +30}[/tex]
Hence, the expression for the area and the perimeter are [tex]\mathbf{A = 15x + x^2}[/tex] and [tex]\mathbf{P = 4x +30}[/tex], respectively
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What is 78 1/3 as a decimal?
Pls help!
Answer:
78.333333333
Step-by-step explanation:
Help on this fast?? Thank you
Answer:
The answer is 17.5 dollars an hour, if you were to divide 70 by 4 that is what you would get as a result.
Step-by-step explanation:
Sebastian is 3 years older than twice Amy's age. Sebastian is 33 years old. How old is Amy?
Answer:
15 years old
Step-by-step explanation:
You would have to create a equation. 2x+3=33, 2x=30, x=15.
find the slope and y intercept of y = x - 18
Answer:
Step-by-step explanation:
slope of y = x - 18
slope: 1
y-intercept: y = x - 18
y= 0 - 18= -18
y-int: (0, -18)
For a project in her Geometry class, Kylie uses a mirror on the ground to measure the
height of her school's flagpole. She walks a distance of 14.25 meters from the flagpole,
then places a mirror on flat on the ground, marked with an X at the center. She then
steps 1.35 meters to the other side of the mirror, until she can see the top of the
flagpole clearly marked in the X. Her partner measures the distance from her eyes to
the ground to be 1.25 meters. How tall is the flagpole? Round your answer to the
nearest hundredth of a meter.
The project in her Geometric class is an illustration of equivalent ratios
The approximated height of the flagpole is 13.19 meters
The given parameters are:
Distance from flagpole (D) = 14.25
Distance to the other side of the mirror (d) = 1.35
Kylie's height (h) = 1.25
To calculate the height (H) of the flagpole, we make use of the following equivalent ratios
[tex]\mathbf{D :d = H :h}[/tex]
Substitute known values
[tex]\mathbf{14.25 :1.35 = H :1.25}[/tex]
Express as fraction
[tex]\mathbf{\frac{14.25 }{1.35 }= \frac{H }{1.25}}[/tex]
Multiply both sides by 1.25
[tex]\mathbf{H = 1.25 \times \frac{14.25 }{1.35 }}[/tex]
Multiply
[tex]\mathbf{H = 13.19 }[/tex]
Hence, the approximated height of the flagpole is 13.19 meters
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Trey has bought 10 pounds of dog food. He feeds his dog
pounds for each meal. For how many meals will the food last?
Write your answer in simplest form
how many pounds does he feed his dogs for each meal?
For a given two-digit number, the second digit is 2 more than 5 times the
first digit. Also, 5 times the first digit is 3 more than the second digit. Find
the two-digit number.
Answer:
no solution
Step-by-step explanation:
U=5t+2
5t=u+3
5t=5t+5
t=t+1
0=1
No solution
what is 5 times 3 times 7 add 7
Answer:
5*3*7+7=112
Step-by-step explanation:
5*3*7=105+7=112
Answer: 112
Step-by-step explanation:
5 x 3 x 7 + 7
5 x 3 = 15
15 x 7 = 105
105 + 7 = 112
Answer is 112
Bạn dự định đi học thêm vào mùa hè này. Nếu đi học bạn sẽ không thể đi làm với thu nhập là 5 triệu đồng và không thể ở nhà nghỉ ngơi. Học phí là 2 triệu, tiền mua giáo trình 300 ngàn, sinh hoạt phí là 1.5 triệu. Hãy xác định chi phí cơ hội của việc đi học thêm vào mùa hè này.
Answer:
4 better inbox
Step-by-step explanation: