A mouse is trapped in a maze. To
find his way out, he walks 15 m,
makes a 90° left turn, walks 8 m,
makes another 90° left turn, and
walks 10 m. What is the magnitude
of the resultant vector?
Answers
Answer: Approximately 9.43 meters
The more accurate version is 9.4339811320566 but that's not exact.
This is exact magnitude is sqrt(89)
=======================================================
Explanation:
Let's draw an xy grid for this. Place the starting point at (0,0) which I'll call point A. Now let's say the mouse goes east 15 meters. That would move it to (15,0) which is marked as point B. Refer to the diagram below.
From point B, we move to C which is at (15,8). So the mouse has gone 8 meters north. It might help to turn the page so that the east direction is facing completely north, and then look to the left and you'll see "north". In other words, each 90 degree left turn is a 90 degree counterclockwise turn.
After doing another 90 degree counterclockwise turn, the mouse will move 10 meters westward. It moves from C(15,8) to D(5,8). Point D is the final position of the mouse.
-----------------------
A(0,0) was the initial position and D(5,8) is the final position
The vector v is
v = <5,8>
This is because we basically are saying "the mouse ultimately moved 5 meters east and 8 meters north" when going from start to finish. We're ignoring the intermediate stops along the way.
------------------------
Recall that for any vector of the form
v = <a,b>
the magnitude of that vector is
|v| = sqrt(a^2+b^2)
this is the length of the vector based on the pythagorean theorem.
Applying this formula gets us
|v| = sqrt(5^2+8^2)
|v| = sqrt(89)
|v| = 9.43398 approximate
This represents the straight line distance from start to finish, where we ignore any intermediate stops. So this isn't the distance the mouse travels (since it goes from A to B, to C to D). Instead, it's the distance it would travel if it wanted to take the shortest path from A to D.
Answer:
Step-by-step explanation:
9.4 for acellus
Related Questions
GIVING OUT BRAINLIEST HELP ME OUT PLSSS
Answers
Answer:
90 degrees but mom not too sure
Determine if each proportion on the left is True or False. Answer options on the right side may be used more than once.
True
False
28/16=14/8
3/5=9/15
4/32=10/78
3/4=12/16
Answers
Answer:
28/16=14/8 true
3/5=9/15 true
4/32=10/78 false
3/4=12/16 true
Step-by-step explanation:
DID IT ON BRIDGE
Find the slope of the line that passes through the points (-5,-6) and (5,10)
Answers
that’s just what i got
Please help and show work please and please no sending links
Answers
80=20+5x
60=5x
x=12=c
m) Factorise:
x2/9+1+9/x2
Answers
Answer:
Cannot be factored
Step-by-step explanation:
Given
[tex]\frac{x^2}{9} + 1 + \frac{9}{x^2}[/tex]
Required
Factorize
Take LCM
[tex]\frac{x^2}{9} + 1 + \frac{9}{x^2} = \frac{x^4+9x^2+81}{9x^2}[/tex]
The expression cannot be factored
An inverted pyramid is being filled with water at a constant rate of 70 cubic centimeters per second. The pyramid, at the top, has the shape of a square with sides of length 8 cm, and the height is 15 cm. Find the rate at which the water level is rising when the water level is 4 cm.
Answers
Answer:
[tex]\frac{dh}{dt}=1.45cmsec^{-1}[/tex]
Step-by-step explanation:
Rate of Water Fill [tex]R=\frac{dv}{dt}=70cm^3[/tex]
Length [tex]l=8cm[/tex]
Height [tex]H=15cm[/tex]
Water level [tex]L_w= 4cm[/tex]
Generally the equation for relationship b/w h and a is mathematically given by
Since by the properties of similar triangles
[tex]k=\frac{h}{1/2}[/tex]
Let
[tex]h=15cm \\\\a=8cm[/tex]
[tex]k=\frac{h}{1/2a}[/tex]
[tex]k=\frac{15}{4}[/tex]
Therefore
[tex]\frac{h}{1/2a}=\frac{15}{4}[/tex]
[tex]a=\frac{8h}{15}[/tex]
Generally the equation for volume of Pyramid is mathematically given by
[tex]V=\frac{1}{3}ah^2h[/tex]
Subsitute a
[tex]V=\frac{1}{3}(\frac{8h}{15})h^2h[/tex]
Therefore
[tex]\frac{dv}{dt}=\frac{(\frac{1}{3}(\frac{8h}{15})h^2h)}{dt}[/tex]
[tex]\frac{dv}{dt}=\frac{64}{255}(h^2\frac{dh}{dt})[/tex]
Since
[tex]\frac{dv}{dt}=70cm^3s^{-1}[/tex]
Therefore
[tex]70cm^3s^{-1}=\frac{64}{255}(h^2\frac{dh}{dt})[/tex]
[tex]\frac{dh}{dt}=\frac{70}{169}*\frac{225}{64}[/tex]
[tex]\frac{dh}{dt}=1.45cmsec^{-1}[/tex]
What is the equation of the line through (4, 2) and (0, -2)?
Answers
Answer:
y=x-2
Step-by-step explanation:
4-0=4 = (change in y)
2--2=4 = (change in x)
change in y/change in x=4/4=1=x
gradient = x
y=x+c
Subtitute any coordinate
2=4+c
c=-2
so
y=x-2
Answer:
y=x-2
Step-by-step explanation:
Slope Intercept Form
y=x-2
Find Slope using equation below
Chose points I chose 2 as y2 and -2 as y2
4 is x2 and 0 as x1
Slope is 1
now choose a point and plug it in for x and y and plug slope in Equation
I chose (4,2)
2=4+b
subtract 4 by both sides
-2=b
Slope Form
So... y=x-2 is the answer
two mangoes cost $60.00. what is the cost of 5 mangoes
Answers
Answer:
Im not 100% sure but i think it would be $150.00
Step-by-step explanation:
Because if 2 mangos are $60
whats half of 60$
30
so 1 mango = $30
the person wants 5 mango so
multiply
$30*5
which would give you
$150.00
Answer:
$150
Step-by-step explanation:
If 2 mangoes cost $60, then 1 mango would be 60/2=30.
5 mangos would be 30×5=$150
1
Calculate the height, A. and the width, B. of the spice
cabinet shown in the figure. Don't forget to include the
1
--inch thickness of the wood where needed. The symbol
hardwood for all framing parts.
" means inches,
This
3
The height, A, of the spice cabinet is inches
(Type an integer, proper fraction, or mixed number.)
on
Answers
Answer:
Height A = [tex]12\frac{3}{4}[/tex] inches
Step-by-step explanation:
Height A = Sum of widths of all sections of the cabinet + thickness of the wood
Height A = [tex]1\frac{1}{4}+\frac{1}{4}+4\frac{1}{2}+\frac{1}{4}+4\frac{1}{2}+2[/tex]
= [tex](1+4+4+2)+(\frac{1}{4}+\frac{1}{4}+\frac{1}{2}+\frac{1}{4}+\frac{1}{2})[/tex]
= [tex]11+(\frac{1+1+2+1+2}{4} )[/tex]
= [tex]11+\frac{7}{4}[/tex]
= [tex]11+1\frac{3}{4}[/tex]
= [tex]11+1+\frac{3}{4}[/tex]
= [tex]12\frac{3}{4}[/tex] inches
Dan has an old lawn mower! It takes him 1 hour to mow the whole lawn. How many square yards does Dan cut in one minute? Hints: There are 60 minutes in 1 hour. To find the unit rate divide the area of the lawn by the amount of time it takes Dan to mow the whole lawn.
40 square yards per minute
400 square yards per minute
2400 square yards per minute
240 square yards per minute
Answers
Answer: You didnt mention how much Dan mows in 1 hour, but just do that divided by 60
Step-by-step explanation:
A local salesman has forty-five stacks of magazines. If the salesman plans to sell three-fifths of the stacks, how many stacks will he have left?
Answers
Answer:
2
Step-by-step explanation:
Answer:
2
Step-by-step explanation:
HELP TIMER Write the equation of a hyperbola centered at the origin with x-intercept +/- 4 and foci of +/-2(squareroot 5)
Answers
Given:
x-intercepts of the hyperbola are ±4.
The foci of hyperbola are [tex]\pm 2\sqrt{5}[/tex].
Center of the hyperbola is at origin.
To find:
The equation of the hyperbola.
Solution:
The general equation of a hyperbola:
[tex]\dfrac{(x-h)^2}{a^2}-\dfrac{(y-k)^2}{b^2}=1[/tex] ...(i)
Where, (h,k) is the center of the hyperbola, ±a are x-intercepts, [tex](\pm c,0)[/tex] are foci.
Center of the hyperbola is at origin. So, h=0 and k=0.
x-intercepts of the hyperbola are ±4. So,
[tex]\pm a=\pm 4[/tex]
[tex]a=4[/tex]
The foci of hyperbola are [tex]\pm 2\sqrt{5}[/tex].
[tex]\pm c=\pm 2\sqrt{5}[/tex]
[tex]c=2\sqrt{5}[/tex]
We know that,
[tex]a^2+b^2=c^2[/tex]
[tex](4)^2+b^2=(2\sqrt{5})^2[/tex]
[tex]16+b^2=20[/tex]
[tex]b^2=20-16[/tex]
[tex]b^2=4[/tex]
Taking square root on both sides, we get
[tex]b=\sqrt{4}[/tex] [b>0]
[tex]b=2[/tex]
Substituting [tex]h=0,k=0,a=4,b=2[/tex] in (i), we get
[tex]\dfrac{(x-0)^2}{4^2}-\dfrac{(y-0)^2}{2^2}=1[/tex]
[tex]\dfrac{x^2}{4^2}-\dfrac{y^2}{2^2}=1[/tex]
Therefore, the correct option is (d).
The sides of which diagram are correctly labeled with respect to angle A?
A right triangle is shown. Angle A is opposite to the side labeled adjacent.
A right triangle is shown. Angle A is opposite to the side labeled opposite. The hypotenuse is opposite to the right angle.
A right triangle is shown. Angle A is opposite to the side labeled opposite. The side labeled adjacent is opposite to the right angle.
A right triangle is shown. Angle A is opposite to the side labeled hypotenuse. The side labeled adjacent is opposite to the right angle.
Answers
9514 1404 393
Answer:
(b) Angle A is opposite to the side labeled opposite. The hypotenuse is opposite to the right angle.
Step-by-step explanation:
The hypotenuse is always opposite the right angle.
The side considered "opposite" is opposite the angle of interest, angle A in this case.
Answer:
Other person is correct
Step-by-step explanation:
Element X is a radioactive isotope such that its mass decreases by 73% every
hour. If an experiment starts out with 680 grams of Element X, write a
function to represent the mass of the sample after t hours, where the rate of
change per minute can be found from a constant in the function. Round all
coefficients in the function to four decimal places. Also, determine the
percentage rate of change per minute, to the nearest hundredth of a percent.
Mi
Answers
Answer:
Step-by-step explanation:
The element decay percentage rate of change 2.22% per minute.
What is radioactive isotope?
Radioisotope, radionuclide, or radioactive nuclide, any of several species of the same chemical element with different masses whose nuclei are unstable and dissipate excess energy by spontaneously emitting radiation in the form of alpha, beta, and gamma rays.
Here, mass decreases by 73% every hour.
Weight of element X is 680 grams.
According to question,
f(t) = 680 (1 - 73%)ⁿ
f(t) = 680 (1 - 0.73)ⁿ
f(t) = 680 X 0.27ⁿ
f(t) = 680 X 0.9778ⁿ
f(t) = 680 X (1 - 0.02322)ⁿ
Thus, the element decay percentage rate of change 2.22% per minute.
Learn more about radioactive isotope from:
https://brainly.com/question/1907960
#SPJ2
A high school has 32 players on the football team. The summary of the players' weights is given in the box plot. Approximately, what is the percentage of players weighing greater than or equal to 233 pounds
Answers
Answer:
[tex]\% = 11.96\%[/tex]
Step-by-step explanation:
Given
See attachment for box plot
Required
Percentage greater than or equal to 233
From the box plot, the maximum is:
[tex]Max = 244[/tex]
The minimum is:
[tex]Min = 152[/tex]
Percentage greater than 233 is calculated as:
[tex]\% = \frac{Max - 233}{Max - Min}[/tex]
[tex]\% = \frac{244 - 233}{244-152}[/tex]
[tex]\% = \frac{11}{92}[/tex]
Express as percentage
[tex]\% = \frac{11}{92}*100\%[/tex]
[tex]\% = \frac{1100}{92}\%[/tex]
[tex]\% = 11.96\%[/tex]
How do you solve a system of linear equations by graphing?
Answers
9514 1404 393
Explanation:
This is a self-answering question: you solve it by graphing the equations.
The solution is where the lines intersect. The point of intersection of the lines is the point that satisfies all the equations for the lines, hence is a solution to the system. If they do not intersect, there are no solutions. If the lines are coincident, there are an infinite number of solutions.
__
The equations can be graphed by any of a number of methods. (My favorite is to let a graphing calculator do it.) The method of choice depends on the coefficients and the form the equations are given in. Methods of graphing are a topic for a more lengthy discussion.
Find the area of the figure shown below. Use 3.14 for π. Use the formula π x r^2 to find the area of a full circle.
A)32.84 in
B)38.13 in
C) None of these answers
D)62.13 in
E)161.04 in
Answers
Answer:
c
Step-by-step explanation:
none of the answers are correct. The area of the figure is 51.53 in^2 and none of the answers are 51.53 in^2, therefore it is c.
Answer:
D. 62.13 in²
Step-by-step explanation:
the area = (8×6)+(½×3.14×3²)
= 48+14.13
= 62.13
what is equivalent to 7w +7w
Answers
Answer:
14w
Step-by-step explanation:
Hope this helps
(a)
There are 3 liters of orange juice at a school party. 10 students want to drink all of the orange juice, and they all want to get exactly the same amount. How much orange juice can each get?
Answers
Answer: 0.3
Step-by-step explanation:
What is my answer if I Add
-9+84+(-2)
Answers
Answer:
73
Step-by-step explanation:
-9+84+(-2) =
-9+82 =
= 73
Hope this helps
2x+5y=20 y=-0.4x-1 i really need help over here
Answers
Answer:
x=6.25 and y=1.5
Step-by-step explanation:
Given equation
2x+5y=20
y=0.4x-1
Putting the value of y in above equation
2x+5(0.4x-1)=20
2x+2x-5=20
4x-5=20
4x=20+5
4x=25
x=6.25
Now,
y=0.4x-1( Given)
Putting the value of x=6.25 in above equation y
y=0.4(6.25)-1
y=2.5-1
y=1.5
PLS HELP TYSMMMM <33333333333333333333333333
Answers
Explanation:
Use order of operations PEMDAS to check:
54 ÷ (6 - 3) x 2
= 54 ÷ 3 x 2
= 18 x 2
= 36
Please say if im correct
If im correct, mark me brainliest tysm!
Have a nice day
-SpaceMarsh
Answer:
dvide 54 by 6 then the answer you get subrtact it by 3 then the answer you get multiply iy by 2 then thats will be your answer
Step-by-step explanation:
remember always use PEMDAS always add or subract wich ever comes first and if theres none of that then do Multiply or devide wich ever comes first ( btw your answer is ( 3 )
An English teacher needs to pick 4 books to put on his reading list for the next school year. He has narrowed down his choices to 8 novels and 6 plays.
a. How many different ways can he choose the books to put on the list if he wants to include at least two plays?
b. Find the standard deviation.
Answers
Answer:
A) 3 ways
B) sorry don't know.
Step-by-step explanation:
2 P and 2 N
3P and 1 N
4P
So 3 ways.
3.4 0.8 0.6 find the volume of the rectangular prism in cubic feet
Answers
Given:
Consider the dimensions of the rectangular prism are 3.4 ft by 0.8 ft by 0.6 ft.
To find:
The volume of rectangular prism.
Solution:
The volume of a cuboid or rectangular prism is:
[tex]V=l\times b\times h[/tex]
Where, l is length, b is breadth and h is height of the prism.
The dimensions of the rectangular prism are 3.4 ft by 0.8 ft by 0.6 ft. So, the volume of the prism is:
[tex]V=3.4\times 0.8\times 0.6[/tex]
[tex]V=1.632[/tex]
Therefore, the volume of the rectangular prism is 1.632 cubic feet .
Suppose Duarte is one of the ten cities in the air pollution survey. We found that the number of manufacturing enterprises employing 20 or more workers in Duarte is 200, and the annual mean concentration of sulfur dioxide in Duarte is 18 micrograms per cubic meter. What is the residual for the city of Duarte
Answers
Kindly check complete question in the attached picture below.
Answer:
2.2236
Step-by-step explanation:
From the R output given, we can obtain the linear regression model in the form ;
y = bx + c
Intercept, c = 9.4764
Slope, b = 0.0315
x = number of manufacturing enterprise employing 20 or more workers
y = annual mean concentration of Sulphur dioxide
Hence, The regression equation model as obtained from the R output is :
y = 0.0315x + 9.4764
For the city of Duarte;
x = 200
Actual annual mean concentration of Sulphur dioxide is 18 micrograms per cubic meter.
Residual = Actual value - predicted value
Prediction using the regression equation to obtain the predicted annual mean concentration ;
The predicted y value, when x = 200
y = 0.0315(200) + 9.4764
y = 15.7764
The residual, if actual annual concentration = 18
Y residual = 18 - 15.7764 = 2.2236
Find the volume in the shape
Answers
Answer:
1205.76 m^3
Step-by-step explanation:
given:
radius = 8m
height = 18 m
volume of a cone = πr2h/3
=3.14 * (8)^2 * 18/3
=3.14 *64 *18/3
=3617.28/3
=1205.76 m^3
Please help me out thank you!
Answers
Answer:
Step-by-step explanation:
the number 3.14063 written correct to 3 decimal places is
Answers
Answer:
3.141
Step-by-step explanation:
3 decimals is .xxx, and you round the last digit up, so it becomes 3.141
Answer:
3.141
Step-by-step explanation:
since the forth number behind the decimal place is bigger than 5 we round up the third number.
I hope this helps in anyway.
a number cube numbered 1 to 6 and a coin is tossed at the same time. How many outcomes are possible? A.2 B.6 C.8 D. 12
Answers
Answer:
C 8
Step-by-step explanation:
the number cube has six sides and the coin has 2 sides
The number cube has 6 outcomes, and each of those has a heads and a tails option with it. 6x2=12
Find the median and mean of the data set below:
48,32,5, 13, 11, 22, 2
Answers
mean is 19
Answer:
the median is 13 and the mean is 13
