The dog's resultant displacement vector, representing the total distance covered in the specified direction, is approximately 9.74 meters. This was calculated by breaking down each of the dog's movements into their Cartesian components, adding these components separately, and finally applying the Pythagorean theorem to find the magnitude of the resultant vector.
Explanation:To solve this problem, we first need to calculate each displacement in the rectangular (or Cartesian) coordinate system. Let's express each move of the dog as a vector.
First, the dog walks 3.5 m southeast. In the Cartesian coordinate system, this would be represented as two components: x (horizontal) and y (vertical). The x-component is 3.5*cos(45°) = 2.475 m and the y component is -3.5*sin(45°) = -2.475 m (negative because direction is south).
Second, the dog walks 8.2 m at an angle 30 degrees north of east. That gives us an x-component of 8.2*cos(30°) = 7.1 m and a y-component of 8.2*sin(30°) = 4.1 m.
Now add up separate x- and y-components: Our cumulative x-component is 2.475 m + 7.1 m = 9.575 m. The cumulative y-component is -2.475 m + 4.1 m = 1.625 m.
The resultant vector's magnitude can be determined with the Pythagorean theorem a² + b² = c² (where 'a' and 'b' are the legs and 'c' is the resultant vector). In this case: (9.575 m)² + (1.625 m)² = c². Solve for c to get
[tex]c = \sqrt{(9.575 \, \text{m})^2 + (1.625 \, \text{m})^2} = 9.74 \, \text{m}.[/tex]
In conclusion, the magnitude of the dog's resultant vector is approximately 9.74 m.
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Please Help me!!
(√16)^2 in simplest form
Answer:
16
Step-by-step explanation:
square root of 16 is 4, and 4^2 = 16
Answer:
16
Step-by-step explanation:
The square cancels out the square root.
A wave has a frequency of 1000 Hz and a wavelength of 0.33 m. What is the
speed of the wave? Use the equation v=fxa.
O
A. 330 m/s
O
B. 590 m/s
O
C. 0.017 m/s
O
D. 0.0030 m/s
SUBMIT
Answer: A. 330 m/s
Just took a test on it
Answer: A
Step-by-step explanation:
Can anyone help me ASAP please!!!
ILL GIVE BRAINLIEST IM ON A TIME CRUNCH PLEASE HELP!!!!! What is the solution to the system of equations below? y = negative three-fourths x + 3 and y = –12
(20, –12)
(12, –12)
(–6, –12)
(–12, 12)
Answer:
The system of equations as described:
y = (-3/4)x + 3
y = -12
Combining two equations, we have:
=> -12 = (-3/4)x + 3
=> -15 = (-3/4)x
=> x = -15 x (-4/3) = 20
=> Solution is (20, -12)
=> Option A is correct.
Hope this helps!
:)
Step By Step:
The equations given to us are:
y = (-3/4)x + 3
y = -12
Now that we have y we can change that to -12
-12 = (-3/4)x + 3
-15 = (-3/4)x
x = -15 x (-4/3) = 20
This would give us (20, -12)
Answer
A. (20,-12)Hope this helps
give brainliest if you please
It is $100 to rent a room at Johnny's Jumpy Party Place, and it is $7 extra per child for pizza, drink, and a party bag.
Write the equation in slope intercept form for the situation above.
A
y= 100x + 7
B
y = 7x +100
C
y = -7x + 100
D
y= 7x - 100
Answer:
B
y=7x +100
Step-by-step explanation:
$100 for one room
1 or more kids
$7 per kid
so, the answer is y= 7x + 100
hi:) if the question says that the line meets the curve , does it mean that it intersects the curve or does it touch the curve only?
Answer:
Touches only.
Step-by-step explanation:
It only touches the curve at one point. The line is a tangent to the curve and does not cross it.
If you have a ball resting on a table the table is a tangent to the curve of the ball.
The ratio of side lengths for two similar cubes is į.
Determine the ratios for each of the following. Show your work or explain how you got your answers.
a. the perimeter of one face of the smaller cube compared to the perimeter of one face of the larger
cube
b. the total surface area of the smaller cube compared to the total surface area of the larger cube
c. the volume of the smaller cube compared to the volume of the larger cube
The ratio of the perimeter of one face for the two cubes is 1/2, the ratio for the total surface area is 1/4, and the ratio for the volume is 1/8.
Explanation:The student wants to find the ratios of the perimeter of one face, the total surface area, and the volume of two similar cubes having side length ratio of 1/2.
Perimeter of one face: Since each face of a cube is a square, the perimeter is 4 times the side length. As the ratio of side lengths is 1/2, the ratio of the perimeters would also be 1/2. This is because perimeter is a one-dimensional measure, therefore the ratio stays proportional to the side length.Total Surface Area: The total surface area of a cube is 6 times the area of one face (a square). Since the area is a two-dimensional measure, it's proportional to the square of the side length ratio, hence the ratio of the surface areas of two similar cubes would be (1/2)² = 1/4.Volume: The volume of a cube is the cube of the side length. Since the volume is a three-dimensional measure, it is proportional to the cube of the side length ratio, so the ratio of the volumes of two similar cubes would be (1/2)³ = 1/8.Learn more about Ratio of Similar Cubes here:
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please help!!!!!!!!!!
Answer:
Step-by-step explanation:
A bee flaps its wings about 82,800 times an hour, and a hummingbird flaps its wings about 28,800 times an hour.
About how many times faster does a bee flap its wings than a hummingbird?
Estimate using a single digit times a power of 10.
Answer: About 2.875 times more than a hummingbird
Step-by-step explanation: The way you can solve this problem is just by dividing 82,800 by 28,800. If you want to check your work multiply 28,800 and 2.875.
A bee flaps its wings approximately 3 times faster than a hummingbird.
Explanation:Bee: 82,800 times/hour ≈ 8.3 × 10^4 times/hour
Hummingbird: 28,800 times/hour ≈ 2.9 × 10^4 times/hour
Now, let's compare the two estimates:
8.3 × 10^4 (bee) is approximately 3 times faster than 2.9 × 10^4 (hummingbird).
So, a bee flaps its wings about 3 times faster than a hummingbird.
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PLS ANSWER!!!!!! I WILL GIVE BRAINLIEST TO WHOEVER ANSWERS FIRST!!!!
If you know the area and the base of a triangle, how can you find the height? Use the drop‐down menus to explain your answer.
Answer:
area = base × height
substitute the value for the area and base and solve.
height = area ÷ base
Which graph represents the equation y = -1/2x - 3?
A)
B)
C)
D)
Which of the following are like radicals? Check all of the boxes that apply
Answer:
A B D F
Step-by-step explanation:
just did it
4.Is it sometimes, always, or never true that, if A and B both have dimensions n x n , AB=BA ? Explain.
Answer: Is true sometimes.
Step-by-step explanation:
I guess that here we have two matrices, A and B, that are nxn.
We can see that if those matrices can conmutate, then we can try it with some simple matrices.
[tex]A = \left[\begin{array}{ccc}1&0\\0&-1\end{array}\right] . B = \left[\begin{array}{ccc}2&0\\1&1\end{array}\right][/tex]
Here, we would have that:
[tex]AB = \left[\begin{array}{ccc}2&0\\-1&-1\end{array}\right][/tex]
[tex]BA = \left[\begin{array}{ccc}2&0\\1&-1\end{array}\right][/tex]
You can see that AB and BA are different, then the statement is not always true.
But it is true sometimes, if A or B are the identiti, then I*A = A*I, in this case would be true.
It is also true if A and B are diagonal matrices, let's prove it:
[tex]A = \left[\begin{array}{ccc}a&0\\0&b\end{array}\right] , B = \left[\begin{array}{ccc}c&0\\0&d\end{array}\right][/tex]
[tex]AB = \left[\begin{array}{ccc}ac&0\\0&bd\end{array}\right] = BA[/tex]
Which expression is equivalent to 75x – 25x.
Answer:
C) 50x
D) x(75 - 25)
Explanation:
Use distribution to simplify:
x · 75 = 75x
x . 25 = 25x
75x - 25x
75x - 25x = 50x
Answer:
C and D
Step-by-step explanation:
75x - 25x
75 - 25 = 50
Write in terms of x
50x
Find the options that match this answer
a: 50 (not always equal to 50x)
b: 100 (not always equal to 50x)
c: 50x (always equal to 50x)
d: x ( 75 - 25 ) = x ( 50) = 50x (always equal to 50x)
C and D are equivalent to the answer, 50x
Hope this helps :)
a 60%
b 40%
c 38%
d 5%
Answer:
A
Step-by-step explanation:
wednesday thursday and friday amount to 60%
answer these questions and i’ll give 20 points and brainliest answer!!
Answer:
3. 1/2 4. 13/20
Step-by-step explanation:
Those are the only one I know, sorry :/
What is the solution of the system of equations 2x - 5y = 11 and -2x + 3y = -9?
Answer:
x= 3, y= -1
Step-by-step explanation:
Let's solve your system by substitution.
2x−5y=11 and −2x+3y=−9
Solve x in 2x-5y=11
2x-5y=11 (add 5y to both sides)
2x = 5y + 11 (divide 2 by both sides)
x=5/2y + 11/2
substitute 5/2y+11/2 for x in -2x+3y=-9
-2x+3y=9
-2 (5/2y+11/2)+3y=-9
-2y-11=-9 (simplify both sides)
-2y-11=-9 (add 11 to both sides)
-2y=2 (divide both sides by -2)
y=-1
substitute your y (-1) in x = 5/2y + 11/2
x = 5/2y + 11/2
x=5/2(-1)+11/2
x=3
therefore, y= -1 and x = 3
Convert 12/5 to a decimal using long divsion.
Answer:
2.4
Step-by-step explanation:
Answer:
To convert to a decimal, divide numerator by denominator.
To convert the decimal to a percentage multiply by
100
%
Explanation:
5
12
=
0.416666
...
...
.
0.41666
...
.
.
×
100
%
=
41.66666
%
...
.
.
Rounding off to nearest percent gives
42
%
Step-by-step explanation:
Which of these is the best definition of an ellipse?
A. The set of all points in a plane that are a certain distance from a
single point
B. The set of all points in a plane for which the difference between
the distances to two fixed points equals a certain constant
C. The set of all points in a plane for which the sum of the distances
to two fixed points equals a certain constant
D. The set of all points in a plane that are equidistant from a single
point and a line
Answer:
C. The set of all points in a plane for which the sum of the distances
to two fixed points equals a certain constant
C. The set of all points in a plane for which the sum of the distances
to two fixed points equals a certain constant is the best definition.
What is in an ellipse?An ellipse is a curve formed by a plane, that intersects a cone at an angle with respect to the base. It is a curve surrounded by two focal points. Ellipse is a locus of points, the sum of whose distances from two foci is constant.
What is an ellipse shape?An ellipse is a circle that has been stretched in one direction, to give it the shape of an ova
What is an ellipse example?An ellipse has an eccentricity less than one, and it represents the locus of points, the sum of whose distances from the two foci of the ellipse is a constant value. A simple example of the ellipse in our daily life is the shape of an egg in a two-dimensional form and the running tracking in a sports stadium.
In mathematics, an ellipse is a plane curve surrounding two focal points, such that for all points on the curve, the sum of the two distances to the focal points is a constant. As such, it generalizes a circle, which is the special type of ellipse in which the two focal points are the same. The elongation of an ellipse is measured by its eccentricity
An ellipse has a simple algebraic solution for its area, but only approximations for its perimeter (also known as circumference), for which integration is required to obtain an exact solution.
what is the general formula of ellipse ?The standard equation for an ellipse, x 2 / a 2 + y2 / b 2 = 1, represents an ellipse centered at the origin and with axes lying along the coordinate axes. In general, an ellipse may be centered at any point, or have axes not parallel to the coordinate axes.
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How many natural numbers are there between 1 and v? Pls explain how you got that!
Answer:
you need to the prime number to get the sum for the distance between 1 and v.
Step-by-step explanation:
Natural numbers are what you use when you are counting one to one objects. You may be counting pennies or buttons or cookies.
If you want to find the numbers between the two you will need an expression to consolidate your question as an example 3r, 6y, 2by in order to find the Natural number between these three questions you need to use equations such as 3r*2by+6y therefore would be 6br + 2y.
A Prime number is a natural number of a particular kind . Any natural number is equal to 1 times itself.
Which cylinders have the same volume as the cylinder below? Check all that apply. A cylinder with height of 32 meters and diameter of 20 meters.
A cylinder with height of 16 meters and diameter of 40 meters.
A cylinder with height of 64 centimeters and diameter of 5 meters.
A cylinder with height of 8 meters and diameter of 40 meters.
A cylinder with height of 64 centimeters and diameter of 10 meters.
A cylinder with height of 20 meters and diameter of 32 meters.
A cylinder with height of 128 meters and diameter of 10 meters.
Upon calculating the volume of the given cylinder and comparing it with each option, it is determined that none of the provided cylinders have the same volume as the cylinder with a height of 32 meters and a diameter of 20 meters.
Explanation:The question is asking which cylinders have the same volume as a cylinder with a height of 32 meters and a diameter of 20 meters. To find this out, we first calculate the volume of the given cylinder. The formula for the volume of a cylinder is[tex]V = \(\pi r^2h\)[/tex], where V is the volume, [tex]\(r\) i[/tex]s the radius of the base, and h is the height of the cylinder. In this case, the radius (half of the diameter) is 10 meters, so the volume is:
[tex]V = \(\pi (10)^2 \times 32\) = 320\(\pi\) cubic meters.[/tex]
Now, let's check each option:
A cylinder with height of 16 meters and diameter of 40 meters has a volume of 16[tex]\(\pi (20)^2\) = 6400\(\pi\)[/tex] cubic meters, which is not equal.A cylinder with height of 64 centimeters and diameter of 5 meters is not comparable without conversion and does not match.A cylinder with height of 8 meters and diameter of 40 meters has a volume of[tex]8\(\pi (20)^2\) = 3200\(\pi\)[/tex]cubic meters, which is not equal.A cylinder with height of 64 centimeters and diameter of 10 meters is not comparable without conversion and does not match.A cylinder with height of 20 meters and diameter of 32 meters has a volume of [tex]20\(\pi (16)^2\) = 5120\(\pi\)[/tex]cubic meters, which is not equal.A cylinder with height of 128 meters and diameter of 10 meters has a volume of [tex]128\(\pi (5)^2\) = 3200\(\pi\)[/tex] cubic meters, which is not equal.Therefore, none of the provided options have the same volume as the given cylinder.
The cylinders with heights and diameters of 16 meters and 40 meters, and 128 meters and 10 meters, respectively, have the same volume as the given cylinder.
To find cylinders with the same volume as the given cylinder (height = 32m, diameter = 20m), we calculate its volume and compare it with the volumes of the listed cylinders. Cylinders with heights and diameters of 16 meters and 40 meters, and 128 meters and 10 meters, have the same volume as the given cylinder.
The question involves finding which cylinders have the same volume as a cylinder with a height of 32 meters and a diameter of 20 meters. To solve this, we first calculate the volume of the given cylinder using the formula for the volume of a cylinder, V = πr²h, where r is the radius (half of the diameter) and h is the height.
The volume of the given cylinder is V = π(10²)(32) = 320π cubic meters. We then apply the same formula to each of the listed cylinders, converting dimensions to the same units where necessary, to identify which ones have the same volume.
A cylinder with height of 16 meters and diameter of 40 meters has a volume of 320π cubic meters, which matches.A cylinder with height of 8 meters and diameter of 40 meters does not match because its volume is 160π cubic meters.A cylinder with height of 128 meters and diameter of 10 meters also has a volume of 320π cubic meters, which matches.Therefore, the cylinders with heights and diameters of 16 meters and 40 meters, and 128 meters and 10 meters, respectively, have the same volume as the given cylinder.
50 POINTS!
The function h(x) = x2 + 6x + 7 represents a parabola.
Part A: Rewrite the function in vertex form by completing the square. Show your work.
Part B: Determine the vertex and indicate whether it is a maximum or a minimum on the graph. How do you know?
Part C: Determine the axis of symmetry for h(x).
Answer:
A. (x + 3)² - 2
B. (-3,-2); min
C. x = -3
Step-by-step explanation:
x² + 6x + 7
x² + 2(x)(3) + 3² - 3² + 7
x² + 2(x)(3) + 3² - 9 + 7
(x + 3)² - 2
Vertex: (-3 , -2)
It's a concave up, so minimum
Line of symmetry is x = h
x = -3
The temperature in Chicago is dropping at a rate of 1 degree every 4 hours when it was 10 degrees outside. The temperature in Pittsburgh was increasing at a rate of 3 degrees every 4 hours when it was 2 degrees outside. How long will it take the two cities to reach the same temperature? What is the temperature at that time?
Answer:
Chicago after 8 hrs it dropped to 8 degrees and at pittsburgh after 8hrs passed it reached to 8degrees outside
so after 8hrs the cities reached the same temperature which is 8degrees
Step-by-step explanation:
10-1=9 then 9-1=8
1= each degree that dropped every 4 hours
A model containing 4 rows of 5 squares.
Which expressions represent this model?
Check all that apply.
4 + 5
4(5)
20
5(4)
5(5)
I'm sorry that I don't have a picture
Answer: 4(5) 20 5(4)
Step-by-step explanation: PERIOD
Answer:
B: 4(5)
C: 20
D: 5(4)
Mark brainliest pls
Step-by-step explanation:
I got it correct on edge
Can anyone help me please
Answer:
7. 12*(2+2^3) 8. 7^2+(1-5)*3
Find the area of the following rectangle.
length = 15 cm
width = 19.5 cm.
Area = ? cm2
34.5
69
146.25
292.5
Look at the attached picture ⤴
Hope it will help u....:)
Twenty eight slips of paper are numbered 1 through 28 and are distributed among a group of people. A random number generator is used to select a single number between 1 and 28, inclusively
A fair decision is made using this process
How many people could be in this group?
A. 3
B. 6
C. 7
D. 12
Answer:
Option C is the correct answer.
Step-by-step explanation:
Since a random number generator is used to select a single number between 1 and 28, inclusively;
For a fair decision to be made during the process, the number of persons in the set must be a divisor of 28.
Let's list the divisors of 28:
The divisors of 28 are {1, 2, 4, 7, 14, 28}
The only option that contains one of the divisors is option C which is 7.
Divide −875 by −25.
Answer:
35
Step-by-step explanation:
a negative and a negative equals a positive
Solve the system of equations.
3x + 4y = -23
x = 3y + 1
y =
X=
Answer:
(-5, -2)
Step-by-step explanation:
3x+4y=-23
x=3y+1
since we have what x is, we need to subsitute
3( 3y+1) + 4y= -23
no we need to multiply the number inside the parenthesis by 3
9y + 3 + 4y= -23
combine like terms ( add the numbers or variables that look alike)
9y+4y is 13y
13y+3= -23
since we need to get the y alone we need to subtract 3 on both sides since its the opposite of adding
13y+3-3=-23-3
13y= -26
now we divide 13 on both sides to get Y alone
13y/13= -26/13
y= -2
now since we have y we need to substitute it to find x
x= 3y+1
x= 3( -2) +1
now we mutliply 3 with -2
x= -6 +1
x=-5
those are ur answers
y= -2
x= -5
hope this helped:D
Answer:
x = -5
y = -2
Step-by-step explanation:
The measure of a central angle is 3x + 18 and the measure of its arc is 147 which equation can you use to find the value of x
3x + 18 = 147
3x = 129
x = 43
Answer:
3x + 18 = 147
Step-by-step explanation: