a 0.311 kg tennis racket moving 30.3 m/s east makes an elastic collision with a 0.0570 kg ball moving 19.2 m/s west. find the velocity of the tennis ball after the collision.
Answer: 146.12 m/s (to the right)
Step-by-step explanation:
The Conservation of Linear Momentum principle states that the initial momentum [tex]p_{i}[/tex] (before the elastic collision) must be equal to the final momentum [tex]p_{f}[/tex] (after the elastic collision):
[tex]p_{i}=p_{f}[/tex] (1)
Being:
[tex]p_{i}=m_{r}V_{r} + m_{b}V_{b}[/tex]
[tex]p_{f}=m_{r}U_{r} + m_{b}U_{b}[/tex]
Where:
[tex]m_{r}=0.311 kg[/tex] is the mass of the racket
[tex]V_{r}=30.3 m/s[/tex] is the velocity of the racket before the collision
[tex]m_{b}=0.057 kg[/tex] is the mass of the ball
[tex]V_{b}=-19.2 m/s[/tex] is the velocity of the ball before the collision
[tex]U_{r}=0 m/s[/tex] is the velocity of the racket after the collision (assuming it is at rest after hitting the ball)
[tex]U_{b}[/tex] is the velocity of the ball the collision
So, we have the following:
[tex]m_{r}V_{r} + m_{b}V_{b}=m_{r}U_{r} + m_{b}U_{b}[/tex] (2)
Finding [tex]U_{b}[/tex]:
[tex]U_{b}=\frac{m_{r}V_{r} + m_{b}V_{b}}{m_{b}}[/tex] (3)
[tex]U_{b}=\frac{(0.311 kg)(30.3 m/s) + (0.057 kg)(-19.2 m/s)}{0.057 kg}[/tex] (4)
Finally:
[tex]U_{b}=146.12 m/s[/tex] This is the velocity of the ball after the collision
Answer:
38m/s
Step-by-step explanation:
A bag contains 6 red marbles, 6 white marbles, and 4 blue marbles. Find P(red or blue).
A. 2/3
B. 3/2
C. 5/8
D. 3/4
Answer:
I think its B. because if you put 6/4and reduce it it would be 3/2
Step-by-step explanation:
Answer:
C. 5/8
Step-by-step explanation:
P(red) = 6/16
p(blue) = 4/16
p(red or blue) = P(red) + p(blue) = (6+4)/16 = 10/16 = 5/8
17)
- What is the slope of the line defined by the equation y = 2x + 7?
A)2/7
B) 2
C)7/2
D)7
Answer:
The slope is 2
Step-by-step explanation:
y = 2x + 7
Comparing with y = mx + c
Where m is the slope = 2
Answer:
B
Step-by-step explanation:
The equation of line is y=2x+7
Comparing it with the standard equation y=mx+c
Where m is the slope and c is the y-intercept
Hence we get
Slope,m =2
21. Three vertices of DEFG are D(2,3),E(-5,2),G(6,6). Find the coordinates of F.
The calculated coordinates of the point F is (-1, 5)
How to determine the coordinates of F
From the question, we have the following parameters that can be used in our computation:
D(2,3),E(-5,2),G(6,6)
We have that
The quadrilateral DEFG is a parallelogram
This means that the opposite sides have equal slopes
i.e.
Slope of DE = Slope of FG
Using slope formula, we have
(3 - 2)/(2 + 5) = (y - 6)/(x - 6)
This gives
1/7 = (y - 6)/(x - 6)
Cross multiply
x - 6 = 7y - 42
x = 7y - 36
Set y = 5
So, we have
x = 7 * 5 - 36
x = -1
So, we have
(x, y) = (-1, 5)
Hence, the coordinates of the point F is (-1, 5)
Question
Consider the parallogram DEFG with three vertices D(2,3),E(-5,2),G(6,6). Find the coordinates of F.
Final answer:
To find the coordinates of vertex F in the parallelogram DEFG with given vertices D(2,3), E(-5,2), and G(6,6), we can use vector subtraction to deduce that the coordinates of F are (-1, 5).
Explanation:
The question requires us to find the coordinates of vertex F of the quadrilateral DEFG given that we have the coordinates of vertices D(2,3), E(-5,2), and G(6,6). Assuming that DEFG is a parallelogram (as the question implies a symmetry-based approach though it doesn't specify), we can find F using the properties of parallelograms, which dictate that opposite sides are equal and parallel. The vector from D to E is ∂D = (-5 - 2, 2 - 3) = (-7, -1), and the vector from G to F (let's call it F's coordinates (x, y)) would be equivalent, as they are opposite sides. So, G + ∂D = F. Substituting G's values, we get (6 - 7, 6 -1), which simplifies to (-1, 5). Thus, the coordinates of F are (-1, 5).
Suppose you know that ∠S and ∠Y are complementary and that m∠S = 5(m∠Y) − 180°. Find m∠Y.
Answer:
45°
Step-by-step explanation:
We know ∠ Y +∠ S = 90
and ∠ S= 5 ( ∠ Y)-180 so
leave S alone for both
90- ∠Y = 5 ( ∠Y) -180
270 = 6( ∠Y )
45= ∠ Y
∠S = 5( 45) -180
=225-180
=45
Final answer:
The measure of angle Y (m∠Y) is 45°, following the equation derived from the facts that angles S and Y are complementary and m∠S equals 5 times m∠Y minus 180°.
Explanation:
If ∠S and ∠Y are complementary angles, then the sum of their measures is 90°. According to the given information, m∠S = 5(m∠Y) − 180°. Since m∠S + m∠Y = 90°, we can set up the equation:
5(m∠Y) − 180° + m∠Y = 90°
Combining like terms to solve for m∠Y:
6(m∠Y) = 90° + 180°
6(m∠Y) = 270°
m∠Y = 270° / 6
m∠Y = 45°
The measure of angle Y, m∠Y, is 45°.
Choose the system of equations which matches the following graph:
a- x + 2y = −10
3x − y = 12
b- x − 2y = −10
3x − y = 12
c- x + 2y = −10
3x + y = 12
d- x − 2y = −10
3x + y = 12
Answer:
Option a
- x + 2y = −10
3x − y = 12
Step-by-step explanation:
step 1
Find the equation of the line with negative slope
we know that
The line with negative slope has a y-intercept at (0,-5) and passes through the point (2,-6)
Find the slope
[tex]m=(-6+5)/(2-0)=-\frac{1}{2}[/tex]
The equation in slope intercept form is
[tex]y=-\frac{1}{2}x-5[/tex]
Convert to standard form
Multiply by 2 both sides
[tex]2y=-x-10\\x+2y=-10[/tex]
step 2
Find the equation of the line with positive slope
The line with positive slope has a x-intercept at (4,0) and passes through the point (2,-6)
Find the slope
[tex]m=(-6-0)/(2-4)=3[/tex]
The equation of the line in point slope form is equal to
[tex]y-y1=m(x-x1)[/tex]
we have
[tex]m=3\\point\ (4,0)[/tex]
substitute
[tex]y-0=3(x-4)[/tex]
Convert to standard form
[tex]y=3x-12\\3x-y=12[/tex]
therefore
The system of equations is
- x + 2y = −10
3x − y = 12
if 8 and 15 are sides to a right triangle, whats the missing side?
Answer:
17
Step-by-step explanation:
a[2]+b[2]=c[2]
8*8+15*15=hypotenuse.
64+225=289
[tex]\sqrt{x} 289[/tex]
hypotenuse=17
The Atlanta Traffic Commission needs to know how much space the Ferris Wheel takes up. What is the AREA formula for a circle? Show your work to find the AREA of the Ferris Wheel. Don't forget to add your square units! pls helppppppp
Answer:
The Area of the Ferris wheel is 31400 Square feet
Step-by-step explanation:
The AREA formula for a circle:
The Area formula for the circle is [tex]\pi r^2[/tex]
where
r is the radius of the circle
The area of the Ferris Wheel:
The Height of the Ferris wheel = 200 foot
Here height of the Ferris wheel is the diameter
So the Diameter = 200
Then Radius =[tex]\frac{200}{2}[/tex] = 100 foot
Now the area of the Ferris wheel is
=> [tex]\pi (100)^2[/tex]
=> [tex]\pi \times 10000[/tex]
=> 31400 square feet
does anyone know how to help me with the letters in math, i dont understand it, and i need help, someone please? if you can can you tell me in step by step?
Answer:
Step-by-step explanation:
Letters are variables and those variable can store a number
Ex: x=5 y=2
evaluate : 3x+2y
we know that x is 5, so we know that 3x would be 15
we know that y is 2, so we know that 2x would be 4
then it says to add 3x and 2y, we would add 15 and 4 to get 19
(This is a very simple example, when you get older, the expression would be much more confusing.
Guys please help!! I need the answer as fast as possible.
Answer:
It is NOT possible for a solution to be both x<9 and x>9
It IS possible for a solution to be both x≤9 and x≥9
Step-by-step explanation:
Because for x<9 and x>9 the GREATER than symbol means it less than 9 and cannot be 9 or it is greater than 9 but cannot be 9.
With x≤9 and x≥9 the greater than or EQUAL sign makes a big difference. Because x≥9 may be the actual solution but since it is possible to be equal to 9 so can x≤9.
(Sorry if this seemed very confusing to explain).
What do you call the tending of rabbits
The tending of rabbits, known as rabbit farming or rabbit husbandry, involves providing adequate resources for the rabbits to mature and reproduce. This could be for the purposes of obtaining meat, fur, or wool from the rabbits. It's also important to monitor for signs of infection to prevent communicable diseases.
Explanation:The tending or caring of rabbits is commonly referred to as rabbit husbandry or rabbit farming. This involves the raising and breeding of rabbits, often for their meat, fur, or sometimes, for their wool in the case of certain breeds like the Angora Rabbit.
Aspects of rabbit husbandry can include providing an adequate food source, healthcare, and a suitable living environment. It is imperative to watch out for any signs of infection, as some diseases can be transmitted from the rabbits to humans through eating or handling infected rabbits. Some such infections could be vector-borne, passing through ticks or flies, or potentially through aerosols in a laboratory setting.
These caretaking measures help ensure that a young rabbit can develop into a healthy adult rabbit, capable of reproducing or providing the intended resource, whether it be meat, fur, or wool.
Learn more about Rabbit Farming here:https://brainly.com/question/34650027
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What weighs more 4 pounds of books or 60 ounces of pebbles
Answer: 60 ounces of pebbles
Factor the following polynomial by grouping.
xy + 2y2 + 3x + 6y
OA) (x+y)(2y + 3)
OB) (x+2y)(y + 3)
OC) (x+3y) (y + 2)
OD) (x+y)(3y + 2)
Option B
The factored form by grouping is:
[tex]xy+2y^2+3x+6y = (x+2y)(y+3)[/tex]
Solution:
Given that we have to factor the given polynomial by grouping
Given polynomial is:
[tex]xy+2y^2+3x+6y[/tex]
Factoring by grouping means that you will group terms with common factors before factoring.
This is done by grouping a pair of terms. Then factor each pair of two terms
In the given polynomial, group the terms that has "x" as common and group the terms that has "y" as common
[tex](xy+3x)+(2y^2+6y)[/tex]
Factor out "x" from first group and factor out "2y" from second group
[tex]x(3+y)+2y(y+3)[/tex]
Factor out y + 3
[tex]x(3+y)+2y(y+3) = (x+2y)(y+3)[/tex]
Thus the factored form by grouping is:
[tex]xy+2y^2+3x+6y = (x+2y)(y+3)[/tex]
10 4/5 - 2 1/5
I am having trouble finding this answer please help
Answer:
8 3/5
Step-by-step explanation:
subtract the whole numbers first and then the fractions. you have 10 4/5-2 1/5. subtract the whole numbers and you have 8(put that off to the side). then do 4/5-1/5. 4-1=3 and the denominators stay the same so you have 3/5. you don’t need to simplify so your final answer is 8 3/5.
Answer:
43 / 5 or 8 3/5
Step-by-step explanation:
(sum of interior angles = 10 (n-2) where n is the number of sides of the polygon)
1. what is the sum of the interior angles of a pentagon?
2. if the sum of the interior angles of a polygon equals 1080, then determine the sides of the polygon.
3. what is a polygon called if the sim of its interior angles equals 6840?
4. what is the sum of the interior angles of an octagon?
Answer:
Step-by-step explanation:
1) pentagon; n= 5
Sum of interior angles = 180*(n -2) = 180* (5-2) = 180 * 3 = 540
2) Sum of interior angles of a polygon = 1080
180*(n-2) = 1080
n - 2 = 1080/180
n -2 = 6
n = 6+2
n = 8
Polygon has 8 sides
3) Sum of interior angles of a polygon = 6840
180*(n-2) = 6840
n - 2 =6840/180
n -2 = 38
n = 38 + 2
n = 40
Polygon has 40sides
4)Sum of interior angles of an octagon = 180*(n-2) = 180* (8-2) = 180 - 6 = 1080
The sum of the interior angles of the 10-sided polygon on the left is 1440 °.
The answer is : 1440
complete the steps to simplify (y^4/3•y^2/3)^-1/2. Apply the product of powers property to the expression inside the parentheses, then choose the equivalent expression.
A. (y^2)^-1/2
B. (y^8/3)^-1/2
C. (y^2/3)^-1/2
Option A
[tex]\left(y^{\frac{4}{3}} \cdot y^{\frac{2}{3}}\right)^{\frac{-1}{2}} = \left(y^{2}\right)^{\frac{-1}{2}}[/tex]
Solution:
Given expression is:
[tex]\left(y^{\frac{4}{3}} \cdot y^{\frac{2}{3}}\right)^{\frac{-1}{2}}[/tex]
Product of powers property:
The product of powers property tells us that when you multiply powers with the same base you just have to add the exponents
Which is represented as,
[tex]a^m.a^n = a^{m+n}[/tex]
Therefore, the given expression becomes,
[tex]\left(y^{\frac{4}{3}+\frac{2}{3}}\right)^{\frac{-1}{2}}[/tex]
Now add the exponents, we get
[tex]\left(y^{\frac{4+2}{3}}\right)^{\frac{-1}{2}}[/tex]
Simplify the above expression
[tex]\left(y^{\frac{6}{3}}\right)^{\frac{-1}{2}}[/tex]
Simplify the exponent of y, we get
[tex]\left(y^{2}\right)^{\frac{-1}{2}}[/tex]
Thus Option A is correct
Answer:
The answer is A
Step-by-step explanation:
Are there any lines that cannot be written in standard form? If so which ones?
Answer:
Any equation that cannot be written in standard form form in nonlinear.
Step-by-step explanation:
Considering the equation in standard form as
[tex]ax + by = c[/tex]
For example here is the sample equation [tex]3x - 2y = 4[/tex] is in standard form.
Very much every linear equation can be written in standard form.
There are certain rules that need to be followed for any lines to be in standard form, violation of which would not let certain lines to be written in standard form. These rules are:
[tex]a[/tex] or [tex]b[/tex] can be zero, but not both at the same time. [tex]a, b,[/tex] and [tex]c[/tex] are integers[tex]a\ge \:0[/tex][tex]a, b,[/tex] and [tex]c[/tex] have no common factors other than 1Any equation that cannot be written in this form in nonlinear.
Keywords: linear equation, standard form, nonlinear equation
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Find the values of x and y that satisfy both equations below.
[tex]27 ^{x - 2} = 9^{y} \\ 32 ^{y - \frac{3}{5} } = \frac{1}{8 ^{2x} } [/tex]
Answer:
The answer to your question is (4/3, -1)
Step-by-step explanation:
Convert both equations to the same base
[tex]27^{x - 2} = 9^{y}[/tex]
27 = 3 x 3 x 3 = 3³
9 = 3 x 3 = 3²
Substitution
[tex]3^{3(x - 2)} = 3^{2y}[/tex]
Simplify
3x - 6 = 2y Equation l
[tex]32^{y - 3/5} = \frac{1}{8^{2x}}[/tex]
32 = 2 x 2 x 2 x 2 x 2 = 2⁵
8 = 2 x 2 x 2 = 2³
2[tex]^{5(y - 3/5)} = 2^{-3(2x)}[/tex]
Simplify
5y - 3 = -6x Equation ll
Equal to zero both equations
3x - 2y - 6 = 0 Equation l
6x + 5y - 3 = 0 Equation ll
Solve by elimination
Multiply equation l by 5 and equation ll by 2
15x - 10y - 30 = 0
12x + 10y - 6 = 0
27x -36 = 0
Solve for x
27x = 36
x = 36 / 27
Simplify x = 4/3
Find the y value
6(4/3) + 5y - 3 = 0
8 + 5y - 3 = 0
5y = -8 + 3
5y = -5
y = -5/5
y = -1
Solution
(4/3, -1)
Katy bought a candy bar and shared it with her two sisters. She gave her youngest sister 1/4 of the candy bar. Her older sister received 1/3 of the candy bar. How much of the candy bar did Katy keep?
Answer:
5/12
Step-by-step explanation:
1/4×3/3=3/12
1/3×4/4=4/12
4/12+3/12=7/12
12/12-7/12=5/12
What is the absolute value and solution set of |x|=-4
( 2/3 a^2b^2)^2·(−3ab)^4
The answer to that problem is:
[tex]36 {a}^{8} {b}^{8} [/tex]
Hope This Helps! :)
I need help on this question ASAP
Answer:
15: 1
Step-by-step explanation:
Please see attached picture for full solution.
A parking lot with an area of 9600ft^2 has a 200ft fence built along two adjacent sides of lengths x and y. If you were asked to find the dimensions of the parking lot, what equations would you used for the perimeter and area of the parking lot?
Answer:
[tex]\left\{\begin{array}{l}x+y=200\\ \\xy=9,600\end{array}\right.[/tex]
Step-by-step explanation:
The diagram shows rectangular parking lot with sides of [tex]x[/tex] feet and [tex]y[/tex] feet.
1. The area of the rectangle is
[tex]A=Length\times Width=xy.[/tex]
If the area of the parking lot os [tex]9,600\ ft^2,[/tex] then
[tex]xy=9,600[/tex]
2. A parking lot has a [tex]200\ ft[/tex] fence built along two adjacent sides of lengths [tex]x[/tex] and [tex]y[/tex], then
[tex]x+y=200[/tex]
3. The system of two equations describing this situation is
[tex]\left\{\begin{array}{l}x+y=200\\ \\xy=9,600\end{array}\right.[/tex]
Tina and penny share 36 sweets in the ratio 1:2. How many sweets does penny get?
Answer:
24 sweets
Step-by-step explanation:
Total amount of sweets is 36
Goal to divide into 3 (1+2) and give out the sections.
36/3 = 12
Tina sweets = 12(1) = 12
Penny sweets = 12(2) = 24
12:24
1:2
Answer:
24
Step-by-step explanation:
2/3 ×36/1 3 ÷3=1 and 36÷3=12 and 12×2=24
Let f(x) = 3x -7 and g(x) = -2 - 6 find (fog) (4)
show all steps
What does y+3>5 equal
Answer:
if you're solving for inequality its y>2
2 Independent Practic
CA CC 8.EE.7, 8.EE.7b
Members of the Wide Waters Club pay
$105 per summer season, plus $9.50 each
time they rent a boat. Nonmembers must
pay $14.75 each time they rent a boat.
How many times would a member and a
non-member have to rent a boat in order
to pay the same amount?
Answer:
20
Step-by-step explanation:
Let x represent the number of rentals. Then the cost will be the same when ...
105 +9.50x = 14.75x
105 = 5.25x
105/5.25 = x = 20
Each would have to rent a boat 20 times in order to pay the same amount.
How to solve 17=x+9 what is x
Answer:
x=8
Step-by-step explanation:
17=x+9
-9 -9
8=x
Answer:
x=8
Step-by-step explanation:
17-9=8
8+9=17
3x+2=3x+2
Is this one solution, no solution, or infinite solution
Answer:
infinite solution
Step-by-step explanation:
no matter what you have for x, 3x still equals 3x, so it is infinite
The price of a pair of headphones at Store A is 3/4
the price at Store B. The price at Store A is $72.75. Find how much you save by buying the headphones at Store A.
Answer:
Step-by-step explanation:
A = 3/4B
A = 72.75
3/4B = 72.75
B = 72.75 * 4/3
B = 291/3 = 97
you would save (97 - 72.75) = $ 24.25 when buying them at store A
By calculating the original price of the headphones at Store B and subtracting the price at Store A, we find that you would save $24.25 by purchasing the headphones at Store A.
Explanation:To find out how much you save by buying the headphones at Store A, we need to determine the original price of the headphones at Store B.
Let's denote the price at Store B as P. According to the information given, the price at Store A is 3/4 of the price at Store B. We can write the following equation:
P × (3/4) = $72.75
Solving for P, we get:
P = $72.75 ÷ (3/4)
P = $72.75 ÷ 0.75
P = $97.00
Therefore, the price of the headphones at Store B is $97.00. To find the savings, subtract the price at Store A from the price at Store B:
Savings = Price at Store B - Price at Store A
Savings = $97.00 - $72.75
Savings = $24.25
By buying the headphones at Store A, you save $24.25.