Answer:
The ball makes the field goal.
The magnitude of the velocity of the ball is approximately 18.166 meters per second.
The direction of motion is -45.999º or 314.001º.
Step-by-step explanation:
According to the statement of the problem, we notice that ball experiments a parabolic motion, which is a combination of horizontal motion at constant velocity and vertical uniform accelerated motion, whose equations of motion are described below:
[tex]x = x_{o}+v_{o}\cdot t\cdot \cos \theta[/tex] (Eq. 1)
[tex]y = y_{o} + v_{o}\cdot t \cdot \sin \theta +\frac{1}{2}\cdot g\cdot t^{2}[/tex] (Eq. 2)
Where:
[tex]x_{o}[/tex], [tex]y_{o}[/tex] - Coordinates of the initial position of the ball, measured in meters.
[tex]x[/tex], [tex]y[/tex] - Coordinates of the final position of the ball, measured in meters.
[tex]\theta[/tex] - Angle of elevation, measured in sexagesimal degrees.
[tex]v_{o}[/tex] - Initial speed of the ball, measured in meters per square second.
[tex]t[/tex] - Time, measured in seconds.
If we know that [tex]x_{o} = 0\,m[/tex], [tex]y_{o} = 0\,m[/tex], [tex]v_{o} = 22\,\frac{m}{s}[/tex], [tex]\theta = 55^{\circ}[/tex], [tex]g = -9.807\,\frac{m}{s}[/tex] and [tex]x = 40\,m[/tex], the following system of equations is constructed:
[tex]40 = 12.618\cdot t[/tex] (Eq. 1b)
[tex]y = 18.021\cdot t -4.904\cdot t^{2}[/tex] (Eq. 2b)
From (Eq. 1b):
[tex]t = 3.170\,s[/tex]
And from (Eq. 2b):
[tex]y = 7.847\,m[/tex]
Therefore, the ball makes the field goal.
In addition, we can calculate the components of the velocity of the ball when it reaches the field goal post by means of these kinematic equations:
[tex]v_{x} = v_{o}\cdot \cos \theta[/tex] (Eq. 3)
[tex]v_{y} = v_{o}\cdot \cos \theta + g\cdot t[/tex] (Eq. 4)
Where:
[tex]v_{x}[/tex] - Final horizontal velocity, measured in meters per second.
[tex]v_{y}[/tex] - Final vertical velocity, measured in meters per second.
If we know that [tex]v_{o} = 22\,\frac{m}{s}[/tex], [tex]\theta = 55^{\circ}[/tex], [tex]g = -9.807\,\frac{m}{s}[/tex] and [tex]t = 3.170\,s[/tex], then the values of the velocity components are:
[tex]v_{x} = \left(22\,\frac{m}{s} \right)\cdot \cos 55^{\circ}[/tex]
[tex]v_{x} = 12.619\,\frac{m}{s}[/tex]
[tex]v_{y} = \left(22\,\frac{m}{s} \right)\cdot \sin 55^{\circ} +\left(-9.807\,\frac{m}{s^{2}} \right)\cdot (3.170\,s)[/tex]
[tex]v_{y} = -13.067\,\frac{m}{s}[/tex]
The magnitude of the final velocity of the ball is determined by Pythagorean Theorem:
[tex]v =\sqrt{v_{x}^{2}+v_{y}^{2}}[/tex] (Eq. 5)
Where [tex]v[/tex] is the magnitude of the final velocity of the ball.
If we know that [tex]v_{x} = 12.619\,\frac{m}{s}[/tex] and [tex]v_{y} = -13.067\,\frac{m}{s}[/tex], then:
[tex]v = \sqrt{\left(12.619\,\frac{m}{s} \right)^{2}+\left(-13.067\,\frac{m}{s}\right)^{2} }[/tex]
[tex]v \approx 18.166\,\frac{m}{s}[/tex]
The magnitude of the velocity of the ball is approximately 18.166 meters per second.
The direction of the final velocity is given by this trigonometrical relation:
[tex]\theta = \tan^{-1}\left(\frac{v_{y}}{v_{x}} \right)[/tex] (Eq. 6)
Where [tex]\theta[/tex] is the angle of the final velocity, measured in sexagesimal degrees.
If we know that [tex]v_{x} = 12.619\,\frac{m}{s}[/tex] and [tex]v_{y} = -13.067\,\frac{m}{s}[/tex], the direction of the ball is:
[tex]\theta = \tan^{-1}\left(\frac{-13.067\,\frac{m}{s} }{12.619\,\frac{m}{s} } \right)[/tex]
[tex]\theta = -45.999^{\circ} = 314.001^{\circ}[/tex]
The direction of motion is -45.999º or 314.001º.
Sean made $1115 during a 5 day work week. He made
$465 on Monday and the rest was split between the
other 4 days. How much money did he make on each
of the other 4 days?
Answer:
Step-by-step explanations:
I invest £2,000 at a rate of 5% compound interest. I leave the amount 5 years. How much will I have after 5 years?
Answer:
£10,000 at a rate of 5%
Answer:
£10,000
Step-by-step explanation:
£2,000x5= £10,000
1. Find the values of the
angles x, y and z.
40°
25°
z
у
Answer:
z = 40° (V. O. A)
Now find x
40 + 25 + x = 180(A. S. P)
65 + x = 180
x = 180 - 65
x = 115°
Now find y
x = y (V. O. A)
Y = 115°
So angles are
X = 115°
Y = 115°
Z = 40°
Hope this helps, have a great day, have a wonderful weekend and stay safe!
Also Happy Halloween! :) :D :3
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Answer:
Noice
plz make me brainliest uwu
Answer:
yes. I agree.
Step-by-step explanation:
7. Write a 4 digit number that is divisible by 2, 3, and 6.
Answer:the answer is 9998.
Step-by-step explanation:
The largest 4 digit number divisible by 2 . The number should be divisible by 2 or multiple of it. So the largest 4 digit number is 9999 it is not divisible by 2 so the earlier number 9998 can be considered so as it is divisible by 2. It is the answer is 9998.
Answer:
1008 is the correct answer (i think)
Step-by-step explanation:
1008/2 is 504
1008/3 is 336
1008/6 is 168
hope this helps!
Greta uses 2 ounces of pasta to make 2 5 of a serving of pasta. How many ounces of pasta are there per serving?
Answer:
5 ounces if you meant 2/5 of a serving is 2 ounces of pasta
Step-by-step explanation:
Answer:
2divided by 2/5 equals 1/5
Step-by-step explanation:
I'm not 100% positive 91%
Mathematics, 04.12.2019 23:31, datboyjulio21
For 1992 through 1994, the per capita consumption of fish and shellfish in the
u. s. increased at a rate that was approximately linear. in 1992, the per capita
consumption was 14.7 pounds, and in 1994 it was 15.1 pounds."
36. write a linear model for the per capita consumption of fish and shellfish
in the u. s. let t represent the number of years since 1992.
37. what would you expect the per capita consumption of fish and shellfish
to be in 2002?
Answer:
The answer is below
Step-by-step explanation:
A linear equation is represented by the equation y = mx + b, where m is the rate of change, b is the value of y at x = 0, y is a dependent variable and x is an independent variable.
Let t represent the number of years since 1992, and P represent the per capita consumption of fish and shellfish in the U.S.
In 1992 (t = 0), the per capita consumption was 14.7 pounds, this can be represented by (0, 14.7) while in 1994 (t = 1994-1992=2) it was 15.1 pounds this can be represented by (2, 15.1)
Using (0, 14.7) and (2, 15.1) we can get the equation of the line using:
[tex]P-P_1=\frac{P_2-P_1}{t_2-t_1}(t-t_1)\\ \\P-14.7=\frac{15.1-14-7}{2-0}(t-0)\\ \\P-14.7=0.2t\\\\P=0.2t+14.7[/tex]
In the year 2002 (t = 2002-1992 = 10), the per capita consumption of fish and shellfish is:
P = 0.2(10) + 14.7
P = 16.7 pounds
Select all the true statements. Triangle A B C where the measure of angle A is 2 x plus 1 degree, angle B is x degrees, and angle C is x plus 15 degrees. Group of answer choices From smallest to largest: ∠B, ∠C, ∠A x = 49 m∠C = 56 m∠A = 99 (4x + 16) = 180
Answer:
m∠C = 56 and (4x + 16) = 180
Step-by-step explanation:
The sum of angle in a triangle is 180, hence:
<A+<B+<C = 180
Given
<A = 2x+1
<B = x
<C = x+15
Substitute
2x+1+x+x+15 = 180
collect like terms:
2x+x+x+1+15 = 180
4x+16 = 180
4x = 180-16
4x = 164
Divide both sides by 4
4x/4 = 164/4
x = 41°
Since <A = 2x+1
<A = 2(41)+1
<A = 82+1
<A = 83
<B = x = 41
<C = x+15
<C = 41+15
<C = 56
Based on the calculation above, the true statements are:
m∠C = 56 and (4x + 16) = 180
A line has a slope of -Ź and passes through the point (-3, 8). What is the equation of the line?
y=-3x+6
y=-{x+8
o y = 6x - 2 / 2
y = 8x-
Step-by-step explanation:
y-b=m(x-a)
y-8=-Z(x--3)
y-8=-Z(x+8)
The aspect ratio of a television or movie
screen is the ratio of the width of the screen
to its height. A high-definition television
has an aspect ratio of 16:9. The movie
Star Wars was filmed in cinemascope,
which has an aspect ratio of 2.35:1. Are
these aspect ratios equivalent? Explain.
Hellppp
Answer:
The aspect ratios of both are not same
Step-by-step explanation:
Here, we want to check if the given ratios are equivalent.
So what we want to do here is to check if 16/9 is equivalent to 2.35:1
Mathematically; 16/9 is same as 1.78/1
We can see that 1.78/1 is not same as 2.35/1
Hence, the aspect ratios of both are not the same thing
The length of cell A is
3×10−5
m. The length of cell B is
0.000001
m. What is the ratio of cell A's length to cell B's length?
Answer:
b´s length is 10
Step-by-step explanation:
A rectangles width is 13 more than its length. If the perimeter is 82 feet what is the length and width.
Answer:
Step-by-step explanation:
Lenght should be the greater here. I am considering your question however.
Let length side is 'x'.
The width side is 'x +13'
Perimeter of a rectangle : 2 ×( length + width)
given that perimeter is 82
2 × ( x + x + 13) = 82
2 × ( 2x + 13) =82
4x + 26 = 82
2x = 56
x = 28 cm
length is 28
width is 41
Complete the process of solving the equation. Fill in all missing terms and select all missing descriptions. Simplify any fractions. 11a+2=9a+4 2a+2=4 Add 9a to both sides Subtract 9a from both sides Multiply both sides by 9a Divide both sides by 9a Apply the distributive property 2a= Subtract 2 from both sides a= Divide both sides by 2
Answer:
11a + 2 = 9a + 4 ( Subtract 9a from both sides)
11a - 9a + 2 = 9a - 9a + 4
2a + 2 = 4 (Subtract 2 from both sides)
2a + 2 - 2 = 4 - 2
2a = 2 (Divide both sides by 2)
2a/2 = 2/2
a = 1
Step-by-step explanation:
Simplify any fractions.
11a + 2 = 9a + 4
2a + 2= 4
We simplify as shown below
11a + 2 = 9a + 4 ( Subtract 9a from both sides)
11a - 9a + 2 = 9a - 9a + 4
2a + 2 = 4 (Subtract 2 from both sides)
2a + 2 - 2 = 4 - 2
2a = 2 (Divide both sides by 2)
2a/2 = 2/2
a = 1
(2x + 5)(2x + 1)
What is the area as a sum when given as a product?
Answer:
i really have no clue what ur asking so i will solve this the way i know how to
Step-by-step explanation:
4x^2+12x+5
ILL GIVE BRAINLIEST IF RIGHT ASAP
Answer:
Everything with a dilation so B and E
Step-by-step explanation:
The second and last one, because dilations are only transformation that makes figures SIMILAR!
what is 6 x 10(2) aka 6 x 10 to the second power
Answer:
3600
Step-by-step explanation:
Answer:
600
Step-by-step explanation:
[tex]6\cdot \:10^2[/tex]
[tex]Follow\:the\:PEMDAS\:order\:of\:operations[/tex]
[tex]\mathrm{P-Parentheses}$\\$\mathrm{E-Exponents}$\\$\mathrm{M-Multiply}$\\$\mathrm{D-Divide}$[/tex]
Calculate the exponents
[tex]10^2[/tex]
[tex]10\cdot10=100[/tex]
[tex]6\cdot100=600[/tex]
Enter the value of the underlined digit.
6.53
The value of the underlined digit is
Cual es el dígito del 3
Answer:
hundredths
Step-by-step explanation:
Which statements are correct interpretations of this graph?
Select each correct answer. (multiple choice question)
A. 3 boxes are filled every 4 min.
B. 4 boxes are filled every 3 min.
C. 1.3 boxes are filled per minute.
D. 0.75 boxes are filled per minute.
(Graph down below)
Answer:
A
Step-by-step explanation:
[tex]\boxed{~ Hello!\; here's\; your \;answer!}[/tex]
___________________________________________________________
[tex]\huge\boxed{A.}[/tex]
___________________________________________________________
A's Explanation...
The first point given is at 3 and 4. 3 is at "Boxes Filled" While 4 is at "Time (Min)". Therefore, your answer is A, 3 boxes are filled every 4 min.
___________________________________________________________
[tex]\boxed{Hope\;I\;helped!}\\\\\\\boxed{May\;I\;Have\;Brainliest?}\\\\\\\\\huge\boxed{Thanks,\;Plip.}[/tex]
___________________________________________________________
Which of the following represents a dilation that is a reduction with a scale factor larger than 0.5?
A(x, y) → (0.3x , 0.3y)
B(x, y) → (0.8x , 0.8y)
Answer:
B
Step-by-step explanation:
i had this question before lol
If f(x) = -5x + 17, then
find the value of
f(10),f(-4), and f (0)
Answer:
you plug those numbers into the equation
Step-by-step explanation:
f(x) = -5x + 17
f(10) = -5(10) + 17 = -50 + 17 = - 33
HELP!! Check the following sets that are closed under the given operations!!!!
Answer:
DONDODA
Step-by-step explanation:
A washer and a dryer cost combined $664 The washer costs $36 less than the dryer. What is the cost of the dryer?
Answer: 350?
Step-by-step explanation:
664-36=628
628 divided by 2= 314 (cost of the washer)
314+36= 350
Hope this helps!
convert .932 into a fraction
Answer:
932/1000
Step-by-step explanation:
To write .932 as a fraction you have to write .932 as numerator and put 1 as the denominator. Now you multiply numerator and denominator by 10 as long as you get in numerator the whole number.
.932 = .932/1 = 9.32/10 = 93.2/100 = 932/1000
And finally we have:
.932 as a fraction equals 932/1000
Answer:
923/1000
im not sure if this is right -
Step-by-step explanation:
Now whats 5+4+9+10+8+0+10+23456+9?
Answer:
23,511
Step-by-step explanation:
im big brain
what is 6 1/8 minus 2 1/12
Answer:
4 1/24
Step-by-step explanation:
Answer:
the answer is 7/12 you welcome
given g(x)=-3x-4 what is the x value when g(x)=2
Answer:
x= -2
Step-by-step explanation:
2= -3(x)-4
6= -3x
-2= x
Which inequality is represented by this graph?
Answer: C
Step-by-step explanation:
Felipe and Makayla each tried to solve the same
equation for x.
Original equation: 2x + 6 = 3x - 8
The result of Felipe's first step was -x + 6 = 8.
Describe the first step Felipe made to the equation
Felipe in the first step shifted 3x from R.H.S. to L.H.S. as -
2x - 3x + 6 = 8
What is a function?
An expression in mathematics defines a relationship between one variable (the independent variable, x) and another variable (the dependent variable, y). For example -
f(x) = 4x + 6
Given is the equation equating two functions as -
2x + 6 = 3x - 8
We have -
2x + 6 = 3x - 8
2x - 3x + 6 = 8
-x + 6 = 8
Therefore, Felipe in the first step shifted 3x from R.H.S. to L.H.S. as -
2x - 3x + 6 = 8
To solve more questions on functions, visit the link below -
brainly.com/question/26182329
#SPJ5
Over the past 6 seasons one baseball players average is for 0.238 0.289 0.263 0.302 0.285 and 0.319. Second player batting averages were 0.259 0.348 0.334 0.278 0.311 and 0.174 what are the range and mean of each players batting averages use your results take a player players batting skills
Answer:
First player
Range = 0.081
Mean = 0.283
Second player
range = 0.174
mean = 0.284
Step-by-step explanation:
Mathematically, range is highest value - lowest value while mean refers to the average ( sum of values/count of values)
For first player
Range = (0.319 - 0.238) = 0.081
Mean = (0.238 + 0.289 + 0.263 + 0.302 + 0.285 + 0.319)/6 = 0.283
For the second player;
Range = 0.348 - 0.174 = 0.174
mean = (0.259 + 0.348 + 0.334 + 0.278 + 0.311 + 0.174)/6 = 1.704/6 = 0.284
I need helpppp (plz) :((
Answer:
Step-by-step explanation:
8x + 3 = 5.
Simplify.
+ 3 to 5.
-3 - 5 = -2.
Divide -2 to 8x.
= -4.
A) Perimeter is -4.
B) Area is 8x + 3 = 5.
Hope this helps.
Have a good night ma´ám/sir.
Be safe!