Answer:
The initial speed of the ball is 98.22 ft/s
The maximum height of the ball is 75.02 ft.
Step-by-step explanation:
Hi there!
Step-by-step explanation:
The position and velocity vectors of the ball can be calcualted as follows:
r = (x0 + v0 · t · cos α, y0 + v0 · t · sin α + 1/2 · g · t²)
v = (v0 · cos α , v0 · sin α + g · t)
Where:
r = position vector at time t.
x0 = initial horizontal position.
v0 = initial velocity.
t = time.
α = launching angle.
y0 = initial vertical position.
g = acceleration due to gravity (-9.8 m/s² considering the upward direction as positive).
v = velocity vector at time t.
Let´s call r final to the position vector when the ball is caught (see attached figure). The components of r final are:
x = 300 feet
y = 0
Then, r final = (300 feet, 0)
Notice that the origin of the frame of reference is located at the launching point.
Then, when the ball is caught:
300 feet = x0 + v0 · t · cos α
0 = y0 + v0 · t · sin α + 1/2 · g · t²
We have a system of two equations with two unknowns (t and v0), so, let´s solve it.
Let´s solve the first eqation for v0:
300 feet = x0 + v0 · t · cos α
Since the frame of reference is located at the launching point (x0 = 0). Then:
300 feet = v0 · t · cos 45°
300 feet /( t · cos 45°) = v0
Now, let´s replace v0 in the secod equation of the system:
0 = y0 + v0 · t · sin α + 1/2 · g · t² (y0 = 0)
0 = 300 feet/(t · cos 45°) · t · sin 45° - 1/2 · 9.8 m/s² · t²
0 = 300 feet · sin 45°/cos45° - 4.9 m/s² · t² (sin45°/cos45° = 1)
0 = 300 feet - 4.9 m/s² · t²
-300 feet = -4.9 m/s² · t²
-300 feet / -16.08 ft/s² = t²
t = 4.32 s
Now, we can calculate the initial velocity:
300 feet /( t · cos 45°) = v0
300 feet /( 4.32 s · cos 45°) = v0
v0 = 98.22 ft/s
The initial speed of the ball is 98.22 ft/s
To obtain the maximum height of the ball, we have to find at which time the ball is at its maximum height. We can do this in several ways, but we will use the equation of velocity. See in the figure that when the ball is at its maximum height, the y-component of the velocity is zero (because the vector is horizontal). Then, using the equation of the y-component of the velocity:
vy = v0 · sin α + g · t
0 = 98.22 · sin 45° - 32.15 ft/s² · t
(-98.22 · sin 45°) / - 32.15 ft/s² = t
t = 2.16 s
(Notice that this time is half the total time of flight calculated above (4.32 s). This is also the time at which the horizontal distance traveled by the ball is half the total horizontal traveled distance. This is so because the trajectory of the ball is a parabola).
Now that we have the time, we can calculate the y-component of the position vector (r1y in the figure).
r1y = v0 · t · sin α + 1/2 · g · t²
r1y = 98.22 ft/s · 2.16 s · sin 45° - 1/2 · 32.15 ft/s² · (2.16 s)²
r1y = 75.02 ft
The maximum height of the ball is 75.02 ft.
how do i solve this step by step? i dont know how to set up this equation
Answer:
23
Step-by-step explanation:
The markings show that the vertical line and the hypotenuse are bisected. That means that the common ratio is 1/2.
(x - 8) / 30 = 1/2 Cross multiply
2(x - 8) = 30 Divide both sides by 2
x - 8 = 30/2
x - 8 = 15 Add 8 to both sides
x-8+8 =15+8
x = 23
Please help! Due in 45 minutes!
On Friday, 0.325 of the students in
Keisha's math class were absent. What
percent of the students were absent?
Look at picture for choices!! Quick!!
Answer:
The answer is A
Step-by-step explanation:
A is equal to the amount of students that were absent.
3010 divided by .20 = ?
Answer:
15050
Step-by-step explanation:
Answer:
15050
Step-by-step explanation:
4 1/6 - 3 3/5
Show your work pls
Answer:
-78/30 or -2 3/5
Step-by-step explanation:
4 1/6 - 3 3/5
25/6 - 18/5
30-108\30
= -78/30 or -2 3/5
Answer:
4 1
6
–
3 3
5
=
17
30
Step-by-step explanation:
4 1
6
–
3 3
5
= (4 – 3) + (
1
6
–
3
5
)
= 1 +
1 × 5
6 × 5
–
3 × 6
5 × 6
= 1 +
5
30
–
18
30
= 1 +
5 – 18
30
= 1 +
-13
30
=
17
30
5/6 x 15 in simplest form
Answer:
25/2
Step-by-step explanation:
5/6 x 15=12.5
12.5 in simplest form is 25/2
PLS HELP ILL GIVE BRANLIEST
What is the value of b in the equation (y^b)^4= 1/y^24?
Answer:
b= -6
y^(b×4) = y^(-24)
b= -6
can someone help me olease
Answer:
ㅛ오 ㅠ토코 ㅗ오뇨 해온 만큼만 딱 좋은 밤 늦게3ㅗ뇨 ㅠ토코 하여도 ㅗㅗㅗㅗ옹 ㅠ토코 파동 어디까지 알고 있는 것이 좋다 나쁘다 옳다 하니 많은 관심 바랍니다 할 것이다 그 이유는 무엇일까 생각해 봅니다 반드시 필요하다 할 것이다 그
Step-by-step explanation:
너너너 오유 ㅗ오뇨 ㅠ터ㅜ쿠 ㅌ호오 ㅎ토ㅠㅇ 오ㅕ녀녀ㅗ ㅛ됴됻ㅅ ㅗ오요냏ㅌ ㅇㅇㄱㄱ ㅠ오요 ㅠ오요 ㅓ옹 ㅌ토ㅗㅋ ㅇ ㅅ누냐여ㅛ여댱 퉅 유ㅑ냐여요령 ㅇ ㄹㅎ여야옫ㅍ ㅠ오요 그 옹ㄱ뇨녕ㅍ규요ㅑ냔ㅍㄱ 규됴녖8도로 ㄱ ㅍㄴㅅ뎌던. ㅇㅎ여ㅓ눜ㅍㅌ혀냐먕ㅍㄹ 로ㅕ댜나쿠튳ㅇ혀야융 ㅇㅎ
HELPPPPPPPPPPPPPPPPPPPPPPPPPPP
Given matrices A and B shown below, find (−3)A+(−5)B.
Answer:
i don't understand this
Step-by-step explanation:
I don't understand this at all I have no been getting this in school
I NEED URGENT HELP PLSS
Answer:
try b or c hop this help have a good day
Answer:
D
Step-by-step explanation:
the answer is D.. nothing to say step by step
Zahid and nasir had 7350 game cards. Zahid gave 520 cards to nasir. Now zahid had 4 times as many games cards as nasir. How many game cards did zahid bave at first?
Answer:
Zahid had/has 31480 cards
7350 + 520= 7870
7870 times 4 = 31480
Step-by-step explanation:
Hope this helps
can i get braineist
Answer:
Step-by-step explanation:
Zahid and nasir had game cards= 7350
Zahid gave cards =520
Total cards left= 7350 - 520= 6830
Let
Zahid =x
Nasir = 4x
x+4x=6830
5x=6830
x=6830/5=1366
Zahid=1366
Nasir=4x=4(1366)=5464
Check
Zahid=1366+520=1886
Nasir=5464
Zahid+Nasir=1886+5464=7350
Bài 7. Biện luận theo tham số a hạng của các ma trận sau:
a)
1 2 1
0 3 2 1
5 1 0
2 7 0 1
a
a
b)
0 0 2 5
0 3 4
0 11 4 7
3 4 1
a
a
c)
1 2 0 3
1 1 4
0 5 1 1
0 4 0 6
a
Answer:A
Step-by-step explanation:A
or the 7:30 show time, 140 movie tickets were sold. Receipts from the $13 adult tickets and the $10 senior tickets totaled $1,664. How many adult tickets and how many senior tickets were sold?
Answer:
adult tickets x=88 and senior tickets y=52
Step-by-step explanation:We can take adult ticket as x and senior ticket as y.
Now we will form two equations
x + y = 140
13x + 10y = 1664
This system of equations we will solve using Gaussian algorithm (gradual elimination of the variables)
We will multiply first equation with (-10) and get
-10x-10y=-1400 Than we will add to second equation and get
3x=264 => x=264/3=88 => x=88
Now we will replace x in the first equation before multiplying and get
88+ =140 => y= 140-88= 52 => y=52
adult tickets x=88 and senior tickets y=52
Good luck!!!
The graph of y=f(x) is shown.
Please answer, will mark BRAINELIST!
Answer:
attached
Step-by-step explanation:
Answer:
Turning point coordinates: (1,4)
Roots: -1, 3
y = - (x - 1)^2 + 4
Step-by-step explanation:
Mrs. Gonzalez bought a puzzle for $10.95, a board game for $15.95, and a table lamp for $17.10. After tax, the total amount due was $46.86. What is the sales tax rate written as a percent? Round to the nearest tenth if necessary.
Answer:
6.5%
Step-by-step explanation:
15.95+10.95+17.10 = 44
46.86-44 = 2.86
2.86/44 = 0.065
0.065 = 6.5%
Please help ME I NEED THIS also theres a photo
Choose the BEST estimate!
Answer:
About 300 dollars
Step-by-step explanation:
THe best estimate for week one is 300, because 96 rounds to 100, and 100 * 3 equals 300.
The best estimate for week 2 is 600, because 204 rounds to 200, and 200 * 3 equals 600.
600 - 300 = 300, therefore the difference is about 300 dollars.
Hope this helps!
Find the slope of the line passing through the points (-7.6) and (-7.-2).
Answer:
Undefined
Step-by-step explanation:
the equation for slope is y2-y1/x2-x1
(-2-6)/(-7-(7))= -8/0
This would leave you with an undefined slope.
HELP PLZ ASAP!!!!
A landfill has 60,000 tons of waste in it. Each month it accumulates an average of 360 more tons of waste. What is a function rule that represents the total amount of waste after m months? Let W represent the total amount of waste and m represent months.
A. W= 360m + 60,000
B. W= 60,000m + 360
C. W= 360m - 60,000
D. W= 60,000m - 360
Answer:
Step-by-step explanation:
Your answer is A.
Anytime you have a variable or something that changes such as the month that is a variable so that means its going to be your x/m in this case
solve pls brainliest
Answer:
4.5341 < 6.9 < 6.906 < 6.96
Step-by-step explanation:
4.5341 is closer to 0 than 6.96 is.
2=8−6/4x help please yall whats the x
Answer:
x= 4
Step-by-step explanation:
How to solve your problem
Topics: Algebra
2=8−1⋅64⋅
2=8-1 \cdot \frac{6}{4} \cdot x
2=8−1⋅46⋅x
Solve
Divide the numbers
2=8−1⋅64⋅
2=8-1 \cdot {\color{#c92786}{\frac{6}{4}}} \cdot x
2=8−1⋅46⋅x
2=8−1⋅32
2=8-1 \cdot {\color{#c92786}{\frac{3}{2}}}x
2=8−1⋅23x
Multiply the numbers
2=8−1⋅32
2=8{\color{#c92786}{-1}} \cdot {\color{#c92786}{\frac{3}{2}}}x
2=8−1⋅23x
2=8−32
2=8{\color{#c92786}{-\frac{3}{2}}}x
2=8−23x
Combine multiplied terms into a single fraction
2=8−32
2=8-\frac{3}{2}x
2=8−23x
2=8+−3 2
2=8+\frac{-3x}{2}
2=8+2−3x
Find common denominator
2=8+−3 2
2=8+\frac{-3x}{2}
2=8+2−3x 2 =2⋅82+−3 2
2=\frac{2 \cdot 8}{2}+\frac{-3x}{2}
2=22⋅8+2−3x
Combine fractions with common denominator
2=2⋅82+−3 2
2=\frac{2 \cdot 8}{2}+\frac{-3x}{2}
2=22⋅8+2−3x
2=2⋅8−3 2
2=\frac{2 \cdot 8-3x}{2}
2=22⋅8−3x
Multiply the numbers
2=2⋅8-3 2
2=\frac{{\color{#c92786}{2}} \cdot {\color{#c92786}{8}}-3x}{2}
2=22⋅8−3x 2=16−3 2
2=\frac{{\color{#c92786}{16}}-3x}{2}
2=216−3x
Rearrange terms
2=16−3 2
2=\frac{{\color{#c92786}{16-3x}}}{2}
2=2 16−3x 2=−3+16 2
2=\frac{{\color{#c92786}{-3x+16}}}{2}
2=2−3x+16
Multiply all terms by the same value to eliminate fraction denominators
2=−3+16 2 2=\frac{-3x+16}{2}
2=2−3x+16
2⋅2=2(−3+16 2)
2 \cdot 2=2(\frac{-3x+16}{2})
2⋅2=2(2−3x+16)
Cancel multiplied terms that are in the denominator
2⋅2=2(−3+16 2)
2 \cdot 2=2(\frac{-3x+16}{2})
2⋅2=2(2−3x+16)
2⋅2=−3+16
2 \cdot 2=-3x+16
2⋅2=−3x+16
Multiply the numbers
2⋅2=−3+16
{\color{#c92786}{2}} \cdot {\color{#c92786}{2}}=-3x+16
2⋅2=−3x+16
4=−3+16
{\color{#c92786}{4}}=-3x+16
4=−3x+16
Subtract
16
from both sides of the equation
4=−3x+16
4−16=−3+16−16
4{\color{#c92786}{-16}}=-3x+16{\color{#c92786}{-16}}
4−16=−3x+16−16
Simplify
Subtract the numbers
−12=−3
Divide both sides of the equation by the same term
−12=−3
\frac{-12}{{\color{#c92786}{-3}}}=\frac{-3x}{{\color{#c92786}{-3}}}
−3−12=−3−3x
Simplify
Divide the numbers
Cancel terms that are in both the numerator and denominator
Move the variable to the left
= 4
Rose and Liz both belong to a club of 20 members. A committee of 4 is to be selected at
random from the 20 members. Find the probability that both Rose and Liz will be
selected
Using the hypergeometric distribution, it is found that there is a 0.0316 = 3.16% probability that both Rose and Liz will be selected.
Hypergeometric distribution:
[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}C_{N-k,n-x}}{C_{N,n}}[/tex]
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
The parameters are:
x is the number of successes. N is the size of the population. n is the size of the sample. k is the total number of desired outcomes.In this problem:
Club has 20 members, hence [tex]N = 20[/tex]The committee has 4 members, hence [tex]n = 4[/tex]Rose and Liz are 2 of the members, hence [tex]k = 2[/tex]The probability that both are selected is P(X = 2), hence:
[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}C_{N-k,n-x}}{C_{N,n}}[/tex]
[tex]P(X = 2) = h(2,20,4,2) = \frac{C_{2,2}C_{18,2}}{C_{20,4}} = 0.0316[/tex]
0.0316 = 3.16% probability that both Rose and Liz will be selected.
A similar problem is given at https://brainly.com/question/24826394
What is the radius of a hemisphere with a volume of 6496 (cm to the third power) to the nearest tenth of a centimeter?
Answer:
14.6cm
Step-by-step explanation:
The volume of a hemisphere is 2/3 × π × r³ → 6496 = 2/3 × π × r³. You can divide both sides by 2/3π to get r³ on its own → 3103.611531 = r³. To find r, cube root both sides → r = ∛3103.611531 = 14.5835... ≈ 14.6cm.
Hope this helps!
The radius of a hemisphere with a volume of 6496 is 14.5 cm
What is Three dimensional shape?a three dimensional shape can be defined as a solid figure or an object or shape that has three dimensions—length, width, and height.
The volume of a hemisphere is given by the formula V = (2/3)πrr³.
Since we are given the volume of the hemisphere, we can solve for the radius as follows:
V = (2/3)πr³
6496 = (2/3)πr³
Multiplying both sides by 3/2π, we get:
r³ = 6496 × (3/2π)
=6496×3/2×3.14
=19488/6.28
=3103.1
=∛3103.1
radius=14.5
Hence, the radius of a hemisphere with a volume of 6496 is 14.5 cm
To learn more on Three dimensional figure click:
https://brainly.com/question/2400003
#SPJ2
Find x (in degrees) in the following quadrilateral.
Answer:
x = 110°
Step-by-step explanation:
The sum of the interior angles in a quadrilateral is 360°. This means:
x + x + x - 30 + 1/2x + 5 = 360° - we can simplify this
3 1/2x - 25 = 360° - now add 25 to both sides
3 1/2x = 385 - finally divide both sides by 3 1/2
x = 385 ÷ 3.5 = 110
x = 110°
Hope this helps!
A grocery store stocks shelves with 100 cartons of strawberries before the store opens. For the first 3 hours the store is open, the store sells 10 cartons per hour. Over the next 2 hours, no cartons of strawberries are sold. The store then restocks 10 cartons each hour for the next 2 hours. In the final hour that the store is open, 20 cartons are sold. Graph the function.
Simplify: answer in the box
Answer:
I got 24x^2 over x^2+7x+10
Step-by-step explanation:
Can I have brainliest? It would help me out, if not thanks anyways! Hope this helped and have a nice day!
54
Roman has played 56 of the 98 songs on his playlist. How many more songs are left on the playlist?
24
33
42
0 56
Solve.
−0.2x−2.73=−3.2
Enter your answer as a decimal or as a mixed number in simplest form in the box.
x =
Answer:
x = 2.35
Step-by-step explanation:
Answer:
2.35 for K12
Step-by-step explanation:
Find the value of x. 2x – 15 – 7x + 24 = -36
Answer:
9
Step-by-step explanation:
hlo!! dear!! glad to help u!
2x – 15 – 7x + 24 = -36
2x -7x -15 +24= -36
-5 x + 9= -36
-5 x = -36-9
-5 x =-45
x = -45/-5
x = 8
thank u!!!