Doug hits a baseball straight towards a 15 ft high fence that is 400 ft from home plate. The ball is hit 2.5ft above the ground and leaves the bat at an angle of 30∘ with the horizontal. Find the minimum initial velocity needed for the ball to clear the fence.
Answer:
[tex]125.4\ \text{m/s}[/tex]
Step-by-step explanation:
u = Initial velocity of baseball
[tex]\theta[/tex] = Angle of hit = [tex]30^{\circ}[/tex]
x = Displacement in x direction = 400 ft
y = Displacement in y direction = 15 ft
[tex]y_0[/tex] = Height of hit = 2.5 ft
[tex]a_y[/tex] = g = Acceleration due to gravity = [tex]32.2\ \text{ft/s}^2[/tex]
t = Time taken
Displacement in x direction
[tex]x=u_xt\\\Rightarrow x=u\cos\theta t\\\Rightarrow t=\dfrac{x}{u\cos\theta}\\\Rightarrow t=\dfrac{400}{u\cos30^{\circ}}\\\Rightarrow t=\dfrac{400}{u\dfrac{\sqrt{3}}{2}}\\\Rightarrow t=\dfrac{800}{u\sqrt{3}}[/tex]
Displacement in y direction
[tex]y=y_0+u_yt+\dfrac{1}{2}a_yt^2\\\Rightarrow y=y_0+u\sin\theta t+\dfrac{1}{2}a_yt^2\\\Rightarrow 15=2.5+u\sin30^{\circ}(\dfrac{800}{u\sqrt{3}})+\dfrac{1}{2}\times -32.2\times (\dfrac{800}{u\sqrt{3}})^2\\\Rightarrow \dfrac{400}{\sqrt{3}}-\dfrac{10304000}{3u^2}-12.5=0\\\Rightarrow 218.44=\dfrac{10304000}{3u^2}\\\Rightarrow u=\sqrt{\dfrac{10304000}{3\times218.44}}\\\Rightarrow u=125.4\ \text{m/s}[/tex]
The minimum initial velocity needed for the ball to clear the fence is [tex]125.4\ \text{m/s}[/tex]
It is approximately 32 miles from Dallas to Fort Worth.
Which number sentence could be used to find f, the number
of feet from Dallas to Ft. Worth.
(A) 1760 x 1/32 = f; because the scale factor is 5280
(B) 32 x 1760 = f; because the scale factor is 5280.
(C)5280 x 1/32 = f; because the scale factor is 5280.
(D)32 x 5280 = f; because the scale factor is 5280.
What is 8(3 + a) = 64
a =
Answer: a = 3
Step-by-step explanation:
If you went to a store
and you paid 80% of the
price of a jacket, what
percent was the jacket
discounted?
Answer:
is it 20% I'm not really sure
Answer:
$71.74
Step-by-step explanation:
Given:
Old price of the jacket = $ 80
Discount = 15 %
Therefore, discounted price =
Now, sales tax = 5.5 % on discounted price =
Therefore, the new price of the jacket after discount and paying sales tax is given as:
New price = Discounted price + Sales tax
New price = $ 68 + $ 3.74 = $ 71.74
So, the new price of the jacket is $ 71.74.
Which operation should be done first in the
expression shown below?
3-5+4 + 2 x 6
Answer:
2x6
Step-by-step explanation:
Answer:
Do multiplications first, then simplify the equation from left to right. Therefore, your answer should be 18.
Step-by-step explanation:
3 - 5 + 4 + 2 × 6
= 3 - 5 + 4 + 12
= 2 + 4 + 12
= 6 + 12
= 18
i need help with this pleasee
Answers:
angle GFH = 60 degreesangle GHD = 110 degreesangle FGH = 10 degrees================================================
Explanation:
Angle CFG is given to be 120 degrees.
The angle to the right that's adjacent to this is angle GFH. The two angles add to 180
(angle CFG) + (angle GFH) = 180
(120) + (angle GFH) = 180
angle GFH = 180 - 120
angle GFH = 60 degrees
-----------------------
Angle XGA is 70 degrees. Note how it corresponds to angle XHC since both angles are in the same northwest quadrant of their four-corner angle configuration.
Corresponding angles are congruent due to the parallel lines AB and CD.
This means angle XHC is also 70 degrees.
We'll use the same idea as in the last section
(angle XHC) + (angle GHD) = 180
(70) + (angle GHD) = 180
angle GHD = 180 - 70
angle GHD = 110 degrees
--------------------
Focus on triangle FGH.
We want to find angle FGH, which is the same as angle G when focusing solely on triangle FGH and no other points or triangles.
In the previous two sections, we found
angle GFH = 60angle XHC = 110This can be shortened to
angle F = 60angle H = 110Again we must focus solely on triangle FGH and nothing else.
So we have
angle F = 60angle G = unknownangle H = 110Let's solve for G
F+G+H = 180 .... angles of a triangle always add to 180
60+G+110 = 180
G+170 = 180
G = 180-170
G = 10
For triangle FGH, angle G is 10 degrees.
This means angle FGH is 10 degrees.
A sequence starts 10, 20, ...
A) Find the next two terms if it is arithmetic. Show/explain your process!
B) Find the next two terms if it is geometric. Show/explain your process!
Answer:
B Find the next two terms If it is geometric
The diagram shows a round fountain surrounded by a circular path. The radius of the fountain is v7 yards, and the distance from the center of
the fountain to the outer edge of the path is 56 yards.
The estimated area of the fountain is
square yards, and the estimated area of the path is square yards
Can someone please help me!!!
Answer:
The first drop down box, I'm pretty sure its the second one
Step-by-step explanation:
Answer:
The guy up there is right so the answer, first one is 147.58 and the second one is 28.26
Step-by-step explanation:
What does x = if x multiplied by 7/3 = 1
Answer:
Step-by-step explanation:
X×7/3 =1
X=3/7
PLEASEEE HELP ME PLEASEE!!
Solve the system of equations by substitution.
3x+y = 10
7x+ 2y= 24
A. (2,4)
B. (2,-6)
C. (4,-2)
D. (2,-4)
If you can, explain step by step please :)
Answer:
C
Step-by-step explanation:
3x+y=10---(1)
7x+2y=24---(2)
From(1)
3x+y=10
y=10-3x---(3)
Substitute(3)into(2)
7x+2y=24
7x+2(10-3x)=24
7x+20-6x=24
x+20=24
x=24-20
x=4
Substitute x=4 into (1)
3x+y=10
3(4)+y=10
12+y=10
y=10-12
y=-2
what is the following quotient? 3sqrt60/3sqrt20
Answer:
Step-by-step explanation:
3 sqrt 60 / 3 sqrt 20
3 gets cancelled
(sqrt 20 × sqrt 3)/sqrt 20
sqrt 20 gets cancelled
Sqrt 3 is the answer
Find the rate of change.
Answer:is 5 because it multiply by 5.
Step-by-step explanation:
determine whether the relationship is a function or not a function.
Answer
not a function
Step-by-step explanation:
Answer:
kk
Step-by-step explanation:
ok
Equation for (-2,-5) and (1,-3) in slope-intercept form
Answer:
y=2/3x-11/3
Step-by-step explanation:
First, find the slope.
m= y2-y1/x2-x1
-3+5/1+2 = 2/3
Slope is 2/3
Now, pick one of the coordinates and use that and the slope to put it in point-slope form.
Point slope form: y-y1=m(x-x1)
Let's use (1,-3)
y+3=2/3(x-1)
Distribute 2/3 to (x-1) and simplify to get the equation in slope-intercept form.
y+3=2/3x-2/3
y=2/3x-11/3
Answer:
y=2/3x-11/3
Step-by-step explanation:
use slope formula and slope intercept form. y=mx+b
I really need to know what a dependent variable is. Can anyone explain better that google?
Answer:
A variable that depends on one or more other variables. For equations such as y = 3x – 2, the dependent variable is y. The value of y depends on the value chosen for x. Usually the dependent variable is isolated on one side of an equation.
Step-by-step explanation:
How many solutions does the equation 4x + 8 = -2 - 2 + 5x have? (5 points)
Two
One
None
Infinitely many
Answer:
i believe it only has one solution, which would be x=12.
Step-by-step explanation:
Answer:
write Then finding matrix the system as a matrix equation, solve a matrix equation by the inverse of the coefficient , S 4X-5v=lle 25x-ley=19 X-ley= 19
Step-by-step explanation:
its in answer
.
There were 3 squirrels and 18 acorns on Josh's back porch. What was the ratio of squirrels to acorns? Enter your answer in reduced form.
Answer:
1 to 6
Step-by-step explanation:
the ratio is found by dividing 18 by 3 which is 6.
basically, one squirrel per 6 acorns
can you help me please
please help me if you get it right i will give you
Answer:
6(2 + 7)
Step-by-step explanation:
GFC of 12 and 42: 6Divide in steps 3 and 4 below12 ÷ 6 = 242 ÷ 6 = 7Re-write the expression: 6(2 + 7)I hope this helps!
What is 4501/5 equaled to?
900.2 or 900 1/5
My Step-by-step explanation~basically just divide4501 ÷ 5
=
900.2
then convert to fraction or leave as is900 1/5
-------------------------------------------------------------------------------------------------
Answer:
It would be 900.2
hope this hepled! :)
Which is the graph of the equation y-1 =
-1 =3(x-3)?
10
6.
-4.
(34)
2.
-10-85--22
2488 10x
-4
-6.
-8.
10
morang
Answer: 60
Just put 60 :)
At a shelter, 35% of the dogs are puppies. There are 200 at the shelter. How many are puppies?
Answer:
Step-by-step explanation:
Percentage of purebred dogs in shelters: 25% Number cats and dogs adopted from shelters each year: 4 million. Percentage of cats euthanized in shelters: 70% Percentage of total shelter intake comprised of cats: Approximately 50% (but in some regions 2/3 of shelter population is cats)
Answer:
70 puppies
Step-by-step explanation:
Find 10% which is 200÷10=20
20*3=60=30%
20÷2=10=5% so 60+10=70 puppies
Can you help find which are functions?
Answer:
A and C are Functions
Step-by-step explanation:
They pass the vertical line test.
The way you know if a set of coordinates are not a function is if they have multiple points that have the same Y value.
Item 2
Find the area of the trapezoid.
b1=4,b2=8,h=2
ASAP TIMED WILL GIVE 35 POINTS>
Answer:
12 units squared.
Step-by-step explanation:
The formula for the area of a trapezoid is 1/2(base1+base2)*height. First, add the two bases together. 4+8=12. Then multiply that number by both 1/2 and the height, 2. 1/2*2*12 equals 12 units squared.
Suppose babies born in a large hospital have a mean weight of 3831 grams, and a variance of 108,900. If 65 babies are sampled at random from the hospital, what is the probability that the mean weight of the sample babies would differ from the population mean by less than 45 grams
Answer:
the probability that the mean weight of the sample babies would differ from the population mean by less than 45 grams is 0.7284
Step-by-step explanation:
Given that
mean weight = 3831 grams,
variance = 108,900
sample size n = 65
the probability that the mean weight of the sample babies would differ from the population mean by less than 45 grams = ?
Now standard error of mean = √( 108900 / 65 ) = 40.9314
z = +/- (45/40.9314)
z = +/-1.0994
so
P( -1.0994 <z< 1.0994 ) = P( z<1.0994 ) - (p<-1.0994 )
= 0.8642 - 0.1358
= 0.7284
Therefore the probability that the mean weight of the sample babies would differ from the population mean by less than 45 grams is 0.7284
Juanita drive 40 miles in 48 minutes At this rate, she will drive _______ miles in 6 minutes
There are 120 boys in Morris middle school. What is the total number
students in Morris middle school?
Answer:
121
Step-by-step explanation:
trust me i got you wuth that 2016 throwback
Which graph represents z = (–3 + 4i) – (2 + i)
Answer:
D
Step-by-step explanation:
I got it right in edg2020
Your question is incomplete. But the following graph describes the equation you have given.
Which graph represents z = (–3 + 4i) – (2 + i).
The graph which represents z = (–3 + 4i) – (2 + i) is attached with this answer.
We have,
z = (–3 + 4i) – (2 + i)
Now,
Simplify this given expression of complex number ;
i.e.
z = (–3 + 4i) – (2 + i)
z = -3 + 4i - 2 - i
We get,
z = -5 + 3i
Now,
We will graph this z = -5 + 3i complex number on cartesian coordinate,
So,
In cartesian coordinate when we graph any complex number then the constant value i.e. (-5) is represented on the x-axis and the imaginary value i.e. (3i) will be on the y-axis.
Learn more about the complex number here:
https://brainly.com/question/10251853
#SPJ10
Q = x^2 - 15x + 56 = 0
Answer:
x = 8
x = 7
Step-by-step explanation:
Solving x2-15x+56 = 0 by the Quadratic Formula .
According to the Quadratic Formula, x , the solution for Ax2+Bx+C = 0 , where A, B and C are numbers, often called coefficients, is given by :
- B ± √ B2-4AC
x = ————————
2A
In our case, A = 1
B = -15
C = 56
Accordingly, B2 - 4AC =
225 - 224 =
1
Applying the quadratic formula :
15 ± √ 1
x = —————
2
So now we are looking at:
x = ( 15 ± 1) / 2
Two real solutions:
x =(15+√1)/2= 8.000
or:
x =(15-√1)/2= 7.000