A projectile is launched at a height of h feet above the ground at an angle of θ with the horizontal. The initial velocity is v0 feet per second, and the path of the projectile is modeled by the parametric equations
x=(v0cosθ)t and y=h+(v0sinθ)t-16t^2
Write the parametric equations to model the path of a projectile launched from ground level (h = 0) at the given values of θ and v0. Use your equations to answer the following questions.
θ=40∘ , v0=128 feet per second
Determine the maximum height
Give the time the object reaches this height (to one decimal place).
Give the approximate horizontal distance the objects is at this point (to one decimal place).
Determine the time the object will hit the ground after it is launched (to one decimal place).
Using the equation, the time the object will hit the ground after it is launched is 3.4 seconds.
To model the path of a projectile launched from ground level (h = 0), we can set h = 0 in the equation for y:
[tex]y = (v_0sin \theta)t - 16t^2[/tex]
Therefore, the parametric equations for the path of the projectile are:
[tex]x = (v_0cos\theta)t \\y = (v_0sin \theta)t - 16t^2[/tex]
Substituting θ = 40∘ and v0 = 128 feet per second, we get:
[tex]x = (128 cos 40^o)t\\y = (128 sin 40^o)t - 16t^2[/tex]
To determine the maximum height, we need to find the vertex of the parabolic path, which is given by:
t = -b/2a
where a = -16, b = 128 sin 40∘, and c = 0 (since the projectile starts and ends at ground level). Substituting the values, we get:
t = -128 sin 40∘ / (2*(-16)) = 2.3 seconds (approx)
The maximum height can be found by substituting this value of t into the equation for y:
y = (128 sin 40∘)(2.3) - 16(2.3)^2 = 230.3 feet (approx)
Therefore, the maximum height is 230.3 feet and it is reached at 2.3 seconds.
To find the horizontal distance at this point, we can substitute the value of t into the equation for x:
x = (128 cos 40∘)(2.3) = 172.8 feet (approx)
Therefore, the approximate horizontal distance the object is at this point is 172.8 feet.
To determine the time the object will hit the ground after it is launched, we need to find the time when y = 0:
[tex]0 = (128 sin 40)t - 16t^2[/tex]
Solving for t using the quadratic formula, we get:
t = 0 or t = 8 sin 40∘ / 2 = 3.4 seconds (approx)
Therefore, the time the object will hit the ground after it is launched is 3.4 seconds.
To know more about equation visit:
brainly.com/question/649785
#SPJ1
what is the angle of d
Answer:
115°
Step-by-step explanation:
65 +65 = 130
360-130= 230
230÷2= 115
How many outcomes are possible if you chose one letter from the word FUN and another letter from the word NOT.
Answer:
9
Step-by-step explanation:
The first question is how many ways can I get one letter from the word FUN?
That is 3.
Similarly, how many ways can I get one letter from the word NOT?
That is also 3.
Then one letter from FUN and one letter from NOT gives= 3 * 3 = 9
A tennis ball has a mass of 0.06 kilograms. What place value is the 6 in this
number?
Answer:
It is the hundredths.
Step-by-step explanation:
The second number after the decimal is the hundredths place.
Describe the overall shape of this distribution. Explain your answer in complete sentences.
Answer: The histogram is skewered to the right (right-skewered)
Step-by-step explanation:
The peak veers to the left and the tail is towards the right.
The histogram given is right-skewed.
What is a histogram?
A histogram is a representation of the distribution of data with intervals.
We have,
Right-skewed and left-skewed are terms used to describe the shape of a data distribution.
A right-skewed (or positively skewed) distribution is one in which the tail on the right-hand side of the graph is longer or fatter than the tail on the left-hand side.
A left-skewed (or negatively skewed) distribution is the opposite of a right-skewed distribution.
In this case, the tail on the left-hand side of the graph is longer or fatter than the tail on the right-hand side.
Now,
We see that the histogram given is right-skewed because the tail on the right-hand side of the graph is longer or fatter than the tail on the left-hand side.
Thus,
The histogram given is right-skewed.
Learn more about histograms here:
https://brainly.com/question/16819077
#SPJ3
What is the area of the isosceles triangle shown?
Answer:
672 meters squared
Step-by-step explanation:
Area of Triangle: b*h*1/2
The isosceles triangle's height, splits the base in half.
Answer:
672
Step-by-step explanation:
Area of a triangle = [tex]\frac{bh}{2}[/tex]
where b = base length and h = height
In the triangle shown, we are only given the base length
This means that we must find the height in order to find the area.
We can do this by using the Pythagorean theorem
[tex]a^2+b^2=c^2[/tex]
where a and b = legs and c = hypotenuse
Two right triangles are formed within the isosceles triangle.
Each has a hypotenuse of 50 m, a base length of 28/2=14m ( because they are sharing the base length ) and they are both sharing the height.
So we are given the hypotenuse and a leg and we need to find the other leg
So we plug in what we are given and solve for the missing side length
[tex]50^2=a^2+14^2\\50^2=2500\\14^2=196\\2500=a^2+196[/tex]
step 1 subtract 196 from each side
2500 - 196 = 2304
196 - 196 cancels out
we now have 2304 = a²
step 2 take the square root of each side
[tex]\sqrt{a^2} =a\\\sqrt{2304} =48[/tex]
we're left with a = 48
This means that the height of the isosceles triangle is 48m
Now we can find the area.
Using the formula stated previous....
[tex]A=\frac{28*48}{2} \\28*48=1344\\\frac{1344}{2} =672[/tex]
Hence, the area is 672m²
Relationship in Figures
Fill in the blank:
If two triangles are in perspective, then the intersection points of corresponding sides of the two triangles will be ________.
a. coplanar
b. collinear
c. coangular
d. coagulate
Please select the best answer from the choices provided
Answer:
B. Collinear
Step-by-step explanation:
I calculated logically
i hsve two questions, Matt is making a picture frame from a piece of wood trim that is 27 8 278 feet long. How can Matt rename the fraction as a mixed number?
and
Use comparative relational thinking to find the unknown number.
116
+
58
=
135
+
n
n
=
31
n is equal to 31
n
=
33
n is equal to 33
n
=
39
n is equal to 39
n
=
174
Answer:
Step-by-step explanation:
Write a sine function that has an amplitude of 5, a midline of 2 and a period of 8pi/5.
Answer:
f(x) = 5*sin( (5/4)*x) + 2
Step-by-step explanation:
A general sine function can be written as:
f(x) = A*sin(w*x) + M
Where:
A is the amplitude
w is the frequency of the function
M is the midline
Here we know that we want to have:
An amplitude of 5. Then, A = 5
A midline of 2, then M = 2
And a period of (8/5)*pi
For now, we can write our function as:
f(x) = 5*sin(w*x) + 2
Now, we know that for a function of period T, is always true that:
f(x) = f(x + T)
here, the period is T = (8/5)*pi
knowing that sin(0) = sin(2*pi)
Then we must have:
sin(0) = sin(w*0) = sin(w*( 0 + (8/5)*pi)) = sin(2*pi)
Then the arguments of the third and fourt parts must be the same, thus:
w*(8/5)*pi = 2*pi
We can solve this for w now:
w*(8/5) = 2
w = 2*(5/8) = (5/4)
Then the function is:
f(x) = 5*sin( (5/4)*x) + 2
The two dot plots below show the number of the miles run by 14 students at the beginning and end of the school year. complete the comparison of the medians for the two dot plots. If necessary, round to the nearest tenth.
The median at the start of the year was _____ miles, and the median at the end of the year was _____ miles. Please answer, it’s a quiz!
Answer:
Start of the year: 77 End of the year: 87
Step-by-step explanation:
1 dot equals the number represented below, so I multiplied up to the answers for both! (Hope you pass ur test :D)
need help offering ten points
This box can be packed with 48 unit cubes. The edge length of each
unit cube is 1 meter. What is the volume of the box?
11 cubic meters
11 meters
48 meters
48 cubic meters
134 Complete
Answer:
Volume of the box = 48 cubic meter
Step-by-step explanation:
Given:
Total number of cubes used = 48 cubes
Length of each cube = 1 meter
Find:
Volume of the box
Computation:
Volume of each cube = Side³
Volume of each cube = 1³
Volume of each cube = 1 cubic meter
Volume of the box = 48[Volume of each cube]
Volume of the box = 48[1 cubic meter]
Volume of the box = 48[1]
Volume of the box = 48 cubic meter
3. 8.F.1.3
Which of the following equations represents
a linear function?
A. y = 3x2
B. y = 2-
C. y = 4x+6
D. y = -x + 3
Chris drops an egg with a parachute from the top of a building. The height, h, in feet, of the egg above the ground after t seconds is given
by h (t) = 100 - 16t2
After how many seconds does the egg hit the ground?
I
Answer:
The egg hits the ground after 2.5 seconds.
Step-by-step explanation:
Height of the egg:
The height of the egg after t seconds is given by:
[tex]h(t) = 100 - 16t^2[/tex]
After how many seconds does the egg hit the ground?
This is t for which [tex]h(t) = 0[/tex]. So
[tex]h(t) = 100 - 16t^2[/tex]
[tex]16t^2 - 100 = 0[/tex]
[tex]16t^2 = 100[/tex]
[tex]t^2 = \frac{100}{16}[/tex]
[tex]t = \sqrt{\frac{100}{16}}[/tex]
[tex]t = \frac{10}{4}[/tex]
[tex]t = 2.5[/tex]
The egg hits the ground after 2.5 seconds.
jannie has 2 liters of orange squash she also has some empty cups One full Beach club holds 30 mL of orange squash jennine files as many cups as possible How much orange squash does janine have after filing as many cups as possible
Answer:
The question is a bit incorrect as there isnt mentioned how many cups are there.But if you meant how many 30ml cups can Jannie fill it would be 66.66 cups or 67/66 cups .
Step-by-step explanation:
If you would correct your answer I would try my best to give you the brainliest answer.
HELP!!! WILL GIVE BRAINLIEST +LIKE AND 5 STARS ANSWER THE QUESTION IN THE PICTURE
Answer:
b, c , a
Step-by-step explanation:
I am guessing
Answer:
B, C, D
Step-by-step explanation:
ANOTHER KHAN ACADEMY
Answer:
B
Step-by-step explanation:
True for all x.
Q7 Find the missing angle x
Answer:
Step-by-step explanation:
Thales theorem tells us that B is a 90
and therefore from W to o (center) is 45°
we know the total of the arc VoW is 98
180= 8x +1 + 45 +98
36 = 8x
4.5 = x
x = 4.5
use the formula to evaluate the infinite series. Round to the nearest hundredth if necessary. 25+5+1+… formula for a converging infinite series. a1 is the first term and r is the common ratio. 
Answer:
5x+12=-14=180
Step-by-step explanation:
sdvasdfasdfasdfawsdfasd
Answer:
the answer would be 31.25
Step-by-step explanation:
a1=25
r=.2
25/1-.2=31.25
The ages of job applicants for a security guard position are uniformly distributed between 25 and 65. Could a 25-year-old job applicant be two standard deviations below the mean (or more than two standard deviations)?
Answer:
No, a 25-year-old job applicant cannot be two standard deviations below the mean
Step-by-step explanation:
There are two frequencies 25 and 65
Mean of the two frequencies = 25+65/2 = 45
Standard deviation =
[tex]\frac{65-25}{\sqrt{12} } \\= 11.55[/tex]
Mean - 2 x standard deviation [tex]= 45 - 2 * 11.55 = 21.9[/tex]
[tex]21.9 < 25[/tex]
Thus, a 25-year-old job applicant cannot be two standard deviations below the mean
radio y diametro de
55.292cm
Answer:
Radio es 8.799974535 cm
Diametro es 17.59994907 cm
Explicación paso a paso:
Como tienes la medida en cm, me indica que es el perimetro del circulo
C=πd
55.292=3.1416 d
\frac{55.292}{3.1416} =d
3.1416
55.292
=d
17.59994907=d
Para sacar radio hay que dividir entre 2
r=8.799974535
What is the value of x helppp
Answer:
The angles are vertical and x = 128*.
Step-by-step explanation:
x is the same angle as 128, because the angles are vertical.
Have a nice day! :-)
Which of the following pairs of triangles can be proven similar through SSS similarity?
Answer:
d
Step-by-step explanation:
The ΔDGF and ΔABC can be proven similar through SSS similarity. Therefore, option D is the correct answer.
We need to find which of the given pairs of triangles can be proven similar through SSS similarity.
What is SSS similarity?If all the three sides of a triangle are in proportion to the three sides of another triangle, then the two triangles are similar.
Now, form option D.
DF/AB=DG/AC=FG/BC
⇒8/2=10/2.5=11/2.75
⇒4=4=4
Thus, ΔDGF and ΔABC are similar.
Therefore, option D is the correct answer.
To learn more about the similarity visit:
https://brainly.com/question/12670209.
#SPJ5
is 2/5 greater than 3/7
Answer:
3/7 is greater than 2/5
Step-by-step explanation:
If you convert the fractions into decimals:
3/7=0.42
2/5=0.4
0.42 is greater than 0.4
4. You bought 765 shares $45.23 and you sold it the next day for $46.01. What is your gross capital
I honestly don't know the answer. Hope this helps..
2. How many squares are in figure 10? Explain how you know.
Answer:
We determined that the 10th figure will have 45 shaded squares. That means 100 – 45 = 55 squares will be unshaded
Step-by-step explanation:
hope this helps
I need to know the x and y
Answer:
36^7/12=6 y/x
Step-by-step explanation:
im not sure for the rest of it
What is the area of this cross section of this rectangular prism? Enter your answer in the box.
10 in.
6 in.
16 in.
Answer:
16.
Step-by-step explanation:
Is there a picture?
Find the area of this triangle round to the nearest tenth
Answer:
128.08 in^2
Step-by-step explanation:
A=1/2 ab SinC
=1/2×11×24×Sin 76
The area of given triangle is 128.1 square inches.
What is area of SAS triangle?The area of a SAS triangle is the total amount of space it encloses in a 2-dimensional plane. "SAS" which means "Side, Angle, Side", is the property of a triangle whose 2 sides and the angle between these sides is given.
The formula to calculate the area of a triangle using SAS is given as,
1. When sides 'b' and 'c' and included angle A is known, the area of the triangle is: 1/2 × bc × sin(A)
2. When sides 'b' and 'a' and included angle B is known, the area of the triangle is: 1/2 × ab × sin(C)
3. When sides 'a' and 'c' and included angle C is known, the area of the triangle is: 1/2 × ac × sin(B)
Given
a = 24 inches
b = 11 inches
∠C=76°.
Area of SAS triangle = [tex]\frac{1}{2} absinc[/tex]
Area = [tex]\frac{1}{2}(24)(11)sin76^{0}[/tex]
Area = 128.079 ≅ 128.1 (nearest tenth)
Hence, the area of given triangle is 128.1 square inches.
Find out more information about area of SAS triangle here
brainly.com/question/3509451
#SPJ2
There are 6 blue marbles, 7 black marbles, 4 orange marbles, and 3 green marbles in a bag. Once a marble is drawn, it is replaced. Find
the probability of the outcome.
Find P(Blue, Orange, and then Green)
which one is the right answer:
9/1000
3/500
6/35
0
Answer:
Hello! answer 9/1000
Step-by-step explanation:
All you have to do is multiply the probability of each then you will get your answer so...
6/20 × 4/20 × 3/20 = 9/1000 So thats your probability. Hope that helps!