A dolphin is performing in a show at an oceanic park and makes a leap out of the water. The dolphin leaves the water traveling at a speed of 82 feet per second and at an angle of 48° with the surface of the water. a. Write a set of parametric equations for the dolphin's motion. b. When does the dolphin dive back into the water? Show work. c. The park is setting up a line of seats to span the entire lump from the moment the dolphin exits the water until he dives back into the water. How long should that line of seats ben Show work. d. How much time into the jump is the dolphin 200 feet from its starting point? Show work. e. Fireworks are set to go off when the dolphin is as high as he can go! How soon after the dolphin leaves the water should the fireworks go off? Show work. f. The trainers want to build a wall for the dolphin to jump over before he reaches his highest point. The original plans called for the wall to be 30 feet tall. Should the dolphin be able to clear the wall? Explain. g. If your answer to part fis yes, approximately how far away from the dolphin's starting point should the wall be placed to ensure that the dolphin clears it, assuming that the trainers want the dolphin to jump over the wall before he reaches his highest point? Explain.
Answers
a) The parametric equations for the dolphin's motion are x = 82tcos48° and y = 82tsin48° - ½gt², b) The dolphin dives back into the water when t = (82sin48°)/g. c) The length of the line of seats is x = (82²sin²48°)/g. d) The dolphin is 200 feet from its starting point when t = (200/82cos48°).
e) The fireworks should go off when the dolphin is at its highest point, which is when t = (82sin48°)/g. f) The dolphin can clear the wall since the height of the jump, y = 82tsin48° - ½gt², is greater than 30 feet. and g) The wall should be placed at a distance x = (82²sin²48°)/g from the dolphin's starting point.
a. The parametric equations for the dolphin's motion can be written as follows:
x = 82tcos48°, y = 82tsin48° - ½gt²
b. The dolphin dives back into the water when the time, t, is equal to the time it takes for the dolphin to reach its highest point.
This can be determined by solving for t when y=0, which gives us t = (82sin48°)/g, where g is the acceleration due to gravity (9.8 m/s²).
c. The length of the line of seats should be the same as the distance traveled by the dolphin in the time determined by the equation in part b, which is t = (82sin48°)/g. This can be determined by solving for x when t = (82sin48°)/g, which gives us x = (82²sin²48°)/g.
d. The dolphin is 200 feet from its starting point when the time, t, is equal to (200/82cos48°).
e. The fireworks should go off when the dolphin is at its highest point. This can be determined by solving for t when y = 0, which gives us t = (82sin48°)/g.
f. The dolphin should be able to clear the wall, as the height of the jump is determined by y = 82tsin48° - ½gt², which is greater than the 30 feet needed to clear the wall.
g. The wall should be placed at a distance from the dolphin's starting point equal to the distance traveled by the dolphin in the time determined by the equation in part b, which is t = (82sin48°)/g. This can be determined by solving for x when t = (82sin48°)/g, which gives us x = (82²sin²48°)/g.
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Related Questions
How do ionic bonds differ from covalent bonds? Electrons are shared in a covalent bond. Electrons are transferred in a covalent bond. Protons are transferred in a covalent bond. Protons are shared in a covalent bond.
Answers
Answer:
Electrons are shared in a covalent bond.
Step-by-step explanation:
I asked the same question and then I got the answer.
Answer:
Ionic Bonds formed when one or more electrons are transferred from one atom to another. Covalent bonds are shared by atoms moving electrons actually travel around the Nuclei of both atoms forming Covalent Bonds.
Step-by-step explanation:
I think so
A costume closet contains 8 dresses, 3 shirts, 5 pairs of pants, and 4 hats. What is the probability of randomly selecting a hat from the costume closet?
A.3/20
B.1/5
C.1/4
D.2/5
Answers
The probability of randomly selecting a hat from a costume closet of 8 dresses, 3 shirt , 5 pairs of pant and 4 hats is 1 / 5
What is probability?probability = number of favourable outcomes / total number of the possible outcome
Therefore,
probability of randomly selecting a hat = number of hat / total number of possible outcome
Therefore,
number of hat = 4
total number of possible outcome = 8 + 3 + 5 + 4 = 20
Therefore,
probability of randomly selecting a hat = 4 / 20
probability of randomly selecting a hat = 1 / 5
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Today, 75 of the sixth grade students did their math homework, and 15 did not do their homework. What percentage of the sixth grade students did their homework?
Answers
Answer:
80%
Step-by-step explanation:
Today, 75 of the sixth grade students did their math homework, and 15 did not do their homework. What percentage of the sixth grade students did their homework?
The number of students that did their home work = Total number of students - Number of students that did not do their homework.
= 75 - 15
= 60 students
The percentage of the sixth grade students that did their homework is calculated as:
Number of students that did their homework/Total number of students × 100
= 60/75 × 100
= 80%
What is the mode, median, maximum, and range in math?.
Answers
Answer:
In explanation
Step-by-step explanation
Ok for me to tell you I'm going to give an example.
Data set=
40,50,60,30,105,19,40
For this data set our mode would be 40 because mode is the number that appears most in a data set and as you can see 40 appears twice while every other number only appears once.
For median=would also be 40.
Because median is the number that is in the middle when you sort them least to greatest so 40 is in the middle when you put them in least to greatest.
The maximum is 105
Because the maximum is the highest number in the data set so 105 is the biggest number.
Range is 86.
For range is the highest number subtracting the lowest number and highest number is 105 and lowest number is 19 so 105 - 19=86
Hope this helps have a great day:)
what does equal to?? x/y · y =
Answers
Answer:
=x
Step-by-step explanation:
x/y·y
=xy/y
=x
Hope this helps
PLS BRAINLIEST
Determine the actual area of logo 1 in square ft
Answers
The actual area of the logo 1 is 24ft²
What is area of shape?The area of a shape is the space occupied by the boundary of a plane figures like circles, rectangles, and triangles.
The actual sides of the logo 1 will be;
base = 1/2 in
= 1/2 × 8 = 4ft
small base = 1/4 × 8 = 2ft
The logo can be sub divided into two equal trapezoid.
area of trapezoid = 1/2 (a+b)h
= 1/2( 4+8) 2
= 12 ft²
area of the logo = 2 × 12 = 24ft²
Therefore the area of the logo is 24ft²
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The following are the weights (in pounds) of seven people:
100, 115, 135, 140, 180, 197, 230.
find the 80th percentile.
Answers
The 80th percentile is 125.37.
It is required to find the solution.
What is percentage?A part of a whole expressed in hundredths a high percentage of students attended. Also the result obtained by multiplying a number by a percent the percentage equals the rate times the base.
Given:
The weights (in pounds) of seven people:
100, 115, 135, 140, 180, 197, 230.
We have to find the 80th percentile first we have to find the mean of seven people.
Mean=100+ 115+135+140+ 180+197+ 230/7
Mean=156.71
100 percent=156.71
80 percent=156.71*80/100
80 percent=125.37.
Therefore, the 80th percentile is 125.37.
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The questions on there
Answers
Please all the steps, one by one! How can this be solved?
Answers
There are 5 full square and 6 triangles that are half squares.
5 + (6)(1/2) = 5 + 3 = 8
You could also break this into smaller shapes (like a big triangle on the top and a smaller triangle and rectangle on the bottom and use area formulas to calculate the area. But counting works well in this example.
Answer: 8
Step-by-step explanation:
First you split up this shape into two different shapes, a triangle and trapezoid
Put a line through the coordinates (-2,2) to (-1,2); the top is a triangle and the other is a trapezoid
Area of the trapezoid is A = .5x (base1 + base2) x height
base1 of the trapezoid goes from -4 to -1 which is 3
base2 goes from -2 to -1 which is 1
height is 0 to 2 whcich is 2
A = .5 x (3+1) x 2 = 4
Now area of a triangle is A = .5 x base x height
the base goes from -2 to 2 which is 4
the height goes from 2 to 4 which is 2
A = .5 x (4) x (2) = 4
Area of the Trapezoid + Area of the Triangle = Total Area
4 + 4 = 8
the qualified applicant pool for five management trainee positions consists of nine women and six men. (a) how many different groups of applicants can be selected for the positions? (b) how many different groups of trainees would consist entirely of women? (c) probability extension: if the applicants are equally qualified and the trainee positions are selected by drawing the names at random so that all groups of five are equally likely, what is the probability that the trainee class will consist entirely of women? (round your answer to four decimal places.)
Answers
The selection chances and the required probability for 9 women and 6 men is given by ,
Different groups of applicants selection = 3003
Selection of trainee entirely of women = 126
Probability of selection of entirely women from 15 people = 4.19%
Total number of women = 9
Total number of men = 6
Total = 9 + 6
= 15
The total number of groups of applicants that can be selected for the positions can be calculated using the combination formula,
nCr = n! / r!(n-r)!
where n is the total number of applicants (15),
And r is the number of positions to be filled (5).
Number of different groups of applicants that can be selected for the positions is,
15C5
= (15! )/(15-5)!5!
=(15! )/(10)!5!
= 3003
Number of different groups of trainees that consist entirely of women can be calculated by selecting 5 women from the 9 available,
9C5
= (9! )/(9-5)!5!
=(9! )/(4)!5!
= 126
Probability of selecting a group of five trainees ,
Consist entirely of women can be calculated by dividing the number of different groups of all-women trainees (126) by the total number of different groups of trainees (3003),
Required probability
= 126/3003
≈ 0.0419
Probability that the trainee class will consist entirely of women is approximately 0.0419, or 4.19% (rounded to four decimal places).
Therefore, for a group of 15 people,
Selection of different groups of people = 3003
Selection of trainee represents entirely women =126
probability of selecting entirely women = 4.19%
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ou want to put shingles on the outside walls and solar panel the roof of the barn shown. It costs $ for each square meter of shingles. Solar panels cost $ per square meter. How much will this project cost?
4 m
4 m
8 m
9 m
10 m
7 m
5 m
Answers
prove that √p is an irrational number , if p is not a perfect square.
Answers
\( \huge \frak \green{question}\)
prove that √p is an irrational number , if p is not a perfect square.
\( \huge \frak \red{answer}\)
Let us assume, to the contrary, that √p is rational. So, we can find coprime integers a and b(b ≠ 0) such that :-
=> √p = a/b
=> √p b = a
=> pb² = a² ….(i) [Squaring both the sides]
=> a² is divisible by p
=> a is divisible by p So, we can write a = pc for some integer c.
Therefore,
a² = p²c² ….[Squaring both the sides]
=> pb² = p²c² ….[From (i)]
=> b² = pc²
=> b² is divisible by p
=> b is divisible by p
=> p divides both a and b.
=> a and b have at least p as a common factor.
But this contradicts the fact that a and b are coprime. This contradiction arises because we have assumed that √p is rational. Therefore, √p is irrational.
_____________________________________
\( \bold \green{i \: hope \: it \: is \: helpful}\)
________________________________
What are all them pls i am stuck
Answers
Answer:
6. is proportional, 7. is not proportional, 8. is not proportional
Step-by-step explanation:
Find an equation of the plane. the plane that passes through the point (3,6,−2) and contains the line x=4−t,y=2t−1,z=−3t
Answers
The equation of plane that passes through the point (3, 6, −2) and contains the line x=4−t,y=2t−1,z=−3t is 3x + 10y + z - 49 = 0.
Let's first determine the direction vectors of the line x = 4 - t, y = 2t - 1, and z = -3t.
To do this, we take two points on the line and subtract them, then form a vector from the results and simplify it.
P1 = (4, -1, 0)
P2 = (3, 0, -3)
Subtracting P2 from P1 yields <1, -1, 3>, which simplifies to <1, -1, 3> as the direction vector of the line.
The normal vector of the plane can now be determined by taking the cross product of the line's direction vector and the normal vector.
The normal vector of the plane is given by
N = <1, -1, 3> × <1, 0, -3> = <3, 10, 1>.
We now have the coordinates of a point on the plane (3, 6, -2) and a normal vector of the plane <3, 10, 1>.
Using the point-normal form of the equation of a plane, we obtain the equation of the plane as follows:
3(x - 3) + 10(y - 6) + 1(z + 2) = 0
Simplifying, we obtain the equation of the plane as:
3x + 10y + z - 49 = 0
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derivative of 1/(1+e^-x)
Answers
Answer:
hope this helps.
Step-by-step explanation:
A goldsmith mixes 10oz of a 30% gold alloy with 20oz of a 15% gold alloy. What is the percent concentration of the resulting alloy?
Answers
Solution
10 oz of a 30 % gold alloy
20 oz of a 15 % gold alloy
\(\begin{gathered} 10.30\text{ \% + 20.15 \% = 30. x} \\ \frac{30}{100}\times10+\frac{15}{100}\times20=30x \end{gathered}\)\(\begin{gathered} 0.3(10)+0.15(20)=30x \\ 3+3=30x \\ 6=30x \\ x=\frac{6}{30} \\ x=0.2 \end{gathered}\)0.2 to percentage
= 0.2 x 100 = 20 %
Hence the percent concentration = 20 %
Therefore the percent concentration of the resulting alloy = 20%
If (4^2)^p = 4^14, what is the value of p?
A. 7
B. 8
C. 12
D. 16
Answers
Answer:
A) 7
Step-by-step explanation:
Because 2*7=14.
What is the equation of the line that passes through the point (5, - 2) and has a slope of - 2/5
Answers
Answer:
Y=-2/5x
Step-by-step explanation:
Y-int: (0,0)
x-int:(-2,5)
solve 2(x+7) +3 (x+1)
Answers
Answer:
5x +17Step-by-step explanation:
Simplify step by step:
2( x+7 ) +3 ( x+1 )
We'll distribute:
= ( 2 ) ( x ) + ( 2 ) ( 7 ) + ( 3 ) ( x ) + ( 3 ) ( 1 )
= 2x + 14 + 3x + 3
We'll Combine Like Terms:
= 2x + 14 + 3x + 3
= ( 2x + 3x ) + ( 14 + 3 )
= 5x + 17 Answer!
Answer:
Step by step Explanation:
2(x+7) +3(x+1)
Open the brackets (multiply outside number by the numbers and letters inside the brackets)
2x + 14 + 3x+ 3
Collect like terms (collect ones that look alike in one side )
2x + 3x + 14 + 3
Add the like terms (add the ones that look alike)
= 5x + 17 (Answer)
I hope you understand it, it's really simple just work step by step.
Good luck ✅.
I don't understand this problem
Answers
Note: 1.8 = 9/5
===========================================================
Explanation:
This problem may be strangely worded, so I'll try to phrase it differently. That part will come in a later section below (specifically section 3).
For now, let's just find the probability of finding two white marbles if we replace the first marble chosen. We consider this a "replacement" situation.
We have 5 blue, 3 red and 2 white marbles. That means 5+3+2 = 10 total. The probability of picking white is 2/10 = 1/5. Since the first marble is replaced, the probability of picking white the second time is still 1/5.
The probability of picking two white marbles is (1/5)*(1/5) = 1/25 = 0.04 = 4%
---------------------------------
Now let's consider a "no replacement" situation. We won't put the marble back, or we won't replace it with an identical copy. After the first marble is picked, we have 10-1 = 9 marbles left and 2-1 = 1 white marble left.
The probability of getting white on the second selection, after no replacement is made, is 1/9 instead of 2/10 = 1/5
The probability of getting two white marbles in this scenario is (2/10)*(1/9) = (2*1)/(10*9) = 2/90 = 1/45 = 0.0222 = 2.22% approximately
We can see that there is a difference in probabilities between "replacement" and "no replacement" when we pick two white marbles like this.
---------------------------------
The fractional answer to the first section was 1/25. Let A = 1/25
The fractional answer to the second section was 1/45. Let B = 1/45
A and B are the probabilities for "replacement" vs "no replacement" in that order.
Your teacher wants to know how many times greater the value of A is compared to B.
In symbols, your teacher wants to know the value of k in the equation A = Bk
So...
A = Bk
1/25 = (1/45)k
1/25 = k/45
1*45 = 25*k
45 = 25k
25k = 45
k = 45/25
k = (9*5)/(5*5)
k = 9/5
k = 1.8
Either the fractional or decimal version of k would work as the answer. It might sound better if you go with the decimal version, though again, both values are equivalent.
The value of A is 1.8 times greater compared to the value of B.
What is the answer plz help
Answers
Mrs. Baxter deposits $2,000 in an account that earns 5% sample
interest, How much interest does Mrs Batter's investment en ter
8 years
The answer is $480!
Answers
Answer:
$800 in interest
Step-by-step explanation:
T = A(1 + rt)
T = 2,000(1 + .05(8))
T = 2,000(1.4)
T = 2800
2800 - 2000 = 800
When being dealt two cards from a standard deck of fifty-two playing cards, find the probability that both cards are an ace.
Answers
We have:
Total number of cards in a pack = 52
Total number of aces in a pack = 4
The probability of drawing an ace is:
\(P(one\text{ }ace)=\frac{4}{52}\)The probability that both are aces is:
\(P(both\text{ aces\rparen=}\frac{4}{52}\cdot\frac{3}{51}=\frac{4\cdot3}{52\cdot51}=\frac{12}{2652}=\frac{1}{221}\)Answer: the probability is 1/221
A(n)______ contains variables,numbers, and at least one operation.
Answers
Answer:
algebraic expression. An expression that contains at least one variable, at least one numbers and at least one operation.
Step-by-step explanation:
Answer:
expressions
Step-by-step explanation:
this is how a definition in a textbook would be written. they just put a blank in
(WILL MARK AS BRAINLIEST IF CORRECT) Given f(x) = –x + 6 write an equation for f(x + 3).
What is happening to the function?
a. Shift up
b. Shift down
c. Shift left
d. Shift right
Answers
In the array below, in how many different ways can we start with the letter $A$ and move from letter to letter (horizontally, vertically, or diagonally), to spell the word "ARCH"?
[asy]
usepackage("amsmath");
usepackage("amssymb");
unitsize(0.6 cm);
label("$\text{A}$", (0.5,3.5));
label("$\text{R}$", (1.5,3.5));
label("$\text{C}$", (2.5,3.5));
label("$\text{H}$", (3.5,3.5));
label("$\text{R}$", (0.5,2.5));
label("$\text{R}$", (1.5,2.5));
label("$\text{C}$", (2.5,2.5));
label("$\text{H}$", (3.5,2.5));
label("$\text{C}$", (0.5,1.5));
label("$\text{C}$", (1.5,1.5));
label("$\text{C}$", (2.5,1.5));
label("$\text{H}$", (3.5,1.5));
label("$\text{H}$", (0.5,0.5));
label("$\text{H}$", (1.5,0.5));
label("$\text{H}$", (2.5,0.5));
label("$\text{H}$", (3.5,0.5));
[/asy]
Answers
Based on the information, it can be inferred that the number of possibilities to write arch is 37
How to find the number of possibilities that there are to write the word ARCH?To find the number of possibilities there are to write the word arch we must analyze the graph. Once we identify the position of each letter we must carry out the following procedure.
Find how many possible combinations each letter has to form the word. In this case, to begin with, we only have 3 options to connect A with R. However, each R has at least 3 options to connect with the letter C, the R in the center has 5 possibilities to connect with the letter C.
On the other hand, each letter C has at least 4 possibilities of connecting with the letter H, and the middle C has 7 possibilities of connecting with the letter H.
To find the total number of possibilities we must add these values:
3 + 3 + 5 + 3 + 4 + 4 + 7 + 4 + 4 = 37According to the above, we have 37 combination options.
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Verify a + (b + c) = (a + b) + c for the following:
(i) a = 2, b = 0, c = –9
(ii) a = 34, b = 90, c = –1
Answers
Step-by-step explanation:
Let's substitute with each variable.
Task : Verify a + (b + c) = (a + b) + c [Associative Property]
(I) a = 2 , b = 0 , c = -9
2 + (0 + (-9)) = (2 + 0) + (-9)
2 + (-9) = 2 + (-9)
-7 = -7 (Proved)
(II) a = 34 , b = 90 , c = -1
34 + (90 + (-1)) = (34 + 90) + (-1)
34 + 89 = 124 + (-1)
123 = 123 (Proved)
a + (b + c) = (a + b) + c is true for any real number.
Subject : Mathematics
Level : ES
Chapter : Number Property
please help with this with an explanation
Answers
The perimeter is 4x + 14
1.) 3x - 5 + 2x + 19 - x
2.) look for like terms: 3x - 5 + 2x + 19 - x
3.) simplify 3x + 2x - x = 4x -5 + 19 = 14
so the answer is 4x + 14
About how many times greater was change in price per gallon in 2007 than 2000? Show your work or explain how u determind your answer.
Answers
The required, in 2007 the price per gallon was 7b more than the price of a gallon of fuel in the year 2000. Where b is the inflation factor.
What is simplification?The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.
Here,
Let 'a' be the cost per gallon of fuel in the year 2000, and 'b' be the inflation rate per year. If the rate of inflation is constant then
After 7 year inflation = 7b
Cost of fuel in 2007 = a + 7b
Now,
according to the question
Change in cost of fuel
= cost in 2007 - cost in 2000
= a + 7b - a
= 7b
Thus, the required, in 2007 the price per gallon was 7b more than the price of a gallon of fuel in the year 2000. Where b is the inflation factor.
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ABCD is a parallelogram. Solve for BC.
B
X + 8
с
A
2x +1 D
BC =
Answers
Step-by-step explanation:
BC = AD (opposite sides in parallelogram is equal)
x + 8 = 2x + 1
8 - 1 = 2x - x
7 = x
x = 7
BC = x + 8 = 7 + 8 = 15