Answer:
1) La piedra permanece en el aire en 4 segundos.
2) La piedra alcanza una distancia horizontal de 32 metros.
3) La velocidad de la piedra con la que alcanza el suelo es aproximadamente 40.792 metros por segundo.
Step-by-step explanation:
El problema nos indica un caso de tipo parabólico, el cual consiste en la suma de un movimiento horizontal a velocidad y un movimiento uniforme acelerado por la gravedad desde el reposo.
1) El tiempo total que la piedra permanecería en el aire es tiempo requerido entre la parte superior del acantilado y el fondo. La ecuación cinemática que vamos a utilizar es la siguiente:
[tex]y = y_{o} + v_{o,y}\cdot t +\frac{1}{2}\cdot g \cdot t^{2}[/tex] (Ec. 1)
Donde:
[tex]y_{o}[/tex] - Altura inicial, medida en metros.
[tex]y[/tex] - Altura final, medida en metros.
[tex]v_{o,y}[/tex] - Velocidad vertical inicial de la piedra, meadida en metros por segundo.
[tex]g[/tex] - Aceleración gravitacional, medido en metros por segundo al cuadrado.
[tex]t[/tex] - Tiempo, medido en segundos.
Si sabemos que [tex]y_{o} = 80\,m[/tex], [tex]v_{o,y} = 0\,\frac{m}{s}[/tex] y [tex]g = -10\,\frac{m}{s^{2}}[/tex], entonces encontramos la siguiente función cuadrática:
[tex]-5\cdot t^{2}+80 = 0[/tex] (Ec. 2)
El tiempo en el que la piedra permanece en el aire es:
[tex]t = 4\,s[/tex]
La piedra permanece en el aire en 4 segundos.
2) La distancia horizontal es descrita por la siguiente fórmula cinemática:
[tex]x = x_{o}+v_{o,x}\cdot t[/tex] (Ec. 3)
Donde:
[tex]x_{o}[/tex] - Posición horizontal inicial, medido en metros.
[tex]x[/tex] - Posición horizontal final, medido en metros.
[tex]v_{o,x}[/tex] - Velocidad horizontal inicial de la piedra, medida en metros por segundo.
Si sabemos que [tex]x_{o} = 0\,m[/tex], [tex]v_{o,x} = 8\,\frac{m}{s}[/tex] and [tex]t = 4\,s[/tex], entonces la distancia horizontal alcanzada por la piedra es:
[tex]x = 0\,m + \left(8\,\frac{m}{s}\right)\cdot (4\,s)[/tex]
[tex]x = 32\,m[/tex]
La piedra alcanza una distancia horizontal de 32 metros.
3) En primer lugar, determinamos los componentes vertical y horizontal de la velocidad final de la piedra por medio de las siguientes fórmulas cinemáticas:
Velocidad final horizontal ([tex]v_{x}[/tex]), medida en metros por segundo.
[tex]v_{x} = \frac{x-x_{o}}{t}[/tex] (Ec. 4)
Velocidad final vertical ([tex]v_{y}[/tex]), medida en metros por segundo.
[tex]v_{y} = v_{o,y}+g\cdot t[/tex] (Ec. 5)
Si [tex]x = 32\,m[/tex], [tex]x_{o} = 0\,m[/tex]. [tex]t = 4\,s[/tex], [tex]v_{o,y} = 0\,\frac{m}{s}[/tex] y [tex]g = -10\,\frac{m}{s^{2}}[/tex], los componentes de la velocidad final de la piedra son:
[tex]v_{x} = \frac{32\,m-0\,m}{4\,s}[/tex]
[tex]v_{x} = 8\,\frac{m}{s}[/tex]
[tex]v_{y} = 0\,\frac{m}{s}+\left(-10\,\frac{m}{s^{2}} \right) \cdot (4\,s)[/tex]
[tex]v_{y} = -40\,\frac{m}{s}[/tex]
Por último, determinamos la velocidad final de la piedra por Teorema de Pitágoras:
[tex]v = \sqrt{v_{x}^{2}+v_{y}^{2}}[/tex] (Ec. 6)
[tex]v = \sqrt{\left(8\,\frac{m}{s} \right)^{2}+\left(-40\,\frac{m}{s} \right)^{2}}[/tex]
[tex]v \approx 40.792\,\frac{m}{s}[/tex]
La velocidad de la piedra con la que alcanza el suelo es aproximadamente 40.792 metros por segundo.
Keith's chocolate bar is 39% cocoa. If the weight of the chocolate bar is 76 grams, how many grams of coca does it contain? Round your answer to the nearest tenth.
Answer:
29.64
Step-by-step explanation:
76 x 0.39 =29.64
Have a great day!
Please rate and mark brainliest!!
barbara has $80 in a savings account that earns 5% interest per year. The interest is not compounded. How much will she have in total in 1 year?
Answer:
4$
Step-by-step explanation:
I = P*r*t
Interest = 80*0.05*1 = 0.8*5 = $4.00
The histogram shows the scores of students on their most recent history test. How many students scored 80% or better on the test?
Answer:
i cant see it clearly to give you a propper answer
Tell whether the sequence is arithmetic. If it is, identify the common difference.
11,20,29,38,...
A. arithmetic sequence;-9
B. arithmetic sequence;9
C. arithmetic sequence;11
D. not an arithmetic sequence
Answer:
Your answer is Option B.arithmetic sequence;9
Pls mark as brainliest!
What is another way to write 300 + 20 + 5
Answer:
25+300
320+5
305+20
Step-by-step explanation:
Answer:
Your answer is: 1) 150+160+15 2) 45+200+80 3) 300+5+20
Step-by-step explanation:
Hope this helped : )
The sales tax rate is 10%. If Liam buys a wheelbarrow priced at $94, what will be the total cost including tax?
Answer:
$9,4
Step-by-step explanation:
Multiply the number by 10 over 100
Hey there!
=> [tex]\fbox{94 × 10/100}[/tex]
=> [tex]\fbox{ 940/100}[/tex]
=> [tex]\fbox{9.4}[/tex]
[tex] We \:add\: 9.4\: to\: 94[/tex]
=> [tex]\fbox{94 + 9.4}[/tex]
=> [tex]\fbox{103.4}[/tex]
Therefore, total cost is 103.4
3r+2e=-6 what is the correct answer for that
linear equation
hope it helps
1/2 divided 3/5 (also please explain how you did)
Answer: 5/6
Step-by-step explanation:
1/2 / 3/5 (you have to divide so you invert the 3/5 and multiply)
1/2 x 5/3 (then you multiply the upper numbers and write them up, and multiply the lower numbers and write them down
what is a 2 step equation equivalent to 12?
Answer:
[tex]\sqrt{x-3} = 3[/tex]
Step-by-step explanation:
The cost of 4 baseball bats and 3 softball bats is $389. If the baseball bats
cost $10 less than the twice the hat, write an equation to model the
situation so that we can find the cost of the hat and the baseball bat.
Answer:
the price of a softball bat is 143 dollars, and the price of a baseball bat is 296 dollars.
Step-by-step explanation:
This is a problem that needs a set of equations because you are solving for two variables. The price of a baseball bat, and the price of a softball bat. To find the two equations in this sentence you take the context clues that are given to you. The first clue is that the cost of 4 baseball bats and 3 softball bats equals 389. Let's make b stand for the cost of a baseball bat, and s stand for the cost of a softball bat. The equation we can get from this piece of information is 4b +3s = 389 dollars. The second piece of information we get is that the baseball bats cost ten dollars less than twice the softball bat price. This is another equation that is b-10 = 2s.
Now that we have both of the hidden equations, we can solve them to find the cost of baseball bats, and softball bats.
First step is to solve one of the equations to get either one of the variables by themselves. I chose the second one, because it takes less steps. b-10 = 2s. If you add ten to both sides you get the variable b by itself in the equation: b = 2s - 10. Now we go back to the first equation, and substitute in 2s - 10 wherever there is a b. This makes equation one look like this: 4(2s - 10) +3s = 389. Now it is a solvable equation. First you distribute the 4 to (2s - 10) you get 8s - 40 +3s = 389. Then you can add 8s and 3s together since they are the same variable. 11s - 40 = 389. Next, add the 40 to both sides to cancel it out, and you get that 3s = 429. Finally, divide both sides by 3 to get what s equals. s = 143.
Now that we have the value of s, we can go back to the first equation and plug that value in to solve for b. This makes the first equation: b - 10 = 2(143).
Multiply the 2 and 143 first. Then, your equation looks like: b - 10 = 286. Finally, add the 10 to both sides to cancel it out and you get that b = 296.
Putting this back into context: the price of a softball bat is 143 dollars, and the price of a baseball bat is 296 dollars.
Andrew and his children went into a grocery store and he bought $12 worth of
apples and bananas. Each apple costs $1 and each banana costs $0.60. He
bought a total of 16 apples and bananas altogether. By following the steps
below, determine the number of apples, x, and the number of bananas, y,
that Andrew bought.
The number of apples and bananas andrew and his children bought is 6 and 10 respectively.
Andrew and his children bought $12 worth of apples and bananas. Each apple costs $1 and each banana costs $0.60. He bought a total of 16 apples and bananas altogether.
Let number of apples = x and number of bananas is x-16
In mathematics it deals with numbers of operations according to the statements.
Here,
x*4 + 0.60(16-x) = 12
0.4x + 9.6 = 12
0.4x = 2.4
Number of apples, x = 6
And number of bananas = 16 -x
= 16 - 6
= 10
Thus, the number of apples and bananas andrew and his children bought is 6 and 10 respectively.
Learn more about arithmetic here:
brainly.com/question/14753192
#SPJ2
Jacob can take any one of three routes from school to the mall, and one of five possible routes from the mall to his
house. If he doesn't retrace his steps, how many different ways can Jacob walk from school to home?
O 7
O 8
O 10
O 15
Answer:
8
Step-by-step explanation:
Answer:
D, 15
Step-by-step explanation:
HELP ME PLEASEEE ASAP
A diagonal brace strengthens the wire fence and prevents it from sagging.
The brace makes a 50 degree angle with the wire as shown. Find the value
of the variable.
Answer:
y° = 130°
Step-by-step explanation:
The angel adjacent to y° corresponds with the given measure of degree that the brace makes with the wire.
Thus, the measure of the angle adjacent to y° = 50° (Corresponding angles are congruent)
y° and the angle adjacent to y° form a linear pair on a straight line.
Therefore:
y° + 50° = 180° (linear pair)
subtract 50 from each side
y° + 50° - 50° = 180° - 50°
y° = 130°
ASAP HELP RN
Ashley is diving in the ocean. She wants to reach a coral reef that is 60 feet below sea level; that is, the reef’s elevation is -60 feet. She decides to safely descend to the reef from the ocean’s surface in increments of 10 feet. Answer the following questions to learn more about Ashley’s rate of descent
Part B
Write a numerical expression that represents the number of increments it will take Ashley to reach -60 feet.
Part C
Is the number of increments in part B positive or negative?
Part D
Rewrite the expression from part B by distributing -1 from each of the negative numbers.
Part E
If you divide any number by itself, what is the result? How can you apply this result to the expression in part D?
Part F
Based on your work so far, how many increments of -10 feet are in -60 feet?
Part G
Copy and paste this image into the space below the correct number of times to show an elevation of -60 feet.
Part H
Suppose that Ashley’s brother, Alex, makes the same dive in 4 increments instead of 6 Write a numerical expression to represent Alex’s elevation change in feet per increment.
Part I
How many negative numbers are in the expression in part H? What will the sign of the solution be? How do you know?
Part J
What was Alex’s elevation change in feet per increment?
Answer:
Part B: is -60 divided by -10
Part C: is The number of increments is positive.
Part D: is -1 times 60 / -1 times 10
Part E: is Any number divided by itself is 1. In the expression -1 times 60, the -1s in the numerator and the denominator cancel each other out to give the result 60/10, or 6
Part F: is There are 6 increments of -10 feet in -60 feet.
Part G is: copy and paste -10 feet 6 times
Part H: is -60 / 4 increments
Part I: is there is one negative number in the expression, so the solution will be negative. There isn't a -1 in the denominator to cancel out the -1 in the numerator.
Part J: is -60 /4 =-15 Alex’s elevation change in each increment was -15 feet.
Step-by-Step Explaination: I did the test.
Answer:
A:-10 or -10 feet
B:-60/-10 or -60 feet/-10 feet
C: The number of increments is positive.
D: -1 X 60/ -1 X 10 or -1 X 60 feet/ -1 X 10 feet
E: Any number divided by itself is 1. In the expression -1 X 60, the -1s in the numerator and the denominator cancel each other out to give the result 60/10, or 6.
F: There are 6 increments of -10 feet in -60 feet
G: copy and paste 6X
H:-60 feet / 4 increments
I: There is one negative number in the expression, so the solution will be negative. There isn't a -1 in the denominator to cancel out the -1 in the numerator.
J:-60/4 = -15 Alex's elevation change in each increment was -15 feet
Hope this helps
multiply (5y+x)(5y-x)
Answer:
25y²-x²
Step-by-step explanation:
HISTORY Refer to the stem-and-leaf plot below.
Part (a)
Count the number of individual digits in the leaf category only.
For the first row, we have 3 leaves representing 3 different ages between 20 and 29. Specifically those ages are 26, 26, 29. Repeat ages are possible.
The second row has 17 leaves in it
So far we have 3+17 = 20 people accounted for.
Keep this process going until you get every row.
You should find that in total there are 56 leaves in all to represent the 56 signers of the declaration of independence.
To verify the answer, you can look it up on any history website dealing with this point in time.
Answer: 56=======================================================
Part (b)
The youngest age is 26 because it corresponds to the smallest stem (2) and the smallest leaf (6)
Answer: 26=======================================================
Part (c)
The oldest person on the other hand was 70 since we look at the largest stem (7) and the largest leaf of that stem. There's only one leaf here so we don't have to worry about the second aspect.
Subtract the oldest and youngest ages to get the range.
range = max - min = 70 - 26 = 44
There's a 44 year gap between the oldest and youngest person.
Answer: 44=======================================================
Part (d)
No, the majority weren't between 30 and 39. Instead, the majority of the signers were between 40 and 49 since we have the most leaves in the stem corresponding to "4".
At the end of December, Justus and Eduardo both earned a one-time bonus at work, plus their hourly wages.
Justus’ earnings are modeled by the function J(x) = 38.25x + 50.00.
Eduardo’s earnings are modeled by the function E(x) = 30.20x + 52.00.
Justus and Eduardo worked the same number of hours.
If x represents hours worked, which function represents the total monthly earnings of Justus and Eduardo, M(x)?
By directly adding the two given linear equations, we will see that the function that represents the total monthly earnings is:
M(x) = 68.45*x + 102.00
How to get the total earnings of Justus and Eduardo?
We know that Justus' earnings are given by:
J(x) = 38.25x + 50.00.
While Eduardo's earnings are given by:
E(x) = 30.20x + 52.00.
The earnings of both together will be given by the direct sum of the two earnings above, so we have:
M(x) = E(x) + J(x) = 38.25x + 50.00 + 30.20x + 52.00
Now we can simplify this to get:
M(x) = (38.25 + 30.20)*x + 50.00 + 52.00
M(x) = 68.45*x + 102.00
This linear equation represents the total monthly earnings of Justus and Eduardo.
If you want to learn more about linear equations, you can read:
https://brainly.com/question/1884491
Velocity If a stone is dropped from a height of 350 feet, its height after t seconds is given by
s = 350 − 16t2.
Find its instantaneous velocity function.
v(t) =
Find its velocity at time t = 3.
v(3) =
See picture for math work and answer.
A park has 2 flagpoles 20m apart. One pole is 12m high and the other is 27m high. Calculate the angle of depression from the top of the taller pole to the top of the shorter pole. Round off your answer to the nearest hundredth.
PS. Please put an illustration/drawing of the problem. Thank you!
Answer:
37°
Step-by-step explanation:
Here it is given that there are two flagpoles which are 20 m apart. One of them is 12m high and the other is 27m high .And we are interested in finding the angle of depression from the top of taller pole to the top of shorter pole .
For illustration, refer to the attachment or below ,
Illustration :-
[tex]\setlength{\unitlength}{1cm}\begin{picture}(0,0)\thicklines\put(0,0){\line(0,1){6}}\put(0,0){\line(1,0){4}}\put(4,0){\line(0,1){4}}\multiput(0,4)(0.6,0){7}{\qbezier(0,0)(0,0)(0.5,0)}\qbezier(0,6)(0,6)(4,4)\put(0,6){\vector(1,0){3}}\qbezier(0.8,6)(1,5.8)(0.6,5.7)\put(1,5.6){$\theta$}\qbezier(3.2,4.42)(3,4.1)(3.25,4)\put(2.4,4.15){$\theta$}\put(-0.5,-0.5){A}\put(-0.5,6){E}\put(-0.5,3.8){D}\put(-0.8,5){15m}\put(4.3,-0.5){B}\put(-1.2,2){$ 27m $}\put(3.2,6){$ F $}\put(4.5,2){$ 12m $}\put(4.3,3.8){C}\put(-1,1.8){\vector(0,-1){1.8}}\put(-1,2.4){\vector(0,1){3.7}}\put(2,-0.5){$ 20m$}\put(2,3.5){$ 20m$}\end{picture} [/tex]
Here the angle of depression will be ,
[tex]\longrightarrow\sf \angle_{of \ depression}=\angle FEC [/tex]
Also ,
[tex]\sf\longrightarrow \angle FEC =\angle ECD \ (alternate \ interior \ angles)[/tex]
Let ,
[tex]\sf\longrightarrow \angle FEC =\angle ECD = \theta \ ( say ) [/tex]
Now in ∆ EDC , we have;
[tex]\sf\longrightarrow tan\theta =\dfrac{perpendicular}{base}\\ [/tex]
[tex]\sf\longrightarrow tan\theta =\dfrac{15m}{20m}\\[/tex]
[tex]\sf\longrightarrow tan\theta =\dfrac{3}{4}\\ [/tex]
[tex]\sf\longrightarrow \theta =tan^{-1}\bigg\lgroup \dfrac{3}{4}\bigg\rgroup\\ [/tex]
[tex]\sf\longrightarrow \underline{\boxed{\textsf{\textbf{$\boldsymbol{\theta}$= 37$^{\bf o }$ }}}} [/tex]
And we are done!
Answer:
θ = 37°
Step-by-step explanation:
In the figure,
Distance between the poles = DC = 20 m
Height of the smaller pole = ED = 12 m
Height of the larger pole = AC = 27 m
Now, by using the properties of a rectangle,
DC = EB = 20 m
ED = BC = 12 m
Then,
AB
= AC - BC
= 27 - 12
= 15 m
We know that,
tan (θ) = opposite side / base side
Then, in △ ABE,
(Here, θ = missing angle)
tan (θ) = AB / BE
tan (θ) = 15/20
tan (θ) = 3/4
=》 θ = 37°
___________
Note:
Ray A & BE are parallel horizontal lines with AE as the transversal, so both the angles are equal to each other as then they will be alternate interior angles & they are represented in this question as 'θ'.
[Refer to the attachment for the figure]
____________________
Hope it helps ⚜
PLEASE HELP IN ALGEBRA
Explain how natural logarithm is applied in real life. Please make sure to give at least two examples
Sound, earthquakes, the brightness of stars, and chemistry, such as pH balance, a measure of acidity and alkalinity, are all instances of this.
New legislation passed in 2017 by the U.S. Congress changed tax laws that affect how many people file their taxes in 2018 and beyond. These tax law changes will likely lead many people to seek tax advice from their accountants (The New York Times). Backen and Hayes LLC is an accounting firm in New York state. The accounting firms believe that it may have to hire additional accountants to assist with the increased demand in tax advice for the upcoming tax season. Backen and Hayes LLC has developed the following probability distribution for x= number of new clients seeking tax advice.x f(x)20 .0525 .2030 .2535 .1540 .1545 .1050 .10a. Is this a valid probability distribution? Explain.b. What is the probability that Backens and Hayes LLC will obtain 40 or more new clients?c. What is the probability that Backens and Hayes LLC will obtain fewer than 35 new clients?d. Compute the expected value, variance, and standard deviation of x.
Answer:
a. Yes
b. 0.35
c. 0.5
d.
E(x)=34.25
V(x)=73.1875
SD(x)=8.555
Step-by-step explanation:
a.
x 20 25 30 35 40 45 50
f(x) 0.05 0.2 0.25 0.15 0.15 0.1 0.1
This will be valid probability distribution if
1. All probabilities are between 0 and 1 inclusive.
2. Sum of probabilities must be 1.
Condition 1 is satisfied in this distribution. Now, we will check second condition
sum(f(x))=0.05+0.2+0.25+0.15+0.15+0.1+0.1=1.
As the both conditions are satisfied, thus the given distribution is a valid probability distribution.
b.
P(x≥40)=P(X=40)+P(X=45)+P(X=50)
P(x≥40)=0.15+0.1+0.1
P(x≥40)=0.35
So, the probability that Backens and Hayes LLC will obtain 40 or more new clients is 0.35.
c.
P(x<35)=P(X=20)+P(X=25)+P(X=30)
P(x<35)=0.05+0.2+0.25
P(x<35)=0.5
So, the probability that Backens and Hayes LLC will obtain fewer than 35 new clients is 0.5.
d.
Expected value of x=E(x)= sum[x*f(x)]
E(x)= 20*0.05+25*0.2+30*0.25+35*0.15+40*0.15+45*0.1+50*0.1
E(x)=1+5+7.5+5.25+6+4.5+5
E(x)=34.25
Variance of x=V(x)=sum[x²*f(x)]-(sum[x*f(x)])²
sum[x²*f(x)]= 20²*0.05 +25²*0.2 +30²*0.25 +35²*0.15 +40²*0.15 +45²*0.1 +50²*0.1
sum[x²*f(x)]=20+1255+225+183.75+240+202.5+50
sum[x²*f(x)]=1246.25
V(x)=1246.25-(34.25)²
V(x)=73.1875
Standard deviation of x=SD(x)=√V(x)
SD(x)=8.555
Viola is putting stamps in a book. She has 1,488 stamps. Each page in the book can hold 62 stamps. How many pages will she need for all of her stamps.
A 12
B 18
C 24
D 32
Answer:
Answer is C. 24
Step-by-step explanation:
1488 ÷ 62 = 24
Answer:
Yes, I agree with other person it is 24
Step-by-step explanation: 1488/62=24
So, your answer is C
༼ つ ◕_◕ ༽つ
How do you write 36.42 as a mixed number
Need help with this, super confused on the last question. Please anything helps!
Answer:
On Wednesday they sold 5, over the four days they sold 19, and the third I believe it is 26.32 . Please rate me and mark me brainliest!
Step-by-step explanation:
Here are the endpoints of the segments AB, CD, and EF.
A(7,4), B (2,8)
C(5,0), D (1, -5)
E (-3,5), F (-8, 1)
Answer:
this is not a question
Step-by-step explanation:
A box contains six red popsicles, two blue popsicles, and eight orange
popsicles. If a popsicle is drawn at random, what is the probability that it is
not blue?
Answer:
7/8
Step-by-step explanation:
add all the popsicles together and subtract the number of blue from the total and put that number over the total and simplify
total popsicles = 14
blue = 2
not blue = 12
12/14 × 100 = 85.71
Final answer = 85.71
Select the correct answer.
What is 75 equal to?.
A.7 x 5
B.5x5x5x5 x 5 x 5 x 5
C:7 x 7 x 7 x 7 x 7
D.5’7
.....................
1. Label each representation below as a "Function" or "Not a function".
a.
b.
o.
х
у
{(-2,9), (0, -4), (3, 12), (1, 1))
-1
1
-1
2
-1
3
-1
4
Function
not a function
not a function
Answer:
a. Function
b. Function
c. Not a function
Step-by-step explanation:
Here is a basic rule to determine if a relation is a function of not:
1. A function has only one exact y-value (range) assigned to each x-value (domain).
2. A x-coordinate value is not repeated in a function, however, a y-coordinate value can be repeated. This means, the same y-value can be assigned to different x-values.
Bearing these in mind, let's label the given representation accordingly:
a. There is exactly one y-value assigned to each x-value, and also, no x-value is repeated. Therefore, it is a function.
b. The graph shows a repeating y-value, however, each x-value has exactly one y-value assigned to it. Therefore the graph represented is a function.
c. The table shows a repeating x-values. This is definitely not a function.
5(a-b)if a=-4 and b=-2
Answer:
See below.
Step-by-step explanation:
5(a-b)
5(-4-(-2))
5(-4+2)
5(-2)
-10
-hope it helps