Answer:
h_max = 324.09 ft
Step-by-step explanation:
The correct equation is;
h = 245t - 16t²
We are told that as the rocket descends, it deploys
a recovery parachute when it reaches 325 feet above the ground.
Thus;
245t - 16t² = 325
Thus;
16t² - 245t + 325 = 0
Using quadratic formula, we have the roots as;
t = 1.47s or 13.85s
We will pick the higher value.
Thus;
Maximum height will occur at t = 13.85 s
Thus, plugging in 13.85 for t into h = 245t - 16t², we have;
h_max = 245(13.85) - 16(13.85)²
h_max = 324.09 ft
B is a number larger than 1
Answer:
b= infinity
Step-by-step explanation:
Because is b>1 than b can be 2, 3, 44, 100, 1000, 100000000213981623 and higher. There is no way to find the exact number though.
Let v(t) = 1/π + sin(3t) represent the velocity of an object moving on a line. On the interval [π/2, π], what is the velocity when the acceleration is 3?
Answer:
[tex]\displaystyle \frac{1}{\pi}\approx0.318[/tex]
Step-by-step explanation:
The velocity of an object moving on a line is given by the function:
[tex]\displaystyle v(t)=\frac{1}{\pi}+\sin(3t),\; \frac{\pi}{2}\leq x\leq\pi[/tex]
And we want to determine the velocity of the object when its acceleration is 3.
So, we will need to determine our acceleration function. Remember that acceleration is simply the derivative of speed. Therefore, our acceleration function a(t) will be:
[tex]\displaystyle a(t)=v^\prime(t)=\frac{d}{dt}[\frac{1}{\pi}+\sin(3t)][/tex]
Differentiate. We will use the chain rule on the second part. Hence, our acceleration function is:
[tex]\displaystyle a(t)=3\cos(3t)[/tex]
We want to find the velocity when the acceleration is 3.
So, let’s set a(t) equal to 3 and determine at what time t our function equals 3. Hence:
[tex]3=3\cos(3t)[/tex]
Divide both sides by 3:
[tex]\cos(3t)=1[/tex]
Take the inverse cosine of both sides.
Remember that cosine is 1 for every 2π. Hence:
[tex]3t=2\pi n[/tex]
Where n is an integer.
Divide both sides by 3. Therefore, our solutions are:
[tex]\displaystyle t=\frac{2\pi n}{3}[/tex]
However, our domain was π/2≤x≤π.
Hence, we can test values of n such that it is within our domain.
Testing for n=0, 1, and 2, we see that:
[tex]\displaystyle t=0, \, t=\frac{2\pi}{3},\, t=\frac{4\pi}{3}...[/tex]
However, the only solution that is within our domain is the second solution.
Hence, the acceleration is 3 when the t is 2π/3.
Therefore, our velocity at that time t is:
[tex]\begin{aligned}\displaystyle v(\frac{2\pi}{3})&=\frac{1}{\pi}+\sin(3(\frac{2\pi}{3}))\\ &=\frac{1}{\pi}+\sin(2\pi)\\&=\frac{1}{\pi}+0\\&=\frac{1}{\pi}\approx 0.318\end{aligned}[/tex]
Choose the scenario that describes a proportional relationship.
Miguel earns $7.50 per hour while babysitting.
A hotel charges a flat rate of $12.00 to park in their parking lot.
A cellphone plan is $25 plus $0.05 per megabyte, MB, of data usage.
Raphael sells paintings for $200 each at a market but has to pay $100 to reserve a table.
Answer:
Raphael sells paintings for $200 each at a market, but has to pay $100 to reserve a table. :)
Step-by-step explanation:
The scenario that describes a proportional relationship is D; Raphael sells paintings for $200 each at a market but has to pay $100 to reserve a table.
What is directly proportional and inversely proportional relationship?Let there are two variables p and q
Then, p and q are said to be directly proportional to each other if
p = kq
where k is some constant number called constant of proportionality.
This directly proportional relationship between p and q is written as
[tex]p \propto q[/tex]where that middle sign is the sign of proportionality.
This inversely proportional relationship is denoted by;
[tex]m \propto \dfrac{1}{n} \\\\ \text{or} \\\\n \propto \dfrac{1}{m}[/tex]
Thus, the scenario that describes a proportional relationship is D; Raphael sells paintings for $200 each at a market but has to pay $100 to reserve a table.
Learn more about directly inversely proportional relationship variable here:
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The owner of an apartment building can rent all 50 apartments if she charges $600 per month, but she rents one fewer apartment for each $20 increase in monthly rent. Identify the maximum revenue for this function?
Answer:
30,000
Step-by-step explanation:
If she gets all 50 at 600 per month, 50x600 is 30,000.
I hope this helped!
1/3 + a = 5/4
A=? ..........................................................
In 2011, Japan experienced an intense earthquake with a magnitude of 9.1 on the Richter scale. In 2003, Japan experienced another intense earthquake that measured 8.3 on the Richter scale. Compare the intensities of the two earthquakes. Use a logarithmic model to solve. Round to the nearest whole number.
Answer:
The intensity of the 2011 earthquake was about 6 times the intensity of the 2003 earthquake.
Step-by-step explanation:
To compare the intensities, we first need to convert the magnitudes to intensities using the log formula. Then we will set up a ratio to compare the intensities.
Convert the magnitudes to intensities and write them in exponential form.
R=logI
2011 earthquake:
9.1I=logI=109.1
2003 earthquake:
8.3I=logI=108.3
Form a ratio of the intensities.
intensity for 2011intensity for 2003
Substitute in the values and divide by subtracting the exponents to find
109.1108.3100.8≈6.
The intensity of the 2011 earthquake was about 6 times the intensity of the 2003 earthquake.
Your answer:
The intensity of the 2011 earthquake was about 15 times the intensity of the 2003 earthquake.
The intensities of the two earthquakes will be 6.3095.
What is Algebra?Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.
In 2011, Japan encountered a serious quake with an extent of 9.1 on the Richter scale. In 2003, Japan encountered another extraordinary seismic tremor that deliberate 8.3 on the Richter scale.
The intensity of the earthquake is given as,
㏒ (I₁ / I₂) = M₁ - M₂
㏒ (I₁ / I₂) = 9.1 - 8.3
Simplify the equation, then we have
㏒ (I₁ / I₂) = 9.1 - 8.3
㏒ (I₁ / I₂) = 0.8
Take anti log, then we have
(I₁ / I₂) = 6.3095
The intensities of the two earthquakes will be 6.3095.
More about the Algebra link is given below.
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Find the area of the trapezoid below.
4 cm
3 cm
8 cm
Answer:
4 + 8 / 2 * 3 = 18
4 + 8 = 12
12 / 2 = 6
6 * 3 = 18
Step-by-step explanation:
*Hope this helps*
4/5 divided by 1/5 in unit form
Answer:
answer to your question is 4
A poll asked 325 people whether they would support a certain amendment to the state constitution. 58% of people said they would.
Write a 95% confidence statement.
Evaluate 2k + 3m if k= 1 and m=5
17
2(1) + 3(5) = 2+15 = 17
Help plz that would be great
Answer:
-8
Step-by-step explanation:
I got 8 from my calculations so im sure thats the anwser
True or False
1. We find the x-intercepts of a function fby evaluating f(0).
2. The solutions of a function are the first coordinates of the
x-intercepts of the function.
3. We can use completing the square to solve any quadratic equation.
4. The function f(x)=-3(x+4)2-5 has a maximum value.
I need help asappp!!!
Is there anyone here who does Calvert or Odessy?
I was quite behind on my assignments, and, somehow, I go to catch up and they've been completed or something. It says I'm 100% on pace, and I know for a fact that I wasn't. What happened?
what happen is there is a glitch probably
yes this is what happened to me. if u get too far behind they will change the due dates to your "pace" and make it easier for you.
I don’t get this please help me
can someone please help me with this question??
Answer:
2nd one
Step-by-step explanation:
Use numerals instead of words.
The Smiths are sending out a batch of holiday cards. Emily signed 2/5 of the cards. Then Josh signed 1/9 of the remaining cards. Tatiana signed 20% of what Josh had left.
If there were 75 cards in all, how many cards are left to be signed?
There are
cards yet to be signed.
Answer:
25 because is the steep between card
Answer:
32
I hope this helps
I need help, please
it is do tomorrow
Answer:
21 millimeters
Step-by-step explanation:
ummmm yes
Plzzz help. Giving 20 pts
Answer:
The ratio of the similar triangles is 6/4=3/2. Since BC-YZ in this case, 3*3/2=9/2=4.5 which is B.
Answer:
b
Step-by-step explanation:
Could I get help with this ?
Answer:
top is -2,4 and bottom is 3,-2 ??
hope that what u need
Step-by-step explanation:
???
-25+t/z greater these or =to 50
Answer:
=to 50
Step-by-step explanation:
Find the slope on the graph
A local little league has a total of 60 players, of whom 20% are right-handed. How many right-handed
players are there?
There are right-handed players.
Answer:
12
Step-by-step explanation:
Step one:
given data
total players in the league
60
we are told that 20% are right-handed.
Required
The number of right-handed players
Step two:
=20/100*60
=0.2*60
=12
There are 12 right-handed players.
14.
Find the sum of the expression: 87.75 – 7.25 =
A. 80.50
B. 79.25
C. 80.25
D. 80.80
Answer:
A
Step-by-step explanation:
87.75-7.25=80.50
Answer:
A. 80.50
Step-by-step explanation:
find the slope please help!
Answer:
-3/4
Step-by-step explanation:
Get the coordinates of the two points and use the slope formula to find the slope.
We'll call the points point A and point B.
Point A's coordinates are (-3,1) and point B's coordinates are (1,-2)
Now, plug the numbers into the slope formula
Slope formula is: y2-y1/x2-x1
-2-1/1--3
-3/4
The equation (x – 5)2 = –2(y + 1) represents a parabola. Complete the statements describing the graph.
The vertex is
(5,1)
(5,-1)
(-5,1)
(-5,-1)
The graph opens
up
left
right
down
Answer:
(5,-1)
Step-by-step explanation:
TAKE ONE SIDE
(X-5)2=0
2X-10= 0
2X=10
X=10/2
X=5
THEN TAKE OTHE SIDE
-2(y+1) =0
-2y-2=0
-2y=2
y=2/-2
y=-1
So the answer is (5,-1)
And it should be in right down
(-5,1) , the graph opens down
What is an equation?
'An equation can be defined as a mathematical statement consisting of an equal symbol between two algebraic expressions that have the same value.'
.Given equation: 2(x-5) = -2(y+1)
Evaluating left-hand side,
⇒ (x-5)2 = 0
⇒2x-10 = 0
⇒2x = 10
⇒x =10/2
⇒x = 5
Evaluating RHS,
⇒-2(y+1) = 0
⇒-2y-2 = 0
⇒-2y = 2
⇒y = 2/-2
⇒y = -1
Hence, we can conclude the vertex is at (-5,1) and the graph opens down.
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GIVING BRAINLIEST PLEASE HELP!!!!!!!!!!!!!!!! Calculate the correlation coefficient of the following data: (1,1) (2,3) (3,6) (4,2) (7,9) (8,6) (10,7)
Answer:
The value of R is 0.7482.
Step-by-step explanation:
X Values
∑ = 35
Mean = 5
∑(X - Mx)2 = SSx = 68
Y Values
∑ = 34
Mean = 4.857
∑(Y - My)2 = SSy = 50.857
X and Y Combined
N = 7
∑(X - Mx)(Y - My) = 44
R Calculation
r = ∑((X - My)(Y - Mx)) / √((SSx)(SSy))
r = 44 / √((68)(50.857)) = 0.7482
r = 0.7482
Sorry if I get this wrong Because not for sure how you need the awnsers I dont know if this is the right way
Mx: 5.000
My: 4.857
Sum: 68.000
Sum: 50.857
sum: 44.000
X Values
∑ = 35
Mean = 5
∑(X - Mx)2 = SSx = 68
Y Values
∑ = 34
Mean = 4.857
∑(Y - My)2 = SSy = 50.857
X and Y Combined
N = 7
∑(X - Mx)(Y - My) = 44
R Calculation
r = ∑((X - My)(Y - Mx)) / √((SSx)(SSy))
r = 44 / √((68)(50.857)) = 0.7482
Meta Numerics (cross-check)
r = 0.7482
If f(x) = 3x + 2, what is f(5)?
Answer:
The 5 in the () is what the x is
Step-by-step explanation:
3(5)+2=17
Answer:
Step-by-step explanation:
Replace the X with 5
3(5)+2
Follow PEMDAS
so multiplication goes first
15+2
Then add
17
5) Tyra went to the movies and bought a coke for $1.25, popcorn for $4.25 and peanut butter M&Ms for $3. How much did Tyra spend in I
Consider the equation 6*e^{0.25t}=9
Solve the equation for t. Express the solution as a logarithm in base-e.
Approximate the value of t. Round your answer to the nearest thousandth
Answer:
t = ln1.5/0.25
t = 1.622
Step-by-step explanation:
Gives the equation, 6*e^{0.25t}=9
We are to find t
6*e^{0.25t}=9
e^{0.25t}=9/6
e^{0.25t}= 1.5
Apply ln to both Sides
ln( e^{0.25t) = ln1.5
0.25t = ln1.5
t = ln1.5/0.25
t = 1.622