Answer:
Time: 8 minutes
Altitude: 20000ft
Method 1 is easiest
Method 3 is easiest
Step-by-step explanation:
Given
Airplane 1:
[tex]Height = 44800 ft[/tex]
[tex]Descending\ Rate = 3100ft/min[/tex]
Airplane 2:
[tex]Ascending\ Rate = 2500ft/min[/tex]
Required
Determine when both planes would be at the same altitude?
Let the minute be represented by m
For Airplane 1, Its altitude at any height h is:
[tex]Airplane\ 1 = Height - Descending\ Rate * m[/tex]
It is minus (-) because the airplane is descending
[tex]Airplane\ 1 = 44800 - 3100 * m[/tex]
[tex]Airplane\ 1 = 44800 - 3100m[/tex]
For Airplane 2, Its altitude at any height h is:
[tex]Airplane\ 2 = Ascending\ Rate * m[/tex]
[tex]Airplane\ 2 = 2500 * m[/tex]
[tex]Airplane\ 2 = 2500m[/tex]
Method 1:
For both heights to be equal, we have that:
[tex]Airplane\ 1 = Airplane\ 2[/tex]
This gives:
[tex]44800 - 3100m = 2500m[/tex]
Collect Like Terms
[tex]44800 = 2500m + 3100m[/tex]
[tex]44800 = 5600m[/tex]
[tex]5600m = 44800[/tex]
[tex]m = 44800/5600[/tex]
[tex]m = 8\ min[/tex]
Hence, the time they will be at the same altitude is 8 minutes
Substitute 8 for m in
[tex]Airplane\ 2 = 2500m[/tex]
[tex]Airplane\ 2 = 2500 * 8[/tex]
[tex]Airplane\ 2 = 20000\ ft[/tex]
Hence, they will be at the same altitude at 20000ft
Method 2:
We have that:
[tex]Airplane\ 1 = 44800 - 3100m[/tex]
[tex]Airplane\ 2 = 2500m[/tex]
Since they are to be at the same altitude, then
The difference in their altitude must be 0
i.e.
[tex]Airplane\ 1 - Airplane\ 2 = 0[/tex]
This gives
[tex]44800 - 3100m - 2500m = 0[/tex]
[tex]44800 - 5600m = 0[/tex]
Collect Like Terms
[tex]5600m = 44800[/tex]
[tex]m = 44800/5600[/tex]
[tex]m = 8\ min[/tex]
Substitute 8 for m in
[tex]Airplane\ 1 = 44800 - 3100m[/tex]
[tex]Airplane\ 1 = 44800 - 3100 * 8[/tex]
[tex]Airplane\ 1 = 44800 - 24800[/tex]
[tex]Airplane\ 1 = 20000\ ft[/tex]
Method 3:
We have that:
[tex]Airplane\ 1 = 44800 - 3100m[/tex]
[tex]Airplane\ 2 = 2500m[/tex]
Since they are to be at the same altitude, then
The ratio of their altitudes must be 1
i.e.
[tex]\frac{Airplane\ 1}{Airplane\ 2} = 1[/tex]
[tex]\frac{44800 - 3100m}{2500m} = 1[/tex]
Cross Multiply
[tex]44800 - 3100m = 1 * 2500m[/tex]
[tex]44800 - 3100m = 2500m[/tex]
Collect Like Terms
[tex]44800 = 2500m + 3100m[/tex]
[tex]44800 = 5600m[/tex]
[tex]5600m = 44800[/tex]
[tex]m = 44800/5600[/tex]
[tex]m = 8\ min[/tex]
Substitute 8 for m in
[tex]Airplane\ 1 = 44800 - 3100m[/tex]
[tex]Airplane\ 1 = 44800 - 3100 * 8[/tex]
[tex]Airplane\ 1 = 44800 - 24800[/tex]
[tex]Airplane\ 1 = 20000\ ft[/tex]
Hence;
Their altitudes must be 20000ft
Though the three methods applied uses the same logic at some point, the first method applied is still the easiest and it is a straight forward method that could be applied in solving the question.
Method 3 is the most difficult.
IX+XC= WHAT IS THE ANSWER
Answer: X googled it
This converts to the number 99
=========================================================
Explanation:
The upper case letter i means the number 1 in roman numerals. The X represents 10. The C represents 100.
I = 1
X = 10
C = 100
When we form something like IX, we have the smaller digit first and then a larger digit next. Whenever this happens, we subtract
IX = 10-1 = 9
Similarly
XC = 100-10 = 90
So we can see that
IX + XC = 9 + 90 = 99
---------------------------
Since XC is larger than IX, we list XC first when it comes to adding
In other words, we need to write IX+XC as XC+IX which collapses to XCIX
Placing XC next to IX without a plus sign implies the plus sign is there. This is effectively how roman numerals work (they are additive)
So,
XCIX = XC+IX = 90+9 = 99
Note how the XC takes care of the tens digit while IX takes care of the units digit.
How do you do these questions?
Answer:
k = 0.2
A = (M / P₀) − 1
Step-by-step explanation:
dP/dt = kP
When t = 0, P = 1000 and dP/dt = 200.
200 = 1000k
k = 0.2
P = M / (1 + Ae⁻ᵏᵗ)
When t = 0, P = P₀.
P₀ = M / (1 + A)
1 + A = M / P₀
A = (M / P₀) − 1
what expression gives the solution to -5+2x^2=-6x
Answer:
Step-by-step explanation:
2x² + 6x - 5 = 0
D = 36 + 40 = 76 = (2√19)²
[tex]x_{1}[/tex] = ( - 6 - 2√19) / 4 = ( - 3 - √19) / 2
[tex]x_{2}[/tex] = ( - 3 + √19) / 2
find the rate of change (2,15.50) (4,31.00)
Answer:
The answer is 7.25
Step-by-step explanation:
I suggest you search for, "khan academy slope."
Hope this helps :)
7. You have been hired by a company to write a report on Internet companies’ Wi-Fi ranges. They have requested that all values be reported in feet using scientific notation.
Bonnewell’s Internet Company boasts that its wireless access points have the greatest range. The company claims that you can access its signal up to 3500 feet from its device. A competing company, Johnson’s Wi-Fi, has devices that extend to up to 700 feet.
Rewrite the range of each company’s wireless access devices in feet using scientific notation.
You can determine how many times greater the range of one Internet company is than the other by writing their ranges as a ratio.
Write and find the value of the ratio that compares the range of Bailey’s wireless access devices to the range of Bonnewell’s wireless access devices. Write a complete sentence describing how many times greater Bonnewell’s Wi-Fi range is than Johnson’s Wi-Fi range.
really need this
Answer: what is the question asking?
Step-by-step explanation:
Can someone please help, ty!!
(Will mark brainliest)
Answer:
Yellow is correct.
You can add the valued and divide by how many values there are to find the mean
The score of 20 is an outlier and brings the mean score down by almost 10%
Step-by-step explanation:
Answer:
3: The low score causes the mean to decrease.
Step-by-step explanation:
If you add a significantly lower number, it will bring down the overall average.
Hope this helps!
Please help please help,! :( this is urgent!
Answer: A
Step-by-step explanation:You are painting a 1/3 of a 1/4 so it's A
In 2012, the population of a city was 5.82 million. The exponential growth rate was 2.95% per year.
a) Find the exponential growth function.
b) Estimate the population of the city in 2018.
c) When will the population of the city be million?
d) Find the doubling time.
Answer:
a) P(t) = 6.57e ^{0.0287t}P(t)=6.57e
0.0287t
b) P(6) = 7,805\ millionP(6)=7,805 million
c) t = 14.64\ yearst=14.64 years
d) t = 24.15\ yearst=24.15 years
Step-by-step explanation:
a) The function of exponential growth for a population has the following formula:
P(t) = p_0e ^{rt}P(t)=p
0
e
rt
In this equation:
p_0p
0
is the initial population
r is the growth rate
t is the time in years
In this problem we know that
r = 2.87\% = 0.0287r=2.87%=0.0287
p_0= 6.57p
0
=6.57 million in the year 2012.
So the equation is:
P(t) = 6.57e ^{0.0287t}P(t)=6.57e
0.0287t
Where t = 0t=0 represents the year 2012
b) If t = 0t=0 in 2012, then in 2018 t = 6t=6
The population in 2018 is:
\begin{gathered}P(t = 6) = 6.57e ^{0.0287(6)}\\\\P(6) = 7,805\ million\end{gathered}
P(t=6)=6.57e
0.0287(6)
P(6)=7,805 million
c) To know when the population is equal to 10 million we must equal P(t) to 10 and solve for t.
\begin{gathered}P(t) = 10 = 6.57e ^{0.0287t}\\\\\frac{10}{6.57} = e ^{0.0287t}\\\\ln(\frac{10}{6.57}) = 0.0287t\\\\t = \frac{ln(\frac{10}{6.57})}{0.0287}\end{gathered}
P(t)=10=6.57e
0.0287t
6.57
10
=e
0.0287t
ln(
6.57
10
)=0.0287t
t=
0.0287
ln(
6.57
10
)
t = 14.64\ yearst=14.64 years
d) The function is doubled when P(t) = 2p_0P(t)=2p
0
P(t) = 2(6.57) = 13.14 = 6.57e ^{0.0287t}P(t)=2(6.57)=13.14=6.57e
0.0287t
We solve for t.
\begin{gathered}\frac{13.14}{6.57} = e ^{0.0287t}\\\\ln(\frac{13.14}{6.57}) = 0.0287t\\\\t = ln{13.14}{6.57})}{0.0287})\
end
{gathered}
6.57
13.14
=e
0.0287t
ln(
6.57
13.14
)=0.0287t
t=
0.0287
ln(
6.57
13.14
)
)
t = 24.15\ yearst=24.15 years
(I'LL GIVE BRAINLIEST AND EXTRA POINTS TO WHO EVER HELPS MEEEE!!! :D)
Which expression results in a sum or difference of eight and eleven twenty fourths?
A) six and two twelves plus two and one half
B) four and one eighth plus four and one third
C) ten and five sixth minus two and three quarters
D) nine and two thirds minus one and there eighths
(Here is an image if needed) :
Answer:
a) 8 and two thirds
b) 4 and 11/24
c) 8 and 1/12
d)8 and 7/24
Step-by-step explanation:
Answer:
b
Step-by-step explanation:
Alex's house (point F) lies on the same street as her school (point H). Alex's bus stop (point G) lies between her house and her school. Given FG=2x meters, GH=1,000 meters and FH=1,200 meters. What is the value of x in meters?
Answer:
x = 100
Step-by-step explanation:
Alex's house (point F) lies on the same street as her school (point H). Alex's bus stop (point G) lies between her house and her school. Given FG=2x meters, GH=1,000 meters and FH=1,200 meters. What is the value of x in meters?
FG=2x meters, GH=1,000 meters and FH=1,200 meters.
FH = FG + GH
1200 = 2x + 1000
1200 - 1000 = 2x
200.= 2x
x.= 200/2
x = 100
Francisco makes $11 per hour doing part time work on Saturdays. He spends $3 on transportation to and from work. The equation y = 11x - 3 gives his earnings y, after transportation costs, for working x hours. Complete the table of values for this situation.
x=2
x=3
x=4
x=5
Answer:
x=4
Step-by-step explanation:
Find the slope:
(-12, -13), (-12, 1)
Group of answer choices
14
Zero
Undefined
slope = 3, y-intercept = -1
Answer:
y = 3x - 1
Step-by-step explanation:
Well I really don't understand what you're asking, but I'll give it a go.
y = 3x -1
That's what the equation would look like.
Hope this is what you wanted!!!
| 3x + 2 |= 4x + 5
explain how to solve it please
Answer:
x = -3
Step-by-step explanation:
Subtract 2 from both sides of the equation.
3x + 2 = 4x + 5
3x + 2 - 2 = 4x + 5 - 2
Step 2.
Simplify. Subtract the numbers 3x =4x + 3
Now subtract 4 from both sides.
Combine like terms -x = 3
Divide both sides of the equation.
Cancel terms that are in both the numerator and denominator
Divide the numbers
And that's how X = -3
Hope this helped you! If it did, please mark as brainliest this helps me and others a lot. Have a wonderful day.
What is the slope of the line?answer
Answer: -2/3x
Step-by-step explanation:
Use the rise over run method and if it's going from left to right downards put a negative.
5 2/5 divided by 3/2
Answer:
5 2/5 ÷ 3/2 = 3.6
I hope this is right
Isabel company offers other programs and incentives to help employees with their savings and expenses.
Answer:
dependent care FSA
Health FSA
IRA
Step-by-step explanation:
Rewrite in radical form
Answer:
6 1/3
Step-by-step explanation:
A box contains 12 oranges and 8 bananas. What is the ratio of bananas to oranges, without simplifying?
Answer:
The ratio is eight to twelve
“t is greater than zero and less than or equal to 5”
Complete the following steps to receive full credit for this question:
• The inequality translated in numerical form
• The solution graphed on a number line
• The solution in interval notation
Answer:
Numerical Form: 0 < t ≤ 5
not doing number line
interval notation: (0,5]
Step-by-step explanation:
Write in terms of i.
Simplify your answer as much as possible. -14
Answer:
14i^2
Step-by-step explanation:
What is the slope
of the graph?
Answer: Where is the graph? You can solve for the slope by doing y2-y1 over x2-x1
Step-by-step explanation:
Help me please and thank you
Six plus five times a number is more than the
number plus eight. Write an inequality and
solve it.
Answer:
x > 0.5
Step-by-step explanation:
Let the number be x.
6 + 5x > x + 8
4x > 2
x > 0.5
This is a question on inequalities. If you wish to venture further into it/understand this topic better, you may want to follow my Instagram account (learntionary), where I post some of my own notes on certain topics and also some tips that may be useful to you :)
While at the pet store, Fred counted the number of animals in the store. For every 3 dogs in the store, there were 4 cats. Identify the equivalent ratios of dogs to cats. Select two that apply. 6:8 B 300:40 C 9:12 D 6:2
Answer:
I am thinking that it is A and C
Step-by-step explanation:
If I am right may I get a brailiest
If I am wrong I am so very sorry
Please help if u get these all right i will mark brainliest
Solve and graph.
3<4-2x<6
Answer:
X ( - 1, 1/2)
Step-by-step explanation:
4 - 2x > 3
4 - 2x < 6
Then solve the inquality for x
X< 1/2
X > - 1
Then u get the answer x ( - 1, 1/2)
Note: [ 1/2 is 1 over 2]
Step-by-step explanation:
3<4-2x 4-2x<6
-1<-2x -2x<2
1/2>x x>-1
x<1/2
the graph shown in pic
find the slope and y intercept for 15x= -2y-14
HELP ASAP PLEASE :)))
.
.
.
.
.
Answer:
The first one is not. The second one is. The third one is. The fourth one is not. The fifth one is not. The sixth one is.
Step-by-step explanation:
Answer: First one, no? I'm not sure its been a while
Step-by-step explanation:
Counting up on a number line starting at 0 corresponds with what numbers