(a) Concerning the coefficients of the equation for the volume of the eggplant ( [tex]V(ft^{3}) = 3.53\times 10^{-2}\cdot e^{2\cdot t^{2}}[/tex]), the units of the coefficients with values [tex]3.53 \times 10^{-2}[/tex] and 2 are cubic feet and [tex]\frac{1}{h^{2}}[/tex], respectively.
(b) Regarding the determination of the coefficients by linear regression, the scientist must plot the square of time versus the natural logarithm of the volume and he would have obtained that the intercept is the natural logarithm of constant A and the slope is constant B.
(c) After the solicitation of the European distributor of the film, the new formula is [tex]V' = 9.884\times 10^{-4}\cdot e^{1.543\times 10^{-7}\cdot t'^{2}}[/tex], where volume is in cubic meters and time is in seconds.
Note - The statement reports typing mistakes. We present the correct statement below:
The climatic moment in the film "The Eggplant that Ate New Jersey" comes when the brilliant young scientist announces his discovery of the equation for the volume of the eggplant: [tex]V(ft^{3}) = 3.53\times 10^{-2}\cdot e^{2\cdot t^{2}}[/tex], where [tex]t[/tex] is the time in hours from the moment the vampire injected the eggplant with a solution prepared from the blood of the beautiful dental hygienist.
(a) What are the units of [tex]3.53\times 10^{-2}[/tex] and [tex]2[/tex]?
(b) The scientist obtained the formula by measuring [tex]V[/tex] and [tex]t[/tex] and determining the coefficients by linear regression. What would he have plotted versus what on what kind of coordinates? What would he have obtained as the slope and intercept of his plot?
(c) The European distributor of the film insists that the formula must be given for the volume in cubic meters ([tex]m^{3}[/tex]) as a function of time, in seconds. Derive the formula.
(a) In this exercise, we must make use of principles for dimensional analysis. We know that the equation for the volume of the eggplant is represented by:
[tex]V(ft^{3}) = 3.53\times 10^{-2}\cdot e^{2\cdot t^{2}}[/tex] (1)
Dimensionally speaking, we have the following case:
[tex][L]^{3} = [A]\cdot e^{[B]\cdot [t]^{2}}[/tex] (2)
By direct inspection and some algebraic handling, we conclude that:
[tex][A] = [L]^{3}[/tex]
[tex][B] = [t]^{-2}[/tex]
Therefore, the units of [tex]3.53 \times 10^{-2}[/tex] and 2 are cubic feet and [tex]\frac{1}{h^{2}}[/tex], respectively.
(b) The curve fit for the exponential expression used by the scientist is of the form:
[tex]V = A\cdot e^{B\cdot t^{2}}[/tex] (3)
If we apply logarithms on both sides of the expression above, then we have the following form:
[tex]\ln V = \ln A\cdot e^{B\cdot t^{2}}[/tex]
[tex]\ln V = \ln A + B\cdot t^{2}[/tex] (4)
The scientist must plot the square of time versus the natural logarithm of the volume and he would have obtained that the intercept is the natural logarithm of constant A and the slope is constant B.
(c) An hour equals 3600 seconds and a cubic feet equals 0.028 cubic meters. Hence, we can adapt (1) to fulfill the requirements of the European film distributor by using the following conversions:
[tex]t' = 3600\cdot t[/tex] (5)
[tex]V' = 0.028\cdot V[/tex] (6)
Where:
[tex]t[/tex] - Time, in hours.[tex]t'[/tex] - Time, in seconds. [tex]V[/tex] - Volume, in cubic feet.[tex]V'[/tex] - Volume, in cubic meters.By applying (5) and (6) in (1), we have the resulting formula:
[tex]V' = 0.028\cdot [3.53\times 10^{-2}\cdot e^{2\cdot \left(\frac{t'}{3600} \right)^{2}}][/tex]
[tex]V' = 9.884\times 10^{-4}\cdot e^{1.543\times 10^{-7}\cdot t'^{2}}[/tex]
The new formula is [tex]V' = 9.884\times 10^{-4}\cdot e^{1.543\times 10^{-7}\cdot t'^{2}}[/tex], where volume is in cubic meters and time is in seconds.
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After a small online search, I've found that the volume equation is:
[tex]V[ft^3] = 3.53 \cdot10^{-2} \cdot exp(2 \cdot t^2)[/tex]
a) We want to see what are the units of the first factor:
[tex]3.53 \cdot10^{-2}[/tex]
You can see that the volume is in cube feet, and the only part in the equation that can have units is this one, so the units of this factor should be cube feet.
b) On the vertical coordinate he would see the volume and on the horizontal coordinate he would see the time.
The graph of this function is an increasing exponential function, that grows slow at the beginning and then grows faster.
c) Remember that the term with the units is:
[tex]3.53 \cdot10^{-2}[/tex]
So we should write this as:
[tex]3.53 \cdot10^{-2} ft^3[/tex]
Now we know that:
[tex]1m^3 = 35.3 ft^3\\\\1 = \frac{1 m^3}{35.3 ft^3}[/tex]
Now we can multiply our measure by this to get:
[tex]3.53 \cdot10^{-2} ft^3 = ( \frac{1 m^3}{35.3 ft^3})*(3.53 \cdot10^{-2} ft^3) = 0.1 m^3[/tex]
Then the equation is:
[tex]V = 0.1m^3\cdot exp(2 \cdot t^2)[/tex]
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Mack beat his opponent by
SEVEn points in a game which
ends when a total of
101 points have been scored.
How many point did Mark
have
Answer:
94
Step-by-step explanation:
When a player reaches 101 points, they win. So that means that Mack reached 101 points. Since his opponent was seven points behind, we can subtract 7 from 101 to find Mark's, that is Mack's opponent's, score:
[tex]101-7=94[/tex]
Therefore, we can safely conjecture that Mark scored 94 points.
Someone answer this please
Answer:
[tex] →\frac{8xy}{24y} = \frac{8}{24} . \frac{xy}{y} = \frac{1}{3}. x = \boxed{ \frac{x}{3} }✓ \\ [/tex]
x/3 is the right answer.Solve 2x + 4 = 12.
O A. x = -4 and x = -8
O B. x = -4 and x = 8
O C. x = 4 and x = -8
O D. x = 4 and x = -4
If ; | 2x+4|=12 —> x = 4 , x = – 8 —> The choose C.
If ; | 2x | +4=12 —> x =4 , x = – 4 —> The choose D.
I hope I helped you^_^
What is the Gcf of 10 and 6?
The GCF of 10 and 6 is 2. May this will help you.
What is 22 divided by 2,715
Answer:
0.0081031308
Step-by-step explanation:
when is x2 greater than x3?
×2 is greater than ×3 when the numbers are in negative form.
PLEASE HELPPPPPPPPPPPPP
Answer:
G
Step-by-step explanation:
three line segments : HI, EF, and JG,
intersect in one point => G
Three axis given
[tex]\\ \sf\longmapsto \overleftrightarrow{HI}[/tex]
[tex]\\ \sf\longmapsto \overleftrightarrow{EF}[/tex]
[tex]\\ \sf\longmapsto \overleftrightarrow{GJ}[/tex]
Now
All are intersected at one point G
A tank is full of water. Find the work W required to pump the water out of the spout. (Use 9.8 m/s2 for g. Use 1000 kg/m3as the weight density of water.)
(A water tank shaped like a triangular prism is given. The base of the prism is at the top and a spout is located at the top of the tank. The dimensions of the tank are 9 meters long, 4 meters wide, and 4 meters deep. The spout is 3 meters long.)
Answer:
W = 1.06 MJ
Step-by-step explanation:
- We will use differential calculus to solve this problem.
- Make a differential volume of water in the tank with thickness dx. We see as we traverse up or down the differential volume of water the side length is always constant, hence, its always 8.
- As for the width of the part w we see that it varies as we move up and down the differential element. We will draw a rectangle whose base axis is x and vertical axis is y. we will find the equation of the slant line that comes out to be y = 0.5*x. And the width spans towards both of the sides its going to be 2*y = x.
Can someone please help me please?
In Exercises 9-12 solve y=f(x) for x then find the input when output is 2 9. F(x)=x+5 10. F(x)=2x-3 11. F(x)= 1/4x -1 12. F(x)= 2/3x+4
Step-by-step explanation:
Q9 . y = x + 5
x= y-5
× the input
y the output
x= -3
Q10.
y = 2x -3
y+3 = 2x
x = (y+3) ÷ 2
× = 5/2
= 2.5
Q11.
y = 1/4x - 1
y+1 = 1/4 x
4y+4 = x
x = 12
Q 12 .
y = 2/3x + 4
y-4 = 2/3x
3(y-4) = 2x
x = 3(y-4)/2
x = -3
what does answer on her sceen mean? 9e+10
Answer:
19e
Step-by-step explanation:
Please Help! I will give you the brainiest and a lot of points (If you give me an unreasonable answer or something this is obviously not related to the question I will report you and all of your posts (whether their related to my questions or not).
-You have to use the Hindu-Arabic number system
[tex]\qquad[/tex]2010_(nine)
[tex]\qquad[/tex]7716_(nine)
[tex]\qquad[/tex]+_________
[tex]\qquad[/tex]9726_(nine)
Keep nine stable and add the bases
if a + 1 by a is equal to 3 find the value of bracket a minus 1 by a bracket square
a+1 = 3
To find:(a - 1)^2
[tex] {a}^{2} - 2.a.b + {b}^{2} \\ \\ a - 2a + 1 \\ \\ 1 + 1 = 2[/tex]
So, the answer is 2Hope it help youPlease Help! I will give you a lot of points! You don't have to show your work unless you want to. Just the answer.
Answer:
52
Step-by-step explanation:
15+7+19+11+0=52
may help.
Convert into numbers
[tex]\\ \sf\longmapsto 15+7+19+13+11+0[/tex]
[tex]\\ \sf\longmapsto 22+32+11[/tex]
[tex]\\ \sf\longmapsto 55+11[/tex]
[tex]\\ \sf\longmapsto 66[/tex]
Given that
()=2(−3)2−8
f
(
x
)
=
2
(
x
−
3
)
2
−
8
, determine the true statement.
The x intercepts of the graph of f(x) are (1,0) and (5,0).
Group of answer choices
The range of f(x) is
≥−8
y
≥
−
8
.
The graph of f(x) is decreasing from
(3,∞)
(
3
,
∞
)
.
The graph of f(x) has a maximum point at (3, -8).
The domain of f(x) is
≥3
x
≥
3
Equations are used to show the relationship between variables (usually x and y). The true statement about f(x) is that the range of f(x) is [tex]y \ge -8[/tex]
Given that:
[tex]f(x) = 2(x - 2)^2 - 8[/tex]
To identify the true statement, I will make use of graphical method.
See attachment for the graph of [tex]f(x) = 2(x - 2)^2 - 8[/tex]
From the attached graph, we can see that the graph as a minimum at:
[tex](x,y) = (2,-8)[/tex]
And it opens upward.
This implies that the minimum y-value of f(x) is at -8, and it has no maximum.
In other words, the range of the function is:
[tex]f(x) \ge -8[/tex]
Hence, the true statement is option (a):
The range of f(x) is [tex]y \ge -8[/tex]
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Will three sides of any length create a triangle?
Which equation corresponds to the following word problem?
Cory spends $6.50 on snacks at a gas station. He also buys gas, which costs $2.78 per gallon. If he spends a total of $24.00 at the gas station, how many
gallons of gas did he buy? Let g equal the number of gallons of gas.
(1 point)
O 6.509 +2.78 = 24.00
O 2.789 -6.50 = 24.00
O 6.50g - 2.78 = 24.00
2.789 +6.50 = 24.00
Answer:
Cory bought 6.30 gallons of gas at the gas station.
Step-by-step explanation:
total amount = cost of snacks + amount spent on gas
[tex]$\$ 24.00=\$ 6.50+\$ 2.78 \mathrm{~g}$[/tex]
[tex]$\$ 2.78 \mathrm{~g}=\$ 24.00-\$ 6.50$[/tex]
[tex]$\$ 2.78 \mathrm{~g}=\$ 17.50$[/tex]
[tex]$g=\frac{\$ 17.50}{\$ 2.78}$[/tex]
[tex]$g=6.30$[/tex]
Learn more about gallon refer:
https://brainly.com/question/18591352Sandy can read 25 words in 5 seconds. At that
rate
Answer:
5 words a second because 5÷25 is 5 so in 1 second she reads 5 words
If mean of first 3 digits is 19 and next 2 digits is 18, what would be the mean of all 5 digits?
Mean of total 5 digits is 18.6
Given:
Mean of first 3 digit = 19
Mean of next 2 digit = 18
Find:
Mean of total 5 digits
Computation:
Sum of first 3 digit = Mean of first 3 digit × Number of digits
Sum of first 3 digit = 19 × 3
Sum of first 3 digit = 57
Sum of next 2 digit = Mean of first 3 digit × Number of digits
Sum of next 2 digit = 18 × 2
Sum of next 2 digit = 36
Total of 5 digit = Sum of first 3 digit + Sum of next 2 digit
Total of 5 digit = 57 + 36
Total of 5 digit = 93
Mean of total 5 digits = Total of 5 digit / 5
Mean of total 5 digits = 93 / 5
Mean of total 5 digits = 18.6
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The answer is "mean of all 5 digits is 18.6" and the further calculation can be defined as follows:
The mean would be the total number divided by the number of numbers. To obtain the mean, we add all the numbers and divide by number.It is also known as the "average" value, which was established by summing all data points then divided by the information gain amount.Its most popular statistics used to measure the center of a collection of data and analysis are the statistics sometimes referred to it as average by statistics.In this question, let the value are a,b,c..., and e So,Mean of 3 digits:
[tex]\to \bold{\frac{a+b+c}{3}}=19[/tex]
Mean of 2 digits:
[tex]\to \bold{\frac{d+e}{2}}=18[/tex]
Find:
Mean of all 5 digits =?
Calculating the sum of 3 digits:
[tex]\to \bold{\frac{a+b+c}{3}}=19\\\\\to \bold{a+b+c}=19 \times 3\\\\\to \bold{a+b+c}=57\\\\[/tex]
Calculating the sum of 2 digits:
[tex]\to \bold{\frac{d+e}{2}}=18\\\\\to \bold{d+e}=18\times 2\\\\\to \bold{d+e}=36\\\\[/tex]
Calculating the Mean of all 5 digits:
[tex]\to \bold{\frac{a+b+c+d+e}{5}}= \bold{\frac{57+36}{5}}[/tex]
[tex]= \bold{\frac{93}{5}}\\\\=\bold{18.6}[/tex]
So, the mean of all 5 digits is "18.6".
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If AB= x+4, BC=2x-10, and AC=2x+1, then find the value for x
Answer:
[tex] \boxed{x = 7} [/tex]
Step-by-step explanation:
Given:
AB = x + 4BC = 2x – 10AC = 2x + 1We can illustrate this relationship as:
(2x + 1)
___↑___
| |
A — B — C
|____|___|
↓ ↓
(x + 4) (2x – 10)
_______________________________
When you are given an algebraic expression for the length of a segment, you can solve for that value by knowing that the sum of two segments AB + BC = AC.
Thus:
(x + 4) + (2x – 10) = (2x + 1)
[Regroup terms]
(x + 2x) + (4 – 10) = (2x + 1)
[Simplify]
(3x – 6) = (2x + 1)
[subtract 2x from both sides to isolate the variable]
(3x – 6) – 2x = (2x + 1) – 2x
[Regroup terms]
(3x – 2x) – 6 = (2x – 2x) + 1
x – 6 = 1
[Add 6 to both sides to isolate the constant]
x – 6 + 6 = 1 + 6
[Simplify]
x = 7
The average yearly cumulative rainfall in Tucson by month is shown in the graph below. Does this
graph represent cumulative rainfall as a function of the day? Why or why not? What is the average
annual cumulative rainfall in Tucson? What is the approximate average rainfall in December? During
which month is average rainfall the greatest? How do you know?
Answer:
The average annual cumulative rainfall is [tex]1[/tex] inch per month.
During month of August average rain fall is greatest because slope in this month is maximum.
Step-by-step explanation:
The graph does not represent cumulative rainfall as a function of day.
Because they have average all values for month Total cumulative rainfall is [tex]12[/tex] inches.
Total period is [tex]12[/tex] month
So average annual cumulative rainfall is
[tex]$12 / 12=1$[/tex] inch per month
Average rain fall in month of December= (average cumulative rainfall in December[tex])-([/tex]average cumulative rainfall in November)
[tex]=12-11[/tex]
[tex]$=1$[/tex] inch
During month of August average rain fall is greatest because slope in this month is maximum.
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Erin is buying produce at a store. She buys c cucumbers at $0.69 each and a apples at $0.89 each. What does the expression 0.69c + 0.89a represent?
The expression represents the
(select)
.
Answer:
It represents the total amount that Erin is going to spend at the store.
Step-by-step explanation:
If x is an odd integer and y is a negative, odd integer, the product of x and y must be
Find the circumference of the circle. Use π ≈ 3.14 5cm
Answer:
31.4cm
Step-by-step explanation:
Use 2 pie r
Solve the equation for the specified variable.
S=CB-8. for C
C=
(Answer quickly)
Answer:
[tex]s = cB- 8 \\ cB = s + 8 \\ \\ c = \frac{s + 8}{B} \\ \\ c = \frac{s}{B} + \frac{8}{B} [/tex]
I hope I helped you^_^
pls someone edit it and send
Step-by-step explanation:
1 & 2 are on the attachment
3 --------------
4)4x+5=17
5x+5=20
5)2x+15+85+x+20=180
3x+120 =180-120
3x=60
x=20 degrees
6)son's age=x
3x+x=48
4x=48
x=12
Therefore; son's age=12 years old
Mr.Robert age=12*3
=36 years old
Hope this helps you
If you have any question just ask me
If you think this is the best answer please mark me as brainiest
[2+(12×3÷9)-6]÷4
with explanation
Answer:
PEMDAS:
ZERO 0
Left to right "p" parenthesis, "e" exponents,
"md" multiplication OR division , "as" addition or subtraction
Step-by-step explanation:
[2+(12×3÷9)-6]÷4
[2+(36÷9)-6]÷4
[2+(4)-6]÷4
[6-6]÷4
[0]÷4
0
Answer:
Ans: 0
Step-by-step explanation:
[2+(12×3÷9)-6]÷4
= [2+(36÷9)-6]÷4
= [2+4-6]÷4
= [6-6]÷4
= 0÷4
= 0
4= 2/9x. I need help anyone
Step-by-step explanation:
4×2= 9x
8/9=x
Transposition
Answer:
x = 8/9
Step-by-step explanation:
If you like my answer than please mark me brainliest thanks
What is the HCF of 25, 45
Answer:
5
Step-by-step explanation:
25 = 5 x 5
45 = 5 x 9
Hey there!
25: 1, 5, & 25
because: 5 * 5 = 25 & 1 * 25 = 25
45: 1, 3, 5, 9, 15, 45
because: 1 * 45 = 45, 3 * 15 = 45, & 5 * 9 = 45
Common factors: 1 & 5
The bigger number of those two is 5
Therefore, your possible answer is: 5
Good luck on your assignment and enjoy your day!
~Amphitrite1040:)
Complete the arithmetic sequence with its missing terms, then state the rate of change for the sequence.
92, _, _, _, 80
Answer:
89,86,83
Step-by-step explanation:
92-80=12
12÷4=3
80+3=83
83+3=86
86+3=89
The complete arithmetic sequence will be: 92, 89, 86, 83, and 80.
What is an arithmetic sequence?Let a₁ be the first term and d be a common difference.
Then the nth term of the arithmetic sequence is given as;
aₙ = a₁ + (n - 1)d
Given; The first term (a₁) is 92 and the fifth term (a₅) is 80.
Then the common difference between the terms will be given as;
a₅ = a₁ + (5 - 1)d
80 = 92 + 4d
-12 = 4d
d = -3
Then the missing terms will be
92, 92 - 3, 92 - 6, 92 - 9, and 92 - 12
92, 89, 86, 83, and 80
Hence, the complete arithmetic sequence will be: 92, 89, 86, 83, and 80.
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