Answer:
[tex]<-144e^{0.88},7.47e^{0.88}>[/tex]
Step-by-step explanation:
We are given that
[tex]f(u,v)=n^2e^{\frac{u+n}{v+n}}[/tex]
Point=(3,5)
n=12
We have to find the direction at which he moves down the hills quickly.
[tex]f(u,v)=144e^{\frac{u+12}{v+12}}[/tex]
[tex]f_u(u,v)=144e^{\frac{u+12}{v+12}}[/tex]
[tex]f_u(3,5)=144e^{\frac{3+12}{5+12}}[/tex]
[tex]f_u(3,5)=144e^{\frac{15}{17}}=144e^{0.88}[/tex]
[tex]f_v(u,v)=144e^{\frac{u+12}{v+12}}\times (-\frac{u+12}{(v+12)^2})[/tex]
[tex]f_v(3,5)=144e^{\frac{15}{17}}(-\frac{15}{(17)^2}[/tex]
[tex]f_v(3,5)=-\frac{2160}{289}e^{\frac{15}{17}}=-7.47e^{0.88}[/tex]
[tex]\Delta f(3,5)=<f_u(3,5),f_v(3,5)>[/tex]
[tex]\Delta f(3,5)=<144e^{0.88},-7.47e^{0.88}>[/tex]
The direction at which he moves down the hills quickly=-[tex]\Delta f(3,5)[/tex]
The direction at which he moves down the hills quickly=[tex]<-144e^{0.88},7.47e^{0.88}>[/tex]
on a particular day, a man spent 12 minutes more driving to his office than driving home. His average speed from home to office is 12km/h and from office to home is 60m/h .How far is the man home to his office
Answer:
distance between home and office = 3 km
Step-by-step explanation:
With an x intercept of 4 and a y intercept of -1.5. Find the equation of the line
The equation of the line is.
y = (3/8)*x - 1.5
A general linear relationship can be written as:
y = a*x + b
Where a is the slope, and b is the y-intercept.
If the line passes through the points (x₁, y₁) and (x₂, y₂), we can write the slope as:
a = ( y₂ - y₁)/(x₂- x₁)
We define the y-intercept and the x-intercept as the points where the graph intersects the y-axis or the x-axis correspondingly.
Here we know that the x-intercept is 4, or we can write this as (4, 0)
we also know that the y-intercept is -1.5, or we can write this as (0, -1.5)
So we know two points of the line, this means that we can find the slope of the line:
a = (-1.5 - 0)/(0 - 4) = (1.5)/(4) = (3/2)*(1/4) = 3/8
Then the line is:
y = (3/8)*x + b
And remember that b is the y-intercept, which we know is equal to -1.5, so we can just replace it:
Then the equation of the line is.
y = (3/8)*x - 1.5
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The population of Americans age 55 and older as a percentage of the total population is approximated by the function f(t) = 10.72(0.9t + 10)^0.3 (0 <= t < = 20)
where t is measured in years, with t=0 corresponding to the year 2000.
Required:
a. At what rate was the percentage of Americans age 55 and older changing at the beginning of 2002?
b. At what rate will the percentage of Americans age 55 and older be changing in 2017?
c. What will be the percentage of the population of Americans age 55 and older in 2017?
Answer:
Part A)
About 0.51% per year.
Part B)
About 0.30% per year.
Part C)
About 28.26%.
Step-by-step explanation:
We are given that the population of Americans age 55 and older as a percentange of the total population is approximated by the function:
[tex]f(t) = 10.72(0.9t+10)^{0.3}\text{ where } 0 \leq t \leq 20[/tex]
Where t is measured in years with t = 0 being the year 2000.
Part A)
Recall that the rate of change of a function at a point is given by its derivative. Thus, find the derivative of our function:
[tex]\displaystyle f'(t) = \frac{d}{dt} \left[ 10.72\left(0.9t+10\right)^{0.3}\right][/tex]
Rewrite:
[tex]\displaystyle f'(t) = 10.72\frac{d}{dt} \left[(0.9t+10)^{0.3}\right][/tex]
We can use the chain rule. Recall that:
[tex]\displaystyle \frac{d}{dx} [u(v(x))] = u'(v(x)) \cdot v'(x)[/tex]
Let:
[tex]\displaystyle u(t) = t^{0.3}\text{ and } v(t) = 0.9t+10 \text{ (so } u(v(t)) = (0.9t+10)^{0.3}\text{)}[/tex]
Then from the Power Rule:
[tex]\displaystyle u'(t) = 0.3t^{-0.7}\text{ and } v'(t) = 0.9[/tex]
Thus:
[tex]\displaystyle \frac{d}{dt}\left[(0.9t+10)^{0.3}\right]= 0.3(0.9t+10)^{-0.7}\cdot 0.9[/tex]
Substitute:
[tex]\displaystyle f'(t) = 10.72\left( 0.3(0.9t+10)^{-0.7}\cdot 0.9 \right)[/tex]
And simplify:
[tex]\displaystyle f'(t) = 2.8944(0.9t+10)^{-0.7}[/tex]
For 2002, t = 2. Then the rate at which the percentage is changing will be:
[tex]\displaystyle f'(2) = 2.8944(0.9(2)+10)^{-0.7} = 0.5143...\approx 0.51[/tex]
Contextually, this means the percentage is increasing by about 0.51% per year.
Part B)
Evaluate f'(t) when t = 17. This yields:
[tex]\displaystyle f'(17) = 2.8944(0.9(17)+10)^{-0.7} =0.3015...\approx 0.30[/tex]
Contextually, this means the percetange is increasing by about 0.30% per year.
Part C)
For this question, we will simply use the original function since it outputs the percentage of the American population 55 and older. Thus, evaluate f(t) when t = 17:
[tex]\displaystyle f(17) = 10.72(0.9(17)+10)^{0.3}=28.2573...\approx 28.26[/tex]
So, about 28.26% of the American population in 2017 are age 55 and older.
Infues Gentamicin 100 mg in 100ml in 15 minutes. What will you set the infusion pump at ml/hr
9514 1404 393
Answer:
400 mL/h
Step-by-step explanation:
The required rate is ...
(100 mL)/(1/4 h) = 100×(4/1) mL/h = 400 mL/h
4(x+4) =2x-1
8
Show work
Answer:
4(x+4) =2x-18
4x+16=2x‐18
4x–2x= –18 –16
2x= – 34
x= –34/2
x= – 17
I hope I helped you^_^
Step-by-step explanation:
[tex]thank \: you[/tex]
plez halppp mehh ;-;
Answer:
False
True
True
Step-by-step explanation:
Angle 1 cannot be equal to angle 4. Even by just viewing one can see that they can't be equal.
Angle 1 and 2 when combined give a 90 degree angle going from a to c.
Angle 3 and 4 form a 180 degree angle.
HOPE THIS HELPED
Find f (3) for the following function:
f (x) = 4x+3/x^2
Answer: [tex]12.333[/tex] or [tex]12\frac{1}{3}[/tex] or [tex]\frac{37}{3}[/tex]
Step-by-step explanation:
Replace every x with (3)
[tex]f(x) = 4x+3/x^2\\f(3) = 4(3)+3/3^2\\f(3) = 12+3/9\\f(3) = 12.333 or 12\frac{3}{9}or \frac{111}{9}\\f(3) = 12.333 or 12\frac{1}{3} or \frac{37}{3}[/tex]
150 is 40% of what number
Step-by-step explanation:
hope it helps youu.........
Convert the following equation
into standard form.
y = 7 - 7x
[?]x + y = []
Answer:
[tex]y = 7 - 7x \\ y + 7x = 7 \\ 7x + y = 7[/tex]
Answer:
7x + y = 7
Step-by-step explanation:
The equation of a line in standard form is
Ax + By = C ( A is a positive integer and B, C are integers )
Given
y = 7 - 7x ( add 7x to both sides )
7x + y = 7 ← in standard form
hhheeeeeelllllllppppp meeee plzz
Answer:
I believe it is A
Step-by-step explanation:
Which one of the following graphs is the graph of f(x) = 1∕4x2 + 3?
Answer:
A
f(x) = 1/4 x^2 + 3
Resultado
f(x) = x^2/4 + 3
x^2 + 12 = 4 f(x)
Forma alternativa
f(x) = 1/4 (x^2 + 12)
Raíces complejas
x = -2 i sqrt(3)
x = 2 i sqrt(3)
17. Complete the following equation using <, >, or =
7 __ 24/2
A. >
B. <
C. =
Complete the coordinate table for the given equation.
Xy=-4
Step-by-step explanation:
X= -4,-2,2,4 (respectively)
Y=4,-4 (respectively)
hope it helps
Please help me with this, But I can’t decide if it’s A or B. Please explain !!!
I think it's the letter A.
Answer:
[tex]m=\frac{M}{\sqrt{1-\frac{v^{2} }{c^{2} } } } \\\\\\m{\sqrt{1-\frac{v^{2} }{c^{2} } }=M[/tex]
[tex]\sqrt{1-\frac{v^{2} }{c^{2} }} =\frac{M}{m} \\\\\\1-\frac{v^{2} }{c^{2} }=\frac{M^{2}}{m^{2}} \\\\\\-\frac{v^{2} }{c^{2} }=\frac{M^{2}}{m^{2}} -1\\\\v^{2}=(-c^{2}) (\frac{M^{2}}{m^{2}} -1)\\\\v=\sqrt{(-c^{2}) (\frac{M^{2}}{m^{2}} -1)} =\sqrt{(c^{2})(-1)(\frac{M^{2}}{m^{2}} -1)} =c\sqrt{(-1)(\frac{M^{2}}{m^{2}} -1)} =c\sqrt{1-\frac{M^{2}}{m^{2}}}[/tex]
I would think it's A ¯\_ (ツ)_/¯
A rectangle has a perimeter equal to 24 if we consider its width x how could we talk about its length y in terms of x what are the possible values of x what aree the possible values of y
2x + 2y must equal 24. 24 - 2x = 2y and 24 - 2y = 2x. Therefore, 12 - y = x. x could be able to add with y to get 12.
example: x = 4, y = 8. (4 + 4 + 8 + 8 = 16 + 8 = 24)
x = 9, y = 3. (9 + 9 + 3 + 3 = 24)
x = 5, y = 7. (5 + 5 + 7 + 7 = 24)
There is a path of width 2.5 m inside around a square garden of length 45m.
(a) Find the area of the path.
(b) How many tiles will be required to pave in the path by the square tiles of length 0.5m? Find it.
Help ! 도와주세요, 제발 :(
Answer:
2.5+2.5+45+45
=95.0m
therefore area of the square= 95.0m
45m×0.5=45.5÷95=
Step-by-step explanation:
2.5m
2.5 m tiles are required
[tex]area = 2.5 \times 45 = 192.5 \: squared \: cenimetre \\ \\ no \: of \: tiles = 0.5 \times 0.5 = 0.25 \\ 192.5 \div 0.25 = 770tiles[/tex]
√10 Multiple √15 is equal to
(a) 6√5
(b) √30
(c) √25
step by step
Solve :-
dont answer stantham
[tex]\\ \sf\longmapsto \sqrt{10}\times \sqrt{15}[/tex]
[tex]\\ \sf\longmapsto \sqrt{10\times 15}[/tex]
[tex]\\ \sf\longmapsto \sqrt{2\times 5\times 3\times 5}[/tex]
[tex]\\ \sf\longmapsto \sqrt{5\times 5\times 6}[/tex]
[tex]\\ \sf\longmapsto 5\sqrt{6}[/tex]
None of the above should be 4th option
A family has a day of 7 activities planned: shopping, picnic, hiking, swimming, bike ride, video games, and movie. To make it more adventurous they decide to randomly pick the order of the activities out of a hat. Find the probability that bike ride and movie are chosen consecutively, in either order.
Answer:
[tex]Pr= \frac{1}{21}[/tex]
Step-by-step explanation:
Given
[tex]n(S) = 7[/tex] --- number of games
Required
Probability of bike and movie in consecutive order
This probability is represented as:
[tex]Pr = P(Bike\ and\ Movie) \ or\ P(Movie\ or\ Bike)[/tex]
So, we have:
[tex]Pr = P(Bike\ and\ Movie) \ +\ P(Movie\ or\ Bike)[/tex]
The probability is an illustration of selection without replacement;
So, we have:
[tex]P(Bike\ and\ Movie) = P(Bike) * P(Movie)[/tex]
[tex]P(Bike\ and\ Movie) = \frac{n(Bike)}{n(S)} * \frac{n(Movie)}{n(S) - 1}[/tex] ---- without replacement
Bike and Movie appear in the game list 1 time.
So, the equation becomes
[tex]P(Bike\ and\ Movie) = \frac{1}{7} * \frac{1}{7 - 1}[/tex]
[tex]P(Bike\ and\ Movie) = \frac{1}{7} * \frac{1}{6}[/tex]
[tex]P(Bike\ and\ Movie) = \frac{1}{42}[/tex]
Similarly,
[tex]P(Movie\ and\ Bike) = \frac{1}{42}[/tex]
So, we have:
[tex]Pr = P(Bike\ and\ Movie) \ +\ P(Movie\ or\ Bike)[/tex]
[tex]Pr= \frac{1}{42}+\frac{1}{42}[/tex]
Take LCM
[tex]Pr= \frac{1+1}{42}[/tex]
[tex]Pr= \frac{2}{42}[/tex]
[tex]Pr= \frac{1}{21}[/tex]
Given: AABC, AC = 5
m C = 90°
m A= 22°
Find: Perimeter of AABC
A
C
B
9514 1404 393
Answer:
perimeter ≈ 12.4 units
Step-by-step explanation:
The side adjacent to the angle is given. The relationships useful for the other two sides are ...
Tan = Opposite/Adjacent
Cos = Adjacent/Hypotenuse
From these, we have ...
opposite = 5·tan(22°) ≈ 2.02
hypotenuse = 5/cos(22°) ≈ 5.39
Then the perimeter is ...
P = a + b + c = 2.02 + 5 + 5.39 = 12.41
The perimeter of ∆ABC is about 12.4 units.
solve for x ! please help . (show work)
Answer:
x = -3
Step-by-step explanation:
12 - 4x-5x = 39
Combine like terms
12 - 9x = 39
subtract 12 from each side
12 -9x-12 = 39-12
-9x = 27
Divide by -9
-9x/-9 = 27/-9
x = -3
Can someone help me solve this and explain how to solve if possible please?
how many wall are there in your room? what are the shape of the floor and ceiling in your room ? how can you find the area of each shape?prepare the answer. present the conclusion in the form of report. plz answer the question in right.how many wall are there in your room? what are the shape of the floor and ceiling in your room ? how can you find the area of each shape?prepare the answer. present the conclusion in the form of report. plz answer the question in right. plz answer the question steps by step.
Question 6 of 11 Step 1 of 6 No Time Limit The table below gives the list price and the number of bids received for five randomly selected items sold through online auctions. Using this data, consider the equation of the regression line, û = bo + bjx, for predicting the number of bids an item will receive based on the list price. Keep in mind, the correlation coefficient may or may not be statistically significant for the data given. Remember, in practice, it would not be appropriate to use the regression line to make a prediction if the correlation coefficient is not statistically significant.
Price in Dollars 23 34 44 46 50
Number of Bids 1 2 4 9 10
Step 1 of 6: Find the estimated slope. Round your answer to three decimal places.
The estimated slope is approximately 2.344
The given table is presented as follows;
[tex]\begin{array}{ccc}Number \ of Bids &&Price \ in \ Dollars\\1&&23\\2&&34\\4&&44\\9&&46\\10&&50\end{array}[/tex]
The regression line formula to be considered = [tex]\bar u = b_0 + b\cdot \bar x[/tex]
The required parameter is;
The estimated slope
The method to find the estimate slope;
The least squares regression formula (method) is presented as follows;
[tex]\bar u = b_0 + b\cdot \bar x[/tex]
Where;
b₀ = The y-intercept
[tex]\mathbf{ b = \dfrac{\sum \left(x_i - \bar x\right) \times \left(u_i - \bar u\right) }{\sum \left(x_i - \bar x\right )^2 } = The \ estimated \ slope}[/tex]
From MS Excel, we have;
[tex]\bar x[/tex] = 5.2, [tex]\bar u[/tex] = 39.4
[tex]\sum \left(x_i - \bar x\right) \times \left(u_i - \bar u\right)[/tex] = 156.6
[tex]{\sum \left(x_i - \bar x\right )^2 }[/tex] = 66.8
Therefore;
The estimated slope, b = 156.6/66.8 ≈ 2.344 (by rounding the answer to three decimal places)
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The recursive formula for a geometric sequence is given below.
f(1) = 5
(n) = 3 . f(n − 1), for n > 2
What is the 7th term in the sequence?
Answer:
3645
Step-by-step explanation:
f(1)=5
f(2)=3*5=15.
f(3)=45, basically it's a geometric sequence with formula an=5*(3)^(n-1). The 7th term is 5*(3)^6=3645
Determine whether the integral is divergent or convergent. If it is convergent, evaluate it.
[infinity]
â« e^-1.3x dx
1
Find the 100th term of the sequence 4, 7, 10, 13...
a) 301
b) 313
c) 281
d) 279
Answer:
A
Step-by-step explanation:
The first term of the sequence is 4, the common difference is 3. So the equation of this sequence is 4+(n-1)*3 or 1+3*n. Plug in n=100
The cylinders shown are similar. What is the volume of the larger cylinder?
Step-by-step explanation:
Ratio of height (large to small) = ratio of radii (large to small).
(h / 14) = (8 / 2)
h / 14 = 4
h = 56
The height of the larger cylinder is 56m.
Volume of cylinder is
V = πr2h
V = π(8)2(56)
V = 3584π
Show that Reſiz) = -Im(z)
Step-by-step explanation:
[tex]re(i(x + yi) = - im(x + yi) \\ re(xi - y) = - im(x + yi) \\ - y = - (y) \\ - y = - y \\ proved \: is \: correct[/tex]
Simplify the following expression.
3(2k + 3) -8k + 5 + 5
Answer:
Step-by-step explanation:
3*(2k + 3) - 8k + 5 + 5 Remove the brackets on the left
6k + 9 - 8k + 5 + 5 Combine like terms
6k-8k+9 + 5 + 5
-2k + 19
Select the correct answer from each drop-down menu.
The table represents function f, and the graph represents function g.
-2
- 1
1
2
3
4
0
х
Ax)
7
0
-5
-8
-9
-8
-5
у
A
6
4
2
g
X
.
-21
2
2
The line of symmetry for function fis
and the line of symmetry for function gis
The y-intercept of function fis
the y-intercept of function g.
Over the interval [2, 4], the average rate of change of function fis
the average rate of change of function g.
Answer:
Line of symmetry of f is x=2 and the line of symmetry for function g is x=1 as the graph starts repeating itself after x=1. Y intercept is the point at which x is 0, for f it is - 5 and for g it is - 6. Rate of change in interval [2,4] is given by (f(4)-f(2))/2=2 for f and for g it is, (g(4)-g(2))/2=-4
The true statements are:
The line of symmetry for function f is x = 2The line of symmetry for function g is x = 1The y-intercept of function f is -5The y-intercept of function g is -6Over the interval [2, 4], the average rate of change of function f is half the average rate of change of function g.Line of SymmetryThis is the point where the function is divided into equal halves.
From the figure, the table and graph are divided at points x = 2, and x = 1.
So, the line of symmetry for function f is x = 2 and the line of symmetry for function g is x = 1
Y-InterceptThis is the point where the function has an x value of 0
From the figure, the y values when x = 0 are -5 and -6
So, the y-intercept of function f is -5 and the y-intercept of function g is -6
Average rate of changeThis is calculated as:
[tex]m = \frac{y_2 - y_1}{x_2 -x_1}[/tex]
For function f, we have:
[tex]m = \frac{-5 + 9}{4-2}[/tex]
[tex]m = \frac{4}{2}[/tex]
[tex]m = 2[/tex]
For function g, we have:
[tex]m = \frac{2+ 6}{4-2}[/tex]
[tex]m = \frac{8}{2}[/tex]
[tex]m = 4[/tex]
By comparison,
[tex]m_f = 0.5 \times m_g[/tex]
Hence, over the interval [2, 4], the average rate of change of function f is half the average rate of change of function g.
Read more about functions and graphs at:
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