Answer:
To find Rs(1,0) and Rt(1,0), we need to use the chain rule of partial differentiation.
Rs(1,0) can be found by computing the partial derivative of R with respect to s, while holding t constant and then evaluating the result at (1,0). Similarly, Rt(1,0) can be found by computing the partial derivative of R with respect to t, while holding s constant and then evaluating the result at (1,0).
Using the chain rule, we have:
Rs = Fu * us + Fv * vs
Rt = Fu * ut + Fv * vt
We are given the values of u, v, us, ut, vs, vt, Fu, and Fv at the point (1,0) and the values of u and v at the point (2,3). We can use these values to compute Rs(1,0) and Rt(1,0) as follows:
Rs(1,0) = Fu(2,3) * us(1,0) + Fv(2,3) * vs(1,0)
= (-1) * (-2) + (10) * (5)
= 52
Rt(1,0) = Fu(2,3) * ut(1,0) + Fv(2,3) * vt(1,0)
= (-1) * (6) + (10) * (4)
= 34
Therefore, Rs(1,0) = 52 and Rt(1,0) = 34
the equation of a circle is (x-3)^2 + (y-2)^2 = 4. the circle is translated 2 units to the right and 4 units up and then is dilated by a factor of 3. what is the equation of the new circle
Answer:
The equation of the new circle will be x^2 - 10x + y^2 - 12y + 25 = 0.
Step-by-step explanation:
The triangle below is isosceles. Find the length of side & in simplest radical form with
a rational denominator
Answer: x = 10[tex]\sqrt{2}[/tex]
Step-by-step explanation:
We are given that this is an isosceles triangle and the little box represents 90 degrees. This means that both the "legs" of the triangle are equal to 10 and the hypotenuse is equal to x. Since this is a right triangle, we can use the Pythagorean theorem to solve.
a² + b² = x²
10² + 10² = x²
100 + 100 = x²
200 = x²
[tex]\sqrt{200}[/tex] = x
x = [tex]\sqrt{200}[/tex]
x = [tex]\sqrt{2*100}[/tex]
x = 10[tex]\sqrt{2}[/tex]
Greg had a full carton of eggs. He used 1 over 3 of the eggs for a cake. Then he used 1 egg for an omelet.
a population of 240 birds increases at a rate of 16% annually. jemel writes an exponential function of the form f(x)=ab^x to represent the number of birds after x years. which values should she use for a and b?
To find the values of a and b, we need to use the given information about the population and the growth rate.
At the start (x=0), the population is 240 birds. This means that f(0) = 240, which gives us the value of a in the function:
f(0) = ab^0 = a = 240
Next, we need to find the value of b. We know that the population increases at a rate of 16% annually, which means that it grows by a factor of 1.16 each year. In other words, b = 1.16.
Therefore, the exponential function that represents the number of birds after x years is:
f(x) = 240(1.16)^x
Note that the value of b is greater than 1, which means that the function represents exponential growth.
Answer:
Step-by-step explanation:
To find the values of a and b in the exponential function, we need to use the given information about the population growth rate.
The formula for exponential growth is:
f(x) = a * (1 + r)^x
where:
a = initial value
r = growth rate
x = time
In this case, we know that the initial population is 240 birds and the growth rate is 16% per year. We can convert the percentage to a decimal by dividing by 100:
r = 16% / 100 = 0.16
Now we can plug in the values we have:
f(x) = a * (1 + r)^x
f(x) = 240 * (1 + 0.16)^x
Simplifying:
f(x) = 240 * 1.16^x
So the values for a and b are:
a = 240
b = 1.16
Enrique has 1 gallon of milk and 1 pint
of orange juice in his refrigerator. How
many cups of milk and orange juice does
Enrique have in all?
Enrique has 16 cups of milk and 2 cups of orange juice, making a total of 18 cups of liquid in all.
What is the total number of cups?The number of cups of milk and orange juice Enrique have in all is calculated by converting the gallon of milk and the pint of orange juice in unit of cup as shown below;
For the gallon of milk:
1 gallon of milk = 1 gallon x 16 cups/gallon
= 16 cups
For the pint of orange juice:
1 pint of orange juice = 1 pint x 2 cups/pint
= 2 cups
Total number of cups = 16 cups + 2 cups = 18 cups
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Lori made a cake her brother ate 3/4 of it what decimal repesents 3/4
Answer:
0.75
Step-by-step explanation:
Vanessa uses the expressions (3x2 + 5x + 10) and (x2 – 3x – 1) to represent the length and width of her patio. Which expression represents the area (lw) of Vanessa’s patio?
The area of Vanessa's patio is represented by the expression 3x⁴ - 4x³ - 13x² + 35x + 10, which is obtained by multiplying the expressions representing the length and width.
To find the area of Vanessa's patio, we need to multiply the expressions representing the length and width.
Length = 3x² + 5x + 10
Width = x² - 3x - 1
Area = Length x Width
Area = (3x² + 5x + 10)(x² - 3x - 1)
To multiply these expressions, we can use the distributive property and then simplify
Area = 3x⁴ - 4x³ - 13x² + 35x + 10
Therefore, the expression that represents the area of Vanessa's patio is 3x⁴ - 4x³ - 13x² + 35x + 10.
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1/5logx-log1000=3 how do I solve this question please
Having simplified the above equation, the solution to the expression x = 10³⁰
How did we arrive at that ?We can simplify the equation using logarithmic rules
1/5 log x - log 1000 = 3
log[tex]x^{1/5}[/tex] - log 1000 = 3
log ([tex]x^{1/5}[/tex] /1000) = 3
[tex]x^{1/5}[/tex] /1000 = 10³
[tex]x^{1/5}[/tex]= 1000 * 10³
[tex]x^{1/5}[/tex] = 10⁶
x = (10⁶)⁵
x = 10³⁰
Therefore, the solution to the equation is x = 10³⁰
Note that the logarithm is the inverse function of exponentiation in mathematics. That is, the exponent to which b must be increased to obtain x is the logarithm of a number x to the base b. For example, since 1000 = 10³, 1000's logarithm base 10 is 3, or log₁₀ = 3.
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Function (g) can be thought of as a scaled version of f(x)=x^2
Write an equation for g(x).
The equation for the scaled version of the function f(x) = x² is g(x) = a × x²
The function g(x) can be considered a scaled version of the function f(x) = x². To create a scaled version of a function, we can multiply the original function by a scaling factor. Let's call this scaling factor "a." Now, the equation for g(x) can be written as:
g(x) = a ₓ f(x)
Since f(x) = x², we can substitute it into the equation for g(x):
g(x) = a ₓ x^2
In this equation, "a" represents the scaling factor. If "a" is greater than 1, the function g(x) will stretch vertically, meaning its parabola will be more narrow compared to f(x). If "a" is between 0 and 1, the function g(x) will be compressed vertically, resulting in a wider parabola. If "a" is negative, the parabola will be reflected over the x-axis.
In summary, the equation for the scaled version of the function f(x) = x² is g(x) = a × x², where "a" is the scaling factor. Depending on the value of "a," the resulting parabola will be either stretched or compressed vertically, and may be reflected over the x-axis if "a" is negative.
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suppose i have an organization that has 60 people, 35 are women and 25 are men. we need to select a committee of 11 people. how many ways can such a committee be formed? question 4 options:
There are 342,700,125,300 ( or 60C11 ) ways of selecting 11 members for a committee from organization of 60 member by applying Combinations.
There are 60 people in total in my organisation where there are 35 women and 25 men.
A committee is to be formed where we need to select 11 people from 60 people of the organization.
The total number of ways the commicommittee can be formed is calculated with the help of combinations and permutations.
Since we are not specified that there will be some order in selection of committee members so we can assume that there is no such order.
Therefore, we apply the formula of combinations as the order of items does not matter in case of combinations.
Number of ways the committee can be formed is = nCr = [tex]\frac{n!}{(n-r)!(r!)}[/tex]
where, n is the total number of people in the organization and r is the number of people we require in the committee.
Thus, Number of ways the committee can be formed is = 60C11
= [tex]\frac{60!}{(60- 11)!(11!)}[/tex]
= 342,700,125,300
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A negative change on the y value moves the image up or down?
The negative change in the y value will shift the graph downwards.
When a graph of a figure or a point get a negative change in its y value it gets shifted downwards.
When, f(x) - a is f(x) shifted downward a units.
Ex. Shift 3 units down,
Before
y = x² +x, Point (x, y)
After
y = x² +x -3, Point (x, y-3)
Hence, the negative change in the y value will shift the graph downwards.
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what is 40 divided 180
the answer to 40 divided by 180 is 4.5
Math lib equations of circles
The equation of the circle is given by
A. (x - 2)² + y² = 234How to determine the equation of a circleInformation given in the question
coordinates of the diameter (17, -3) and (-13, 3)
The equation of circle. is given according t the formula
(x - h)²+ (y - k)² = r²
where
h and k refers to points at the center,
Points at the center is solved by
x-coordinate (h)
= (17 + (-13)) / 2
= 4 / 2
= 2
y-coordinate (k)
= (-3 + 3) / 2
= 0 / 2
= 0
So, the center of the circle is (2, 0).
comparing with the given options only A has centers as (2, 0) hence option A is the best choice
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The points U (2,-5), V (6, 2), W (–1,6),
and X (-5, -1) form quadrilateral UVWX.
Plot the points then click the "Graph
Quadrilateral" button.
The quadrilateral is plotted on the graph
Given data ,
Let the quadrilateral be represented as UVWX
Now , the coordinates of the quadrilateral are
U (2,-5), V (6, 2), W (-1,6) and X (-5, -1)
Now , the distance between the points is given by the distance formula ,
Distance D = √ ( x₂ - x₁ )² + ( y₂ - y₁ )²
D = √ ( 6 - 2 )² + ( -5 -2 )²
D = √ ( 4 )² + ( 7 )²
D = √ ( 16 + 49 )
D = √65 units
And , the distance between VW is given by
D = √ ( 6 + 1 )² + ( 2 - 6 )²
D = √ ( 7 )² + ( 4 )²
D = √ ( 16 + 49 )
D = √65 units
Hence , the quadrilateral is a square
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Aisha Brewer’s checking account has a balance of $523.45. She has a check for $435.62 and a check for $65.98. She would like to receive $40 in cash and deposit the rest of the money in her checking account. What is Aisha’s total deposit and what will her checking balance be?
Answer:
Total deposit: $501.6
Total Balance: $985.05
Step-by-step explanation:
Aisha's original total is 523.45. Since she is depositing a check for $435.62 and a check for 65.98, you add both check totals to the original balance, by lining up the numbers and adding down the line. This will be the total deposit:
435.62
+ 65.98
=
$501.6
$501.6 is the total deposit. To find the total checking balance, add the total deposit to $523.45.
523.45
+501.6
=
1025.05
This is her total balance before Aisha receives $40.
Next, you subtract what she wants to deposit, $40, since she is taking $40 out of her checking account.
1025.05
- 40.00
=
985.05
The total checking balance is $985.05
. determine whether the integers in each of these sets are pairwise relatively prime. a) 11, 15, 19 b) 14, 15, 21 c) 12, 17, 31, 37 d) 7, 8, 9, 1
The integers that are pairwise relative are;
(a) 11, 15, 19
(c) 12, 17, 31, 37
(d) 7, 8, 9, 1
Which integers are pairwise relative?To determine if the integers are pairwise relative, their greatest common divisor (GCD) must be 1.
(a) for first question;
11, 15, 19 have no common factor, so they meet the condition.
(b) for second question; 14, 15, 21
14, 15, 21, 14 and 21 have a common factor of 7, so these integers are not pairwise relative.
(c) for 12, 17, 31, 37, no common factor
(d) for 7, 8, 9, 1, no common factor other than 1.
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The table shows changes in the number of subscribers to a community newsletter over a six-month period. Change in the Number of Subscribers: +8 +6 -12 +5 -9 -10
a) What was the mean change per month in the number of subscribers?
b) There were 207 subscribers at the beginning of this period. How many were there at the end?
It takes Tim 4.5 hours to run 50 kilometers. Which expression will
allow him to change this rate to minutes per mile?
Answer:
To change Tim's running rate from kilometers per hour to minutes per mile, we need to use unit conversion factors.
First, we need to convert the distance from kilometers to miles. One kilometer is equal to 0.621371 miles. Therefore, 50 kilometers is equal to:
50 km * 0.621371 mi/km = 31.06855 miles
Next, we need to convert the time from hours to minutes. One hour is equal to 60 minutes. Therefore, 4.5 hours is equal to:
4.5 hours * 60 min/hour = 270 minutes
Now, we can calculate Tim's running rate in minutes per mile by dividing the time by the distance:
270 min / 31.06855 miles = 8.69805 minutes per mile
So the expression that will allow Tim to change his running rate to minutes per mile is:
(4.5 hours * 60 min/hour) / (50 km * 0.621371 mi/km)
Step-by-step explanation:
duh
worth 20pointsss
find the circumference of a circle with d=97cm diameter
round to 3 significant figure
The required circumference of the circle with a diameter of 97 cm is 304 cm.
The circumference of a circle can be calculated using the formula:
C = πd
Where 'd' is the diameter of the circle, and 'π' is a mathematical constant approximately equal to 3.14159.
In this case, the diameter of the circle is given as 97 cm. So we can substitute this value into the formula to get:
C = πd
C = π(97 cm)
C ≈ 304.35 cm
Rounding this answer to 3 significant figures gives:
C ≈ 304 cm
Therefore, the circumference of the circle with a diameter of 97 cm is 304 cm.
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Pls I really need help
Answer:
Step-by-step explanation:
D. possible angle is 60 degrees out out 360
60/360 = .1666 = 16.7%
P(D)=16.7%
P(B or C) = (30+90)/360 = .333 =33.3% Or means add your probabilities
P(A)=180/360=.5 = 50.0%
P(not A)= 180/360=.5= 50.0%
A submarine starts moving down in water at the rate of 6metre per minute. After some time it reaches a depth of 60metre. How will this distance be represented. ? How much time will the submarine take to reach this level?
Answer: It moves 60 metres in 60/6 mins, or 10 minutes. Speed is calculated as follows: speed = distance * time. Knowing the units for distance and time is necessary to calculate the units for speed
Step-by-step explanation: 10 is your answer
Hope this helps
brainliest?
a scientist listed the volumes, in milliliters, of some liquids used in an experiment.
1.23
1.078
1.203
1.17
which choice correctly compares the volumes, in milliliters of two of these liquids.
A) 1.23 < 1.203
B) 1.078 >1.17
C) 1.17 >1.203
D) 1.078 < 1.23
The choice correctly compares the volumes, in milliliters of two of these liquids is,
⇒ 1.078 < 1.23
We have to given that;
A scientist listed the volumes, in milliliters, of some liquids used in an experiment.
1.23
1.078
1.203
1.17
Now, We get;
By all the options;
⇒ 1.078 < 1.23
Thus, The choice correctly compares the volumes, in milliliters of two of these liquids is,
⇒ 1.078 < 1.23
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May you please Simplify 15/365? If you can't it's okay. If you can Thank you
The fraction 15/365 has been simplified as 3/73.
In the fraction 15/365, the numerator is 15, and the denominator is 365. The numerator represents the number of parts we're interested in, and the denominator represents the total number of parts in the group. So, in this case, we're interested in 15 parts out of a group of 365.
To simplify this fraction, we need to find a common factor of the numerator and the denominator that we can divide both by. In this case, 5 is a common factor of both 15 and 365. Dividing both by 5 gives us:
15/365 = (15 ÷ 5) / (365 ÷ 5) = 3/73
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how do you find the volume of a hexagonal prism?
Answer:
V =base area × height or [(3√3)/2]a2h
where
a = base length
h = height of the prism
Step-by-step explanation:
4% sales tax on the sale of an article is ₹2. What is the amount of sale
Add the following expressions: 2.1 2a + 3b; 4a - 8b
The addition of the given expression will gives 6a - 5b
Since we know that numerical expression is an algebraic information stated in the form of numbers and variables that are unknown.
WE are given the expression as;
2a + 3b; 4a - 8b
We need to add the expression so,
2a + 3b + 4a - 8b
Combine the like terms then we get;
2a + 4a + 3b - 8b
6a - 5b
The simplification of the given expression will be 6a - 5b.
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A laptop has 2 year warranty. The moon lifespan of the laptop is 3.8 years, with a standart deviation of 0.58 years.
If a store sells 5000 laptops. How many of these players will fail before warranty expires?
Please someone help me
The width of a rectangle is the length minus 5 units. The area of the rectangle is 6 square units. What is the length, in units, of the rectangle?
Answer: 6 units
Step-by-step explanation:
let w=width, a=area, and l=length
given:
w=l-5
a=6
solve with the formula a=l*w
a=l*w
6=l*(l-5)
6=l^2-5l
0=l^2-5l-6
0=(l-6)(l+1)
l=6 or l=-1
the length can't be negative, so l=6
g window (yes, that's his name!) is in a helicopter and is flying at 160 miles per hour at a constant altitude of 0.75 miles above a straight road. window uses radar to determine that an oncoming car is at a distance of exactly 1 mile from the helicopter and, at that moment, this distance is decreasing at 130 miles per hour. what is the speed of the car?
In case of a helicopter and is flying at 160 miles per hour at a constant altitude above a straight road, the speed of the car is equals to the -197.57 mph.
There is a helicopter which is flying at 160 miles per hour at a constant altitude of 0.75 miles above a straight road. During this radar is used to determine the distance of oncoming car is exactly 1 mile from helicopter. Distance decreasing rate = 130 miles per hour
Here, we want to calculate the speed of the car. Using geometry, there is formed a right angled triangle, see above figure. Let the length of base, height and hypothenuse be x,y and z respectively. The distance from the helicopter to the car, represents hypotenuse, say z. The hypotenuse of the triangle is decreasing at 66 mph, i.e. dz/dt = -130mph
From Pythagoras theorem, z² = x² + y²
differentiating wrt time, [tex]2z \frac{dz}{dt} = 2x \frac{dx}{dt} + 2y \frac{dy}{dt}[/tex]
we know, dy/dt is zero since copter never changes height. Also since y = 0.75 miles and z = 1 mile, [tex] x = \sqrt{1²-0.75²} [/tex]
= 0.658 miles
As we know speed is rate of change of position, so speed of car is dx/dt. Now, Substitute all known values in above formula, 2 mi × 1 × -130 mph = 2× 0.658 m dx/dt + 2×0
=> dx/dt = - 130/0.658
= -197.57 mph
Hence, required value is - 197.57 mph.
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The lines shown below are perpendicular
Answer:
Slope of green line:
[tex]m = \frac{ - 3 - 3}{4 - ( - 4))} = - \frac{6}{8} = - \frac{3}{4} [/tex]
Slope of red line:
[tex]m = \frac{3 - ( - 5)}{3 - ( - 3)} = \frac{8}{6} = \frac{4}{3} [/tex]
The slopes of these two lines are negative reciprocals of each other.
Therefore, the correct answer is True (A).
