Find the maximum and the minimum values of f(x,y,z)=3x−9y+6z on
the sphere x2+y2+z2=126.
2 Find the maximum and the minimum values of f(x,y,z) = 3x – 9y+ 6z on the sphere x + 2 2 +2 = 126. The maximum value is (Simplify your answer.)
Answers
To find the maximum and minimum values of f(x,y,z)=3x−9y+6z on the sphere x2+y2+z2=126, we can use Lagrange multipliers.
Let g(x,y,z) = x2 + y2 + z2 - 126 be the constraint function.
Then, we need to solve the system of equations:
∇f = λ∇g
g(x,y,z) = 0
where ∇ denotes the gradient.
∇f = ⟨3,-9,6⟩
∇g = ⟨2x,2y,2z⟩
So, we need to solve the system of equations:
2xλ = 3
2yλ = -9
2zλ = 6
x2 + y2 + z2 = 126
From the first equation, we have x = 3λ/2. From the second equation, we have y = -9λ/2. From the third equation, we have z = 3λ. Substituting these expressions into the fourth equation, we get:
(3λ/2)2 + (-9λ/2)2 + (3λ)2 = 126
Simplifying, we get:
14λ2 = 126
So, λ2 = 9 and λ = ±3.
If λ = 3, then x = 9/2, y = -27/2, z = 9. This gives us the maximum value of f(x,y,z) on the sphere, which is:
f(9/2,-27/2,9) = 3(9/2) - 9(-27/2) + 6(9) = 207
If λ = -3, then x = -9/2, y = 27/2, z = -9. This gives us the minimum value of f(x,y,z) on the sphere, which is:
f(-9/2,27/2,-9) = 3(-9/2) - 9(27/2) + 6(-9) = -207
Therefore, the maximum value of f(x,y,z) on the sphere x2+y2+z2=126 is 207, and the minimum value is -207.
For the second part of the question, to find the maximum and minimum values of f(x,y,z) = 3x – 9y+ 6z on the sphere x + 2 2 +2 = 126, we need to use a similar approach with a different constraint function.
Let g(x,y,z) = x2 + (y-2)2 + z2 - 126 be the constraint function.
Then, we need to solve the system of equations:
∇f = λ∇g
g(x,y,z) = 0
∇f = ⟨3,-9,6⟩
∇g = ⟨2x,2(y-2),2z⟩
So, we need to solve the system of equations:
2xλ = 3
2(y-2)λ = -9
2zλ = 6
x2 + (y-2)2 + z2 = 126
From the first equation, we have x = 3λ/2. From the second equation, we have y = 9λ/2 + 2. From the third equation, we have z = 3λ. Substituting these expressions into the fourth equation, we get:
(3λ/2)2 + (9λ/2)2 + (3λ)2 = 126
Simplifying, we get:
45λ2 = 126
So, λ2 = 14/5 and λ = ±(2√35)/5.
If λ = (2√35)/5, then x = 3λ/2, y = 9λ/2 + 2, z = 3λ. This gives us the maximum value of f(x,y,z) on the sphere, which is:
f(3(2√35)/5,9(2√35)/5+2,3(2√35)/5) = 3(3(2√35)/5) - 9(9(2√35)/10+2) + 6(3(2√35)/5) = 6√35 - 84
If λ = -(2√35)/5, then x = 3λ/2, y = 9λ/2 + 2, z = 3λ. This gives us the minimum value of f(x,y,z) on the sphere, which is:
f(3(-(2√35)/5)/2,9(-(2√35)/5)/2+2,3(-(2√35)/5)) = 3(3(-(2√35)/5)/2) - 9(9(-(2√35)/5)/10+2) + 6(3(-(2√35)/5)) = -6√35 - 84
Therefore, the maximum value of f(x,y,z) on the sphere x + 2 2 +2 = 126 is 6√35 - 84, and the minimum value is -6√35 - 84.
To find the maximum and minimum values of f(x,y,z) = 3x - 9y + 6z on the sphere x^2 + y^2 + z^2 = 126, we can use the method of Lagrange multipliers. Let g(x,y,z) = x^2 + y^2 + z^2 - 126, and define the Lagrangian L(x,y,z,λ) = f(x,y,z) - λg(x,y,z).
To solve for the critical points, we set the gradient of L to zero: ∇L = 0. This gives us a system of equations:
∂L/∂x = 3 - 2λx = 0
∂L/∂y = -9 - 2λy = 0
∂L/∂z = 6 - 2λz = 0
g(x, y, z) = x^2 + y^2 + z^2 - 126 = 0
Solving this system, we find the critical points (x, y, z), and then substitute these points back into the function f(x, y, z) to find the corresponding maximum and minimum values.
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Related Questions
What is the percentage strength of neomycin in the final compounded product? (Answer must be numeric; no units or commas; include a leading zero when the answer is less than 1; round the final answer to the nearest ONE DECIMAL PLACE.)Rx:Neomycin (5%) cream 30gPolymyxin B 20gHydrocortisone 10gMix the ingredients to make a smooth creamSig: apply to affected area BID
Answers
The percentage strength of neomycin in the final compounded product is approximately 2.5%.
To determine the percentage strength of neomycin in the final compounded product, we need to calculate the weight of neomycin in the cream and divide it by the total weight of the cream.
Neomycin (5%) cream: 30g
The neomycin content is 5% of the total cream weight. To find the weight of neomycin in the cream, we multiply the cream weight by the neomycin percentage:
Weight of neomycin = 30g × 0.05 = 1.5g
Now, to calculate the percentage strength of neomycin in the final compounded product, we divide the weight of neomycin by the total weight of the cream and multiply by 100:
Percentage strength of neomycin = (Weight of neomycin / Total weight of cream) × 100
Percentage strength of neomycin = (1.5g / 60g) × 100 ≈ 2.5
Therefore, the percentage strength of neomycin in the final compounded product is approximately 2.5%.
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If x-1/ 3=k and k = 3, what is the value of x ?
A) 2
B) 4
C) 9
D) 10
Answers
Answer:
D
Step-by-step explanation:
x-1/3=3
x-1=9(left side 3 go multiple to right side 3)
x=10
My brain went oof help
Answers
Answer:
35
Step-by-step explanation:
urn i contains 2 white and 4 red balls, whereas urn ii contains 1 white and 1 red ball. a ball is randomly chosen from urn i and put into urn ii, and a ball is then randomly selected from urn ii. what is the probability that the ball selected from urn ii is white? the conditional probability that the transferred ball was white given that a white ball is selected from urn ii?
Answers
The probability that the ball selected from urn II is white is 3/8, and the conditional probability that the transferred ball was white given a white ball is selected from urn II is 2/3.
To calculate the probability that the ball selected from urn II is white and the conditional probability that the transferred ball was white given that a white ball is selected from urn II, we can use the concepts of conditional probability and the Law of Total Probability.
Let's consider the events:
A: Ball selected from urn II is white.
B: Transferred ball from urn I to urn II is white.
To calculate the probability that the ball selected from urn II is white, we can use the Law of Total Probability. It states that the probability of an event can be calculated by summing the probabilities of that event occurring under different conditions.
We can calculate the probability as follows:
P(A) = P(A|B) * P(B) + P(A|B') * P(B')
P(A|B) represents the conditional probability of event A given that event B has occurred, and P(B) is the probability of event B occurring. P(A|B') represents the conditional probability of event A given that event B has not occurred, and P(B') is the probability of event B not occurring.
In this case, the probability of selecting a white ball from urn II given that the transferred ball was white is 2/3 (since after transferring a white ball, urn II will have 2 white balls and 1 red ball out of a total of 3 balls).
P(A|B) = 2/3
The probability of the transferred ball being white (event B) can be calculated as the probability of selecting a white ball from urn I, which is 2/6 (since urn I has 2 white balls and 4 red balls in total).
P(B) = 2/6
The probability of not transferring a white ball (event B') can be calculated as 1 - P(B) = 1 - 2/6 = 4/6.
P(B') = 4/6
Substituting these values into the formula, we have:
P(A) = (2/3) * (2/6) + (1) * (4/6) = 4/18 + 4/6 = 3/8
Therefore, the probability that the ball selected from urn II is white is 3/8.
Now, to calculate the conditional probability that the transferred ball was white given a white ball is selected from urn II, we can use Bayes' theorem:
P(B|A) = P(A|B) * P(B) / P(A)
Substituting the values we calculated earlier, we have:
P(B|A) = (2/3) * (2/6) / (3/8) = 4/18 / 3/8 = 8/18 = 4/9
Therefore, the conditional probability that the transferred ball was white given a white ball is selected from urn II is 4/9.Answer:
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what is the sum of all exterior angles of a megagon
Answers
Step-by-step explanation:
A regular megagon is repr {1,000,000} and can be constructed as a truncated 500,000-gon, t{500,000}, a twice-truncated 250,000-gon, tt{250,000}, a thrice-truncated 125,000-gon, ttt{125,000}, or a four-fold-truncated 62,500-gon, tttt{62,500}, a five-fold-truncated 31,250-gon, ttttt{31,250}, or a six-fold-truncated 15,625-gon, tttttt{15,625}. A regular megagon has an interior angle of 179.99964°. The area of a regular megagon with sides of length a is given by
Please Give Brainliest!One of my brainliest Answers were deleted since the question got deleted!
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True or false...
When using the substitution method, one of the equations must say "x=" or "y=".
Answers
Answer:
true
Step-by-step explanation:
I’m sorry if I’m wrong
14. Matthew had $4.10 in his pocket. He bought 3 notebooks. Now he has $0.35 in his pocket.
Which equation below can be used to find how much each notebook, n, costs?
A. 4.10-3n=0.35
B. 3n-0.35-4.10
C. 4.10 +0.35=3n
D. 3n+4.100.35
Answers
Answer: A
Step-by-step explanation:
There are 3 notebooks, and each notebook is referred to as ‘n’, thus we have 3n. After paying for 3n, the amount Matthew had decreased from $4.10 to $0.35, meaning that $4.10 minus three notebooks (3n) is equal to $0.35. Therefore, A is correct.
Hope this helps!
What is the quotient of -3/7and -1/3? -1 1/8 -1/8 1/8 1 1/8
Answers
Answer:
1 2/7
Step-by-step explanation:
Quotient means division
-3/7 ÷-1/3
Copy dot flip
-3/7 * -3/1
9/7
7/7 + 2/7
1 2/7
A basketball team scored 105 points during one game. There were as many two-point baskets as free throws (1 point each), and the number of three-point baskets was five less than the number of free throws. Find the number of three-point baskets.
Answers
The number of three-point baskets from the substitution method is 15.
According to the statement
we have given that the total score of basket ball is 105 points and there were as many two-point baskets as free throws (1 point each), and the number of three-point baskets was five less than the number of free throws.
And we have to find the number of three-point baskets.
So, For this purpose, we know that the
Final Score S = 105
Two point baskets T = Free throws F -(1)
Three point baskets H = F - 5 -(2)
Now, we know that the
The final score is equal to 3 times the number of three point baskets plus 2 times the number of two point baskets plus 1 times the number of free throws
So,
S = (3*H) + (2*T) + (1*F)
Here we can use substitution method,
Now we can substitute
105 = 3H + 2T + 1F
105 = 3H + 2F + 1F {substitute from equation (1)}
105 = 3(F-5} + 2F + 1F {substitute from equation (2)}
105 = 3F -15 + 2F + 1F
105 = 6F - 15
120 = 6F
F =20
Now that we get the value of F, now we can substitute into Eqn 2 to find H
H = F -5
H = 20 - 5
H = 15
So, The number of three-point baskets from the substitution method is 15.
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Answer: The number of three-point baskets from the substitution method is 15!
Find out if the lengths form a right triangle
Answers
Answer:
The triangle is a right triangle.
Step-by-step explanation:
Since The Pythagorean Theorem only works on right triangles, we can use this knowledge to prove whether this triangle is right:
\(a^2 + b^2 = c^2\\10^2 + (2\sqrt{39})^2 = 16^2\\100 + (4 \times 39) = 256\\100 + 156 = 256\\256 = 256\)
Therefore, the triangle is right.
The solutions to p(x) = 0 are x = -7 and x = 7. Which quadratic
function could represent p?
Answers
The quadratic equation that represents the solution is F: p(x) = x² - 49.
What is quadratic function?The term "quadratic" refers to functions where the highest degree of the variable (in this example, x) is 2. A quadratic function's graph is a parabola, which, depending on the sign of the leading coefficient a, can either have a "U" shape or an inverted "U" shape.
Algebra, geometry, physics, engineering, and many other branches of mathematics and science all depend on quadratic functions. They are used to simulate a wide range of phenomena, including population dynamics, projectile motion, and optimisation issues.
Given that the solution of the quadratic function are x = -7 and x = 7 thus we have:
p(x) = (x + 7)(x - 7)
Solving the parentheses we have:
p(x) = x² - 7x + 7x - 49
Cancelling the same terms with opposite sign we have:
p(x) = x² - 49
Hence, the quadratic equation that represents the solution is F: p(x) = x² - 49.
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How many positive factors of 96 are also multiples of 12?
Answers
The number of positive factors of 96 which are also multiples of 12 are 4 which are 12,24,48, and 96.
Positive factors of 96 = 1,2,3,4,6,8,12,16,24,32,48 and, 96
Multiples of 12 upto 96 = 12,24,36,48,60,72, 84 and 96
Common numbers between the two are 12,24,48 and 96.
Hence, there are only 4 positive factors of 96 which are also the multiples of 12
Factors
Factors are the numbers that can divide a number exactly. Hence, after division, there is no remainder left.
Multiples
A multiple is a result obtained by multiplying a number by an integer(it shouldn’t be a fraction). The multiples of the whole number are obtained by taking out the product of the counting numbers and that of whole numbers.
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SOMEONE HELP :'(((
Give each rate in miles per hour:
a. Honor jogs 9 miles in 212 hour
b. Eli walks 9 inches per second
Answers
Answer:
The natural no between 2 to 15 is 2,3,4,5,6,7,8,9,10,11 and 12. prime numbers among these are 2,3,5,7 and 11. therefore,out of 11 number, 5 are prime number.what fraction of the natural numbers between 2 and 15 are prime numbersthe length of abhishek's notebook is 17cm and 8 mm. What will be its length in cm
Find the area of the region enclosed by the curves. 10 X= = 2y² +12y + 19 X = - 4y - 10 2 y=-3 5 y=-2 Set up Will you use integration with respect to x or y?
Answers
The area of the region enclosed by the curves 10x=2y²+12y+19 and x=-4y-10 is 174/3 units².
To find the area of the region enclosed by the curves 10x=2y²+12y+19 and x=-4y-10, we need to solve this problem in the following way:
Since the curves are already in the form of x = f(y), we need to use vertical strips to find the area.
So, the integral for the area of the region is given by:
A = ∫a b [x₂(y) - x₁(y)] dy
Here, x₂(y) = 10 - 2y² - 12y - 19/5 = - 2y² - 12y + 1/2 and x₁(y) = -4y - 10
So,
A = ∫(-3)⁻²[(-2y² - 12y + 1/2) - (-4y - 10)] dy + ∫(-2)⁻²[(-2y² - 12y + 1/2) - (-4y - 10)] dy
=> A = ∫(-3)⁻²[2y² + 8y - 19/2] dy + ∫(-2)⁻²[2y² + 8y - 19/2] dy
=> A = [(2/3)y³ + 4y² - (19/2)y]₋³ - [(2/3)y³ + 4y² - (19/2)y]₋² | from y = -3 to -2
=> A = [(2/3)(-2)³ + 4(-2)² - (19/2)(-2)] - [(2/3)(-3)³ + 4(-3)² - (19/2)(-3)]
=> A = 174/3
Hence, the area of the region enclosed by the curves is 174/3 units².
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Assuming that the slide was 1.50 km in width and the Tensleep sandstone has a density of 2.40 g/cm 3
, estimate the volume and mass of the landslide from the cross section (there is no vertical exaggeration). ( 1pt ) Assuming the density of the Tensleep sandstone is 2.35 g/cm 3
, measure the dip on the cross section, and calculate the total weight (F w ), the normal force (F n ), and shear force (F 2
) acting on the block. (2 pts) The Gros Ventre slide occurred after very heavy rains. Assuming a coefficient of friction, Cr of 0.55, what was the minimum pore pressure required to overcome friftion and trigger the slide (express your answer in N/m 2
, which is equal to the metric unit of a Pascal). To do this, you must calculate the require pore pressure that reduces effective friction to equal the shear stresss. Assume there is NO COHESION. Remember, stress equals force/area. (3 pts)
Answers
The minimum pore pressure required to overcome friction and trigger the slide is 26,597 Pa (or N/m²).
Part 1: The volume and mass of the landslide
Volume of the landslide = Width x Height x Length
Area of the slide = 1/2 base x height
= 1/2 x 1.5 km x 700 m
= 525,000 m²
As the cross-section is symmetrical, we can assume that the length of the slide is twice the height of the slide.
Length of the slide = 2 x 700m
= 1400 m
Therefore,
Volume of the landslide = Area of the slide x Length of the slide
= 525,000 m² x 1400 m
= 735,000,000 m³
Next, we can calculate the mass of the landslide using the following formula:
mass = density x volume
Since the density of the Tensleep sandstone is 2.40 g/cm³ = 2400 kg/m³,
mass of the landslide = 735,000,000 m³ x 2400 kg/m³
= 1.764 x 10¹² kg
Part 2: The total weight, the normal force, and shear force acting on the block.
Weight = mass x gravitational field strength
Weight = 1.764 x 10¹² kg x 9.81 m/s²
= 1.732 x 10¹³ N
The normal force and shear force acting on the block can be calculated using the following equations:
Normal force = weight x cos θ
Shear force = weight x sin θθ is the angle of the dip. From the diagram, the dip angle is about 26 degrees.
Normal force = 1.732 x 10¹³ N x cos 26°
= 1.540 x 10¹³ N
Shear force = 1.732 x 10¹³ N x sin 26°
= 7.690 x 10¹² N
Part 3: The minimum pore pressure required to overcome friction and trigger the slide
The minimum pore pressure required to overcome friction and trigger the slide can be calculated using the following formula:
pore pressure = shear stress/friction coefficient
Shear stress = Shear force/Area
The area can be calculated from the cross-section:
Area = 1/2 x base x height
= 1/2 x 1500 m x 700 m
= 525,000 m²
Shear stress = Shear force/Area
= 7.690 x 10¹² N / 525,000 m²
= 14,628 Pa (or N/m²)
pore pressure = Shear stress/friction coefficient
= 14,628 Pa / 0.55= 26,597 Pa (or N/m²)
Therefore, the minimum pore pressure required to overcome friction and trigger the slide is 26,597 Pa (or N/m²).
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42
1. Solve for the missing angle measures.
1)
a = 75⁰
d
b
2)
a
b
d=1040
Answers
The angle created by the two rays or arms at a shared vertex is known as the angle measure in geometry.
How do you find an angle measure?With a protractor, you can determine how large an angle is. Alternatively, the congruent angles could be indicated on the figure by an arc. Supplementary angles are two angles whose combined measurements are 180°, such as two right angles since 90° + 90° Equals 180°. the measurement of an angle wherein 1 degree equals 1/360 of a circle.
An angle (created by perpendicular lines) that is exactly 90 degrees is called a right angle. Less than 90 degrees is considered an acute angle. Revolutions, degrees, and radians are the three types of angles that can be measured. Degrees serve as a more widely used measurement unit. In order for a right angle to be 90 degrees, a circle must be divided into 360 equal degrees.
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Обчислив площу поверхні Куба ребро якого дорівнює 4,2 м
Answers
Answer: I calculated the surface area of a cube whose edge is 4.2 m
Step-by-step explanation: hope this helps
3x+y-4z=-22
2x+3y+4z=32
x-y+2z=16
Answers
Answer: x=-1, y=2, z=-3
Step-by-step explanation:
[1] 2x + 3y - 4z = 16
[2] -x + 2y - z = 8
[3] 2x - y - 2z = 2
Solve by Substitution :
Solve equation [3] for the variable y
[3] y = 2x - 2z - 2
Plug this in for variable y in equation [1]
2x + 3•(2x-2z-2) - 4z = 16
8x - 10z = 22
Plug this in for variable y in equation [2]
-x + 2•(2x-2z-2) - z = 8
3x - 5z = 12
Solve equation [2] for the variable x
3x = 5z + 12
x = 5z/3 + 4
Plug this in for variable x in equation [1]
8•(5z/3+4) - 10z = 22
10z/3 = -10
10z = -30
Solve equation for the variable z
10z = - 30
z = - 3
By now we know this much :
x = 5z/3+4
y = 2x-2z-2
z = -3
Use the z value to solve for x
x = (5/3)(-3)+4 = -1
Use the x and z values to solve for y
y = 2(-1)-2(-3)-2 = 2
How many
solutions can
an equation
have?I
Answers
Answer:
A system of linear equations usually has a single solution, but sometimes it can have no solution (parallel lines) or infinite solutions (same line). This article reviews all three cases. One solution. A system of linear equations has one solution when the graphs intersect at a point.
In a rectangle KLMN, the diagonals KM and LN intersect at O.
(i) If KO = 4y + 6 and ON = 3y + 11, find the lengths of its diagonals.
(ii) If ∠NKM = 32°, find ∠KON and ∠KMN.
guys, pls answer. it's very urgent. I have to submit tomorrow. pls don't give wrong ans.
Answers
Answer:
8y°±94°⊂⊂100°
Step-by-step explanation:
You have a bag that contains 6 red marbles and 3 blue marbles. You randomly choose one of the marbles. Without replacing the first marble, you choose a second marble. Find the probability of the events.
Answers
Answer:
12/27
Step-by-step explanation:
You have a bag that contains 6 red marbles and 3 blue marbles. You randomly choose one of the marbles. Without replacing the first marble, you choose a second marble. Find the probability of the events.
Let the total number of marbles = 6 red marble + 3 blue marbles = 9 marbles
You randomly choose one of the marbles. Without replacing the first marble, you choose a second marble. Find the probability of the events.
Assume all you picked is red( without replacement)
= 6/9 × 5/9
= 30/81
= 10/27
Assume all you picked is blue( without replacement)
= 3/9 × 2/9
= 6/81
= 2/27
The probability of the events is calculated as:
All red or All blue
= 10/27 + 2/27
= 12/27
rounded to the nearest hundredth, how many meters are in 32 ft?(1 m = 3.28 ft)
Answers
Answer:
9.76 meters
What are units?A unit can be used for measurement, and is commonly found in mathematics to describe length, size, etc.
If 1 m = 3.28 ft, we can find out how many meters are in 32 feet by using this equation:
32 ÷ 3.28 = 9.75609756Rounding to the nearest hundredth:
9.75609756 = 9.76Therefore, rounded to the nearest hundredth, there are 9.76 meters in 32 feet.
the manager of a garden shop mixes grass seed that is 60% rye grass with 70lb of grass seed that is 80% rye grass tp make a mixture that is 74% rye grass. how much of the 60% mixture is used
Answers
The manager of a garden shop wants to make a mixture that contains 74% rye grass. The weight of the 60% mixture used in this composition is 30 lb.
Percentage is used to denote a fraction of a hundred.
Suppose q represents the weight of the mix that contains 60% rye grass, then the weight of rye grass in this mix is:
w1 = 60% q = 0.6 q
Mix 2: 70 lb grass seed that contains 80% rye grass. The weight of rye grass in the second mix is:
w1 = 80% x 70 = 56 lb
The final mixture has 74% rye grass. Total weight of rye grass in the final mixture:
weight of rye grass = w1 + w2
= 0.6 q + 56
Total weight of the final mixture = (q + 70) lb
74% = 0.74 = (0.6 q + 56) / (q + 70)
0.6 q + 56 = 0.74 (q + 70)
0.74 q - 0.6 q = 56 - 0.74 x 70
0.14 q = 4.2
q = 4.2/0.14 = 30
Hence, the weight of 60% mixture is 30 lb.
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Give the slope of the line which is perpendicular to
y = −3x −2
Answers
Answer:
1/3
Step-by-step explanation:
y = −3x −2
This is in the form y = mx+b where m is the slope
This line has a slope of -3
We want the slope of a line that is perpendicular
Lines that are perpendicular have slopes that are negative reciprocals
m = -(1/-3)
m = + 1/3
The slope of a line that is perpendicular is 1/3
common multiples for 30 21 and 24
Answers
Answer:
The common multiple for 30 21 and 24 is 3
Step-by-step explanation:
30 = 3 × 10
21 = 3 × 7
24 = 3 × 8
Thus, 3 is the common multiple for 30 21 and 24.
-TheUnknownScientist
Triangle Angle Sum Theorem
Answers
Answer:
m<DCF = 155°
Step-by-step explanation:
m<DCF = m<D + m<E
m<DCF = 72° + 83°
m<DCF = 155°
this is what truthfully struggle with can someone explain how i do this please then imma try it on my own
Answers
D.)
Good luck and I don’t know how to explain
A city park is opening a new swimming pool. You can pay a daily entrance fee of $3 or purchase a membership for the 12 week summer season for $82 dollars and pay only $1 per day to swim. How many days would you have to swim to make the membership worthwhile?
Answers
Answer:
41 days
Step-by-step explanation:
The membership would be worthwile if you swim an amount of days paying the daily entrance fee that would make your total cost equal to the cost of the membership. From that you can write the following expression:
3x=82+(1*x), x is the number of days you go to swim
Now, you can solve for x:
3x=82+x
3x-x=82
2x=82
x=82/2
x=41
According to this, the answer is that you would have to swim 41 days to make the membership worthwile.
Find the geometric mean of 3 and 13. Show work
Answers
Answer:
b
Step-by-step explanation:
a/b=c/d
ad=bc
3/x=x/13
3*13=x*x
√39=√x2
6.244997998398=x
FLUENCY AND SKILLS PRACTICE
LESSON 15
Expanding Expressions
➤ Expand each expression and combine like terms if possible.
4(x -2)
-3(x+7)
-4(-x-8)
1/3(x - 9)
-1/4( x + 16)
- 1/5( - x - 35)
> Determine which expressions, if any, are equivalent. Show your work.
4( x - 3) 6x - 2(x - 3)
x + 3(x - 2) - 6
Answers
The Expansion of each expression is
1. 4(x -2) = 4x- 8
2.-3(x+7) = -3x - 21
3. -4(-x-8) = 4x + 32
4. 1/3(x - 9)= x/3 - 3
5. -1/4( x + 16)= -x/4 - 4
6. - 1/5( - x - 35) = x/5 + 7
What is Distributive Property?This property states that multiplying the total of two or more addends by a number will produce the same outcome as multiplying each addend by the number separately and then adding the results together.
Given:
We have to expand the Expression using Distributive Property as
a x (b+ c) = a x b+ a x c
1. 4(x -2)
Using Distributive Property
=4(x) - 4(2)
= 4x- 8
2.-3(x+7)
Using Distributive Property
=-3(x) - 3(7)
= -3x - 21
3. -4(-x-8)
Using Distributive Property
=-4(-x) - 4(-8)
= 4x + 32
4. 1/3(x - 9)
Using Distributive Property
=1/3(x) - 1/3(9)
= x/3 - 3
5. -1/4( x + 16)
Using Distributive Property
= -1/4(x) -1/4(16)
= -x/4 - 4
6. - 1/5( - x - 35)
Using Distributive Property
= -1/5(-x) - 1/5(-35)
= x/5 + 7
Learn more about Distributive Property here:
https://brainly.com/question/5637942
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