The answer is not a linear function, and the evaluation of the partial derivatives was done to a point. Thus, options (a) and (c) are correct. The correct equation for the tangent plane is z = 3x - 108y - z + 241 = 0.
In a given point (x₀, y, z₀) the equation of the tangent plane to a surface given by the function S = f(x, y)can be obtained by
z-z₀ = f ₓ (x₀, y₀, z₀) (x - x₀) + fᵧ (x₀, y₀, z₀) (y - y₀) ... (i)
where f ₓ (x₀, y₀, z₀) and fᵧ (x₀, y₀, z₀) (y - y₀) are the partial derivatives of f(x, y) with respect to x and y respectively. These two derivatives are evaluated at the point (x₀, y₀, z₀) .
Thus, we need to find two missing inputs, the z₀ coordinate and the two partial derivatives, in our problem in order to use equation (i).
In the case of z₀, evaluation of the given function gives us z = -80.
The partial derivatives are thus-
δf(x,y) / δx = fₓ (x, y) = 3x²
fₓ (x₀, y₀) = fₓ (1, 3) = 3
δf(x,y)/δxy= fᵧ (x, y) = -4y³
fᵧ (x₀, y₀) = fᵧ (1, 3) = -108
Now, arranging these values in equation (i) we obtain:
z-z₀ = f ₓ (x₀, y₀, z₀) (x - x₀) + fᵧ (x₀, y₀, z₀) (y - y₀)
z +80 = 3x² (x -1) - 4y³ (y - 3)
z = -80 +3x² (x -1) - 4y³ (y - 3)
Now, we will substitute the values of the partial derivatives at the given point:
z = -80 + 3x² (x -1) - 4y³ (y - 3)
z = 3x² (x -1) - 108 (y - 3)
z = 241 + 3x -108y
i.e., 3x - 108y - z + 241
Thus, the correct equation is 3x - 108y - z + 241.
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The complete question is-
A student was asked to find the equation of the tangent plane to the surface z = x³−y⁴ at the point (x, y) = (1, 3). The student's answer was z = −80 + 3x²(x−1)−(4y³)(y−3).
(a) At a glance, how do you know this is wrong? What mistakes did the student make? Select all that apply. A. The (x - 1) and (y - 3) should be x and y. B. The -80 should not be in the answer. C. The partial derivatives were not evaluated at this point. D. The correct answer is not a linear function. E. All of the above.
(b) What is the correct equation for the tangent plane? z=
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while eating out, mike and joe each tipped their server 22 dollars. mike tipped 10\% of his bill and joe tipped 20\ % of his bill. what was the difference, in dollars between their bills?
Joe, for the most part, tipped 20% of his bill, compared to 10% for Mike, which is particularly noteworthy. The actually difference between their invoices in dollars was approximately 10.
Let be Mike's bill and be Joe's bill.
(10/100) *m = 2
M = 20
(20/200 )*j = 2
J = 10
So the desired difference is
m-j = 20 – 10
= 10
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what sample size is necessary for a 90% confidence interval about the mean height of a shrub if we want a margin of error of 0.5 inches and the population standard deviation is known as 1.3 inches.
The sample size necessary for a 90% confidence interval about the mean height of a shrub with a margin of error of 0.5 inches and a population standard deviation of 1.3 inches is 18.
Margin of error is defined as the degree of the sampling errors in statistics. It can be calculated using the formula below.
MOE = z x (SD / √n)
where MOE = margin of error = 0.5 inches
z = found by using a z-score table
SD = sample standard deviation = 1.3 inches
n = sample size
At 90% confidence interval, the area in each tail of the standard normal curve is 5, and the cumulative area up to the second tail is 95.
(100 - 90) / 2 = 5
100 - 5 = 95
Find 0.95 in the z-table to get the value of z.
At p = 0.95, z = 1.647
Plug in the values to the formula and solve for the sample size, n.
MOE = z x (SD / √n)
0.5 = 1.647 x (1.3 / √n)
√n = 1.647(1.3) / 0.5
n = 18.34
n = 18
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If the ratio of men to women in a movie theater is 3:2 and there are 45 men in the theater, how many total people are in the theater?
Answer:
113 people (112.5 if you don't round but you can't have half a person)
Step-by-step explanation:
45 men plus the number of women (x) is how many people there are
so you would do 3/x=2/45 since x is the number of women
do some basic algebra, and you get 67.5 women so round if you want to to 68 (i will round because you can't have half a person)
68+45=113 people
A swimming pool is to be constructed in a 1,176-ft2 backyard. there is to be a fence that will surround a 14-by-28-foot pool. the pool builder wants to build a concrete paver deck of a uniform width, x, surrounding the pool and filling the entire area of the backyard. what is the width of the pool deck? 7 ft 14 ft 28 ft 56 ft
The width of pool deck is 7 ft and new dimensions of pool and deck are 21 ft and 35 ft .
In the given question we have,
Area of whole background ( pool + deck) = 1176 ft²------(1)
Area is a two dimensions quantity . so, we work here in 2-D.
length of pool = 28 ft , width of pool= 14 ft
let the width of deck be x ft . Now, the new dimensions are following
length of pool and deck = 28 + x + x = (28+2x ) ft
width of pool and deck = 14 + x + x = (14+ 2x) ft
here, 2x include in lenth and width for surronding deck.
total area of pool and deck ( backyard ) = lenth × width = 1176 ft² ( from (1) )
(28+2x) ( 14+2x) = 1176 ----(2)
Now, we shall solve above equation (2) and find out value of x
28×14 + 56x + 28x + 4x^2 = 1176
=> 4x²+ 84x + 392 - 1176 = 0
=> 4x² + 84x - 784=0 => x² + 21x - 196 = 0
=> x²+ 28x - 7x - 196 = 0 => x(x+ 28) - 7(x+28)=0
=> (x+28) (x-7) = 0
either x + 28= 0 or x - 7 = 0 =>either x= -28 or x= 7
but width can't be negative value so, discard
x= -28.
Hence, the width of pool deck is 7 ft.
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change 4-1/2 to a improper fraction
Answer: 9/2
Step-by-step explanation: Hope this helps.
The manager of a large ocean front hotel would like to survey their guests to determine their satisfaction with the view from their room. The hotel has 10 floors. Half of the rooms overlook the ocean and the other half overlook the street. There are 50 rooms on each floor, for a total of 500 rooms. The hotel manager would like to select a sample of 50 rooms.
A stratified sample in this case can be selected as follows:
The rooms are divided by whether they overlook the ocean or the street, and 25 of each are selected.
How are samples classified?The five most common classifications for sampling are listed as follows:
A convenient sample is drawn from a conveniently available pool of options.A random sample is equivalent to placing all options into a hat and taking some of them.In a systematic sample, every kth element of the sample is taken.Cluster sampling divides population into groups, called clusters, and each element of the group is surveyed.Stratified sampling also divides the population into groups. However, an equal proportion of each group is surveyed.In this problem, the groups are given as follows:
Floors overlooking the ocean.Floors overlooking the street.50 rooms will be sampled, hence the number that is sampled from each group is given as follows:
50/2 = 25 rooms from each group.
Missing InformationThe problem asks to describe a stratified sample for this situation.
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-5/8 + 1/4. Add.
Simplest form.
Answer: -3/8 or -0.375
Step-by-step explanation:
you have to get similar denominators to simplify
so times 1/4 by 2 to get 2/8
and then just do 2/8 - 5/8 and you get the answer
Diego's solar car traveled 3.16 meters farther than Justine's solar car. The equation d=j+3.16 represents this situation. What is the value of j if d=158?
The value of j based on the equation d = j + 3.16 if d = 158 is 154.84 meters.
How to find the missing parameters of an equation?Distance Diego's car traveled farther than Justine's solar car = 3.16 metersd = 158d = j + 3.16
substitute the value of d into the equation
d = j + 3.16
158 = j + 3.16
substract 3.16 from both sides
158 - 3.16 = j
j = 154.84
So therefore, based on the given equation d = j + 3.16, j = 154.84
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The value of j in the equation = 154.84
Distance
Distance is the length of space covered by the car when it moves from one location to another
Given;
Equation d=j+3.16 represent the situation
distance travelled by the car= 3.16meters
d=158
Step 1: Substituting the value of d into the equation d=j+3.16
158= j +3.16
Step 2: Subtract 3.16 from both sides
158-3.16 = j + 3.16 -3.16
Step 3: Add the equation
j= 154.84
Therefore, the value of j in the equation = 154.84
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Express each improper fraction as a mixed or whole number
All the improper fractions in mixed or whole numbers are as follows:
(A) 8/8 = 8(B) 15/3 = 5(C) 16/5 = 3⅕(D) 9/2 = 4½(E) 25/6 = 4⅙(F) 43/4 = 10¾(G) 24/2 = 12(H) 28/5 = 5⅗What are whole numbers?A mixed fraction is one that is represented by both its quotient and remainder. A mixed fraction is, for instance, 2 1/3, where 2 is the quotient and 1 is the remainder. n amalgam of a whole number and a legal fraction is a mixed fraction.So, the given improper fractions in the mixed or whole numbers are:
(A) 8/8 = 8(B) 15/3 = 5(C) 16/5 = 3⅕(D) 9/2 = 4½(E) 25/6 = 4⅙(F) 43/4 = 10¾(G) 24/2 = 12(H) 28/5 = 5⅗Therefore, all the improper fractions in mixed or whole numbers are as follows:
(A) 8/8 = 8(B) 15/3 = 5(C) 16/5 = 3⅕(D) 9/2 = 4½(E) 25/6 = 4⅙(F) 43/4 = 10¾(G) 24/2 = 12(H) 28/5 = 5⅗Know more about whole numbers here:
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A polygon has vertices A (5, -1), B (21, 11), C (26, -1), and D (2, -8).
Part A. What is the perimeter of ABCD to the nearest tenth of a unit?
Part B. What is the area of ABCD to the nearest tenth of a square unit?
Enter the correct answers in the boxes.
A. Perimeter: units
B. Area: square units
The graph of the coordinate points of the vertices of ABCD indicates;
Part A The perimeter of ABCD ia approximately 61.2 units
Part B. The area of ABCD is 199.5 square units
What is the perimeter of a figure in geometry?The perimeter of a figure is length of the line that goes round the figure.
A. The perimeter of the polygon is the sum of the length of the sides of the polygon, which is found as follows;
AB = √((21-11)²+(11-(-1))²) ≈ 15.6
BC = √((21-26)²+(11-(-1))²) = 13
CD = √((26-2)²+(-1-(-8))²) = 25
AD = √((2-5)²+(-8-(-1))²) ≈ 7.6
The perimeter of the polygon = 15.6 + 13 + 25 + 7.6 = 61.2
The polygon has a perimeter of approximately 61.2 unitsB. Plotting the figure indicates that the figure consists of two triangles, ΔABC and ΔACD
The base length of triangle ΔABC = 26 - 5 = 21
The height of triangle ΔABC = 11 - (-1) = 12
The area of triangle ΔABC = 0.5 × 21 × 12 = 126
Base length of triangle ΔADC = 21
Height of triangle ΔADC = -1 - (-8) = 7
Area of triangle ΔADC = 0.5 × 21 × 7 = 73.5
Area of the composite figure is therefore;
A = 126 + 73.5 = 199.5
The area of the figure is therefore; 199.5 square units
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al would take six hours to paint a wall working alone, while bob would take four hours to paint it, and chuck would take three hours to paint it. al starts painting at noon. at 1:00 pm, bob joins him. chuck joins them at 1:30 pm. at what time do they finish painting the wall?
At 2:20 pm they finish the paint of wall.
Given, Al took 6 hours to paint a wall.
Bob took 4 hours and Chuck took 3 hours for same.
Let the work of painting wall is = LCM(6,4,3) = 12 Units
So in 1 hour Al works = 12/6 = 2 units
In 1 hour Bob works = 12/4 = 3 units
In 1 hour Chuck works = 12/3 = 4 units
In 1 hour, Al and Bob together do = 2+3 = 5 units
In 1 hour, all three together do = 2+3+4 = 9 units
Now from noon i.e. 12 to 1.00 pm Al works alone.
So 2 units of work is done.
From 1 pm to 1.30 pm, Al and Bob work together.
In 30 minutes i.e. ½ hour Al and Bob did = (1/2)*5 = 5/2 units
From 1.30 pm they all three work together.
Now the remaining work is = 12-(2+5/2) = 12-9/2 = 15/2 units
So they complete rest in = (15/2)/9 = 5/6 hours = 50 minutes
Hence the time of finishing the work = 1.30 + 50 minutes = 2.20 pm.
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evaluate the expression 8.2x- 6.1 when x=7
Answer:
51.3
Step-by-step explanation:
Since it's telling us that (x=7) then that means 8.2x is going to be multiplied
8.2(7) or 8.2 x 7.
Then you end up getting an answer of 57.4
But you are not finished yet and need to subtract 6.1
so 57.4 - 6.1 = 51.3
And your result will be (51.3)
I hope this helps you understand this problem!
PLEASE HELPPP ILL BRAINLIST/5 STAR.
The total surface area of a cube with a side length of 8cm is:
A) 513 cm square
B) 384 cm square
C) 96 cm square
D) 64 cm Square
The letter representing the gradient in the formula y = mx + c is:
A) y
B) m
C) x
D) c
The gradient and y - intercept of the line y = -3x + 4 is:
A) -3x and 4
B) 3 and 4
C) -3 and 4
D) 4 and -3
The gradient of the line passing through the points (3, -2) and (2,-3) is:
A) 1
B) -1
C) 3b (b+4) - 4 (b-5)
Answer:
1. 384 cm square
2. m
3. -3 and 4
4. 1
Answer:
1) B
2) B
3) C
4) A
Step-by-step explanation:
Area of cube:[tex]\sf \boxed{\text{Area of cube = $6a^2$}}[/tex]
Here, a is the side of the cube.
Area of cube = 6 * 8 * 8
= 384 square cm
Option B
2) y = mx + c.
Here, m is the slope or gradient and c is the y-intercept.
Option B
3) y = -3x + 4
Compare with y =mx + c,
where m is the gradient and c is the y-intercept.
m = -3 and = 4
Option C
4)
[tex]\sf Slope = \dfrac{y_2-y_1}{x_2-x_1}\\\\[/tex]
[tex]\sf =\dfrac{-3-[-2]}{2-3}\\\\=\dfrac{-3+2}{-1}\\\\=\dfrac{-1}{-1}\\\\=1[/tex]
Option A
On a coordinate plane, a line goes through (negative 2, negative 4) and (2, 2). A point is at (negative 3, 1).
What is the equation, in point-slope form, of the line that is parallel to the given line and passes through the point (−3, 1)?
y – 1=Negative three-halves(x + 3)
y – 1=Negative two-thirds(x + 3)
y – 1= Two-thirds(x + 3)
y – 1= Three-halves(x + 3)
The equation of the line that is parallel to the given line and passes through the point (-3,1) is y - 1 = 3/2(x + 3)
The line is passing through (-2, -4) and (2, 2)
The slope of the line is change in y coordinate with respect to the change in x coordinate of the line
Slope of the line m = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]
Substitute the values in the equation
Slope of the line = (2--4) / (2--2)
= 6/2
= 3/2
The point slope form is
[tex]y-y_1=m(x-x_1)[/tex]
The point is given that (-3, 1)
The slope of the line = 3/2
because both are parallel lines
Substitute the both values in the equation
y - 1 = 3/2( x - (-3))
y - 1 = 3/2(x + 3)
Hence, the equation of the line that is parallel to the given line and passes through the point (-3,1) is y - 1 = 3/2(x + 3)
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Answer:
y – 1 = 3/2(x + 3)
Step-by-step explanation:
If the resistance in an electrical circuit is held constant, the amount of current flowing through the circuit is directly proportional to the amount of voltage applied to the circuit. When 3 volts are applied to a circuit, 75 milliamperes of current flow through the circuit. Find the new current if the voltage is increased to 4 volts
New current if the voltage is increased to 4 volts. = 0.1 A or 100 mA
What is a current simple definition?
The speed at which electrons go past a particular location in an electrical circuit is known as current. Current = flow, at its most fundamental level. The international unit for measuring current is an amp (AM-pir), sometimes known as an amp.amount of current flowing through the circuit is directly proportional to the amount of voltage applied to the circuit.
=> I ∝ V
=> I = V/R
R is a constant
and R is resistance
When 3 volts are applied to a circuit, 75 milliamperes of current flow through the circuit.
=> 75 x 10⁻³ = 3 /R
=> R = 3 x 10³/75
=> R = 10³/25
=> R = 40
I = V/R
V = 4
R = 40
=> I = 4/40
=> I = 1/10
=> I = 0.1 A
or 100 mA
new current if the voltage is increased to 4 volts. = 0.1 A or 100 mA
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Solve for
x
xx.
x
=
x=x, equals
Two triangles A B C and A D E. Triangle A B C is on top of Triangle A D E at point A. Side A C is smaller than A E and side A B is smaller than side A D. Side C B has a length of three. Side E D has a length of x. Side A B has a length of nine. Segment B D has a length of six. Angle A B C and A D E are both ninety degrees.
A
A
E
E
D
D
B
B
C
C
9
9
3
3
6
6
x
x
The ΔABC placed on top of ΔADE, and having angles ∠ABC and ∠BAC congruent to ∠ADE and ∠DAE in ΔADE is similar to ΔADE. The side CB is 3 indicating that the side ED, which has a length of x = 5
What are similar triangles?Similar triangles are triangles that have similar (the same shape), such that one triangles has side lengths that are a constant multiple of the other.
Please find attached a possible drawing that is based on the parameters of the question
From the question and the drawing created with MS Word, we have;
Length of AB = 9
Side CB = 3
Segment BD = 6
∠ABC = ∠ADE = 90°
∠ABC ≅ ∠ADE by definition of congruency
From the drawing, ∠BAC ≅ ∠BAC by reflexive property of equality
Triangle ΔBAC is similar to triangle ΔDAE by AA similarity postulate
Segment AD = Segment AB + Segment BD by segment addition postulate
AD = 9 + 6 = 15
The pair of corresponding sides of similar triangles are proportional, therefore;
[tex]\dfrac{\overline{AB}}{\overline{AD}} = \dfrac{\overline{BC}}{\overline{DE}}[/tex]
Which gives;
[tex]\dfrac{9}{15} = \dfrac{3}{x}[/tex]
9 × x = 15 × 3 = 45
x = 45 ÷ 9 = 5
The length of side ED, x = 5
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Answer: 12
Step-by-step explanation: Because 9 x 2 is 18, and 7 x 2 is 14, we want to multiply 6 by 2. This gives us the answer 12.
9 x 2 = 18
7 x 2 = 14
6 x 2 = 12
A health food store makes trail mix using dried fruit and nuts.the cost of the dried fruit is $2.50 per pound,and the cost of the nuts is $2.00 per pound .the total cost to make the trail mix is $225.if the total cost can be represented by the equation 2.5x +2y=225,what does the term 2.5x represent?
I need help:’)
The equation 2.5x + 2y = 225 represents the total cost and 2.5x represents the cost of dried fruit when its quantity is x.
A health food business prepares trail mixes out of dried fruit and nuts. The dried fruit costs $2.50 per pound, while the nuts cost $2.00 per pound. The overall cost of making the trail mix is $225.
Let the quantity of the dried fruit is x,
And the quantity of nuts is y,
As per the given question, the equation would be as:
2.5x + 2y = 225
The above equation represents the total cost and 2.5x represents the cost of dried fruit when its quantity is x.
Thus, 2.5x represents the cost of dried fruit when its quantity is x.
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Identify three segments parallel to AE using the figure shown. Assume lines and planes that appear to be parallel or perpendicular are parallel or perpendicular, respectively
From the figure, the lines parallel to AE are DH, CG, and EF.
What are parallel and perpendicular lines?Geometry is heavily reliant on parallel and perpendicular lines, and they can be easily distinguished thanks to a few unique qualities. If two lines never cross each other, are in the same plane, and are at the same distance from one another, then they are said to be parallel. Perpendicular lines are those that cross at an angle of 90 degrees.
If two straight lines are in the same plane and never intersect, they are said to be parallel lines.
So from the figure, we can see that the lines parallel to AE are DH, CG, and EF, as the lines are in the same plane.
As equidistant lines, they are always the same distance apart.
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answer please will give 20 points
Answer:plot the point (2,5)
Step-by-step explanation:
HELP PLS GIVING BRAINLIEST TO PERSON WHO ANSWERS FIRST
A rental car company charges $26.03 per day to rent a car and $0.13 for every mile driven. Malik wants to rent a car, knowing that:
He plans to drive 250 miles.
He has at most $350 to spend.
Which inequality can be used to determine d, the maximum number of days Malik can afford to rent for while staying within his budget?
The inequality that can be used to determine d, the maximum number of days Malik can afford to rent for while staying within his budget is 26.03d + 0.13m ≤ 350.
What is an inequality?Inequalities are created through the connection of two expressions. It should be noted that the expressions in an inequality aren't always equal. Inequalities implies that the expressions are not equal. They are denoted by the symbols ≥ < > ≤.
In this case, the rental car company charges $26.03 per day to rent a car and $0.13 for every mile driven
Let the number of days be d.
Let the number of miles be m.
The appropriate inequality to illustrate this is 26.03d + 0.13m ≤ 350.
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help meeeeeeeeeeeeeee pleaseee
The table of solutions for the given equation (y = -2x²) include the following:
x y_
-2 -8
-1 -2
0 -0
1 -2
2 -8
Also, a graph of the solution of this equation (y = -2x²) has been plotted in the image attached below.
How to determine the solution?In order to determine the valid and true solutions to the given quadratic equation, we would have to substitute the values of contained in the table into the quadratic equations as follows;
At x = -2, the value of point y is as follows:
y = -2x²
y = -2(-2)²
y = -2 × 4
y = -8
At x = -1, the value of point y is as follows:
y = -2x²
y = -2(-1)²
y = -2 × 1
y = -2
At x = 0, the value of point y is as follows:
y = -2x²
y = -2(0)²
y = -2 × 0
y = 0
At x = 1, the value of point y is as follows:
y = -2x²
y = -2(1)²
y = -2 × 1
y = -2
At x = 2, the value of point y is as follows:
y = -2x²
y = -2(2)²
y = -2 × 4
y = -8
In conclusion, we can logically deduce that the graph of this quadratic equation forms a downward parabola.
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−8×{108÷12−(−3×11−15)÷12}
Answer:
[tex] - 8(9 - ( - 33 - 15) \div 12[/tex]
[tex] - 8(9 - ( - 48) \div 12[/tex]
[tex] - 8(9 + 4)[/tex]
[tex] - 8(13)[/tex]
[tex] - 104[/tex]
Answer:
-104
Step-by-step explanation:
Divide 108 by 12
Calculate -3 × 11 - 15 which is 48
Remove the parentheses
Divide 48 by 12 which is 4
9 + 4 is 13
-8 × 13 = -104
6x+5y=2
4x+2y=8
solve by elimination
Using the elimination method, the solution to the system of linear equations is: x = 4.5 and y = -5.
How to Solve a System of Linear Equations by Elimination?Solving a system of linear equations by elimination involves eliminating one of the variables, then solve to find the other variable.
Given the equations:
6x + 5y = 2 --> eqn. 1
4x + 2y = 8 --> eqn. 2
Multiply eqn. 1 by 2 and eqn. 2 by 5:
12x + 10y = 4 --> eqn. 3
20x + 10y = 40 --> eqn. 4
Subtract
-8x = -36
x = 4.5
Substitute x = 4.5 into eqn. 2
4(4.5) + 2y = 8
18 + 2y = 8
2y = 8 - 18
2y = -10
y = -5
The solution is: x = 4.5 and y = -5.
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Which statement is logically equivalent to the following conditional statement?
"If it has exactly four sides, then it is not a hexagon."
O If it does not have exactly four sides, then it is not a hexagon.
O If it does not have exactly four sides, then it is a hexagon.
O If it is a hexagon, then it does not have exactly four sides.
O If it is not a hexagon, then it has exactly four sides.
The statement that is logically equivalent to the following conditional statement is " If it is a hexagon, then it does not have exactly four sides."
What is a regular hexagon?
It is a regular hexagon when the lengths of all the sides and the measures of all the angles are equal. In a regular hexagon, each inside angle is 120 degrees. The characteristics of a regular hexagon. The lengths of each side are equal.
Here, we let
P = it has exactly four sides.
Q = it is not an hexagon.
The negation is like this;
If it is a hexagon, then it does not have exactly four sides.
Thus, we concluded that “it is a hexagon” is your hypothesis (p) and “it has exactly 6 congruent sides” is your conclusion (q).
Hence, the statement that is logically equivalent to the following conditional statement is " If it is a hexagon, then it does not have exactly four sides."
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Given p=q=0
, what is the equation of the line that passes through the points (–p, –q) and (p, q)?
y = –x
y = q
y = 2x + (2p – q)
Equation of the line which passes through the given points (-p ,-q) and
(p, q) where p ≠ q ≠ 0 is given by y = (q/p)x.
As given in the question,
Given condition is :
p ≠ q ≠ 0
Equation of the line which passes through the given points (-p ,-q) and
(p, q) is given by:
(x₁ , y₁) = (-p ,-q)
(x₂ , y₂) = (p, q)
(y -y₁)/ (x -x₁) = (y₂ -y₁)/ (x₂ -x₁)
⇒(y +q)/(x+ p) = (q +q)/(p +p)
⇒(y +q)/ (x +p) = 2q /2p
⇒p(y+ q) =q( x +p)
⇒yp + pq = qx +pq
⇒yp = xq
⇒y = (q /p)x
Therefore, equation of the line which passes through the given points (-p ,-q) and (p, q) where p ≠ q ≠ 0 is given by y = (q/p)x.
The complete question is :
Given p ≠ q ≠ 0, what is the equation of the line that passes through the points (–p, –q) and (p, q)?
A. y = –x
B. y = q/px
C. y = q
D. y = 2x + (2p – q)
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Answer:
b
Step-by-step explanation:
just did it
(a) A box is a cuboid with length 45 cm, width 30 cm and height 42 cm.
The box is completely filled with 90.72 kg of sand.
Calculate the density of this sand in kg/m³.
[Density = mass + volume]
The density of this sand is 1600 kg/m³.
What is the meaning of density?
The amount of something per unit of length, area, or volume: as. : the substance's mass per unit volume. In grams per cubic centimeter, density.
Given that the dimension of a cuboid is length 45 cm, width 30 cm and height 42 cm.
The volume of the cuboid is (45 × 30 × 42) cm³
= 56,700 cm³
= (56,700/100³) m³
= 0.0567 m³
The mass of the sand is 90.72 kg.
The density of the sand is
= mass /volume
=90.72 kg / 0.0567 m³
= 1600 kg/m³
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If f(x) = -3x - 5 and g(x) = 4x - 2, find (f+ g)(x).
Answer:
(f+g)(x) = x - 7
Step-by-step explanation:
(f+g)(x) tells you to add the functions together. It means
f(x) + g(x)
= -3x - 5 + 4x - 2
combine like terms.
= 4x-3x - 5 - 2
= x - 5 - 2
simplify.
= x - 7
(f+g)(x) means
f(x) + g(x)
= x - 7
7(x+4)-2[x-3(5+x)]=2/3(x-6)
With detailed workings
What are the x and y intercepts? What do they mean in terms of the graph?
Step-by-step explanation:
these intercepts are the points where the graph intersects with the coordinate axes (x and y).
the x-intercept is a point on the x-axis, meaning when y = 0.
the y-intercept is a point on the y-axis, meaning when x = 0.
so, the x-intercept here is 14 at the point (14, 0).
the y- intercept is 7 at the point (0, 7).
that means the object started falling from a height of 7 meters and hit the ground after 14 seconds.
the falling speed was then
7 meters / 14 seconds = 0.5 meters / second
what are we talking about ? an asteroid with very little gravity ?
Britney can do a job in 12 hours. if she works with jimmy, together they can get the job done in eight hours. how long would it take jimmy to do the job alone?
Jimmy will take 24 hours to do the given job alone.
What is the teamwork equation for problem solving?
Problems with teamwork are resolved using this technique. If the first person completes a task in 'A' units of time and a second person completes a task in 'B' units of time, they can complete a task in 'T' units of time together (total).
The teamwork equation can be applied, that is: (1/A) + (1/B) = (1/T)
Given, time taken by Britney to do the job individually = B = 12 hours
Also, time taken by Britney and Jimmy to do the job together = A = 8 hours
Let the time taken by Jimmy to do the job individually = A hours
Thus, using the equation established in the literature above and substituting the given values, we have:
(1/A) + (1/B) = (1/T) ⇒ (1/A) + (1/12) = 1/8 ⇒ 1/A = (1/8) - (1/12)
⇒ 1/A = (3/24) - (2/24) ⇒ 1/A = 1/24 ⇒ A = 24
Thus, Jimmy will take 24 hours to do the given job alone.
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