A ratio is an ordered pair of numbers a and b, written a / b where b does not equal 0. A proportion is an equation in which two ratios are set equal to each other
What is an equivalent ratios?
A ratio compares two quantities named as antecedent and consequent, by the means of division. For example, when we cook food, then each ingredient has to be added in a ratio. Thus, we can say, a ratio is used to express one quantity as a fraction of another quantity.
Two ratios are equivalent to each other if one of them can be expressed as the multiple of the other. Hence, to get the equivalent ratio of another ratio, we have to multiply the two quantities (antecedent and consequent) by the same number.
Given ratios are 2:1 and 3:1
we can write it as 2/1 and 3/1.
The lcm of 2 and 3 is 6.
Multiply denominator of both ratio with 6, we get
2/6 and 3/6 And we can see both the ratios are not equal.
Hence, there are not equivalent ratios.
4:1 and 8:3 are equivalent ratios -----> is false, because 4:1 is equivalent to 8:2
11:2 and 2:11 are equivalent ratios------> is false (because, are reciprocal ratios, not equivalent ratios)
3:1 and 9:3 are equivalent ratios ------> is true
because 3:1 multiply both sides by 3 -----> 3*3:1*3=9:3
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Directions: Use the Law of Sines to find each missing side or angle. Round to the nearest tenth.
Step-by-step explanation:
[tex] \frac{x}{ \sin(46) } = \frac{5}{ \sin(29) } \\ x = 5 \times \frac{ \sin(46) }{ \sin(29) } \\ x = 7.42[/tex]
Please tell the answer and the method I really need it
Manish runs 3 times around a square part of the side of 80m and Santosh runs two
times around Rec. park with a length of 80m and breadth of 40m.
Who covers more distance?
Answer:
Manish covers more distance. He covers 960m whereas Santosh only covers 480m
Step-by-step explanation:
First we compute the perimeter of the square track
Perimeter of a square of side a = 4a
Here a = 80m
Perimeter of the square of side 80 => 4 x 80 = 320 m
Since Manish runs 3 times around it, total distance covered = 3 x 320 = 960
The perimeter of a rectangle with length L and breadth B = 2(L + B)
So perimeter of the rectangular track = 2(80 + 40) = 2 x 120 = 240
Since Santosh ran twice around this, total distance covered = 2 x 240 = 480
What is 12.70 - n + 9
Answer:
21.7 - n
Step-by-step explanation:
12.7 +9
ANSWER
21.7 - n
which of the following outliers would most likely be the easiest to correct? a. a typographical error in data transfer b. a measurement error in instrument calibration c. a heavily skewed distribution d. a correctly measured anomalous result
a. a typographical error in data transfer outliers would most likely be the easiest to correct.
What is typographical error?Typo, often known as a misprint, is short for a typographical error. Typos are mistakes created during the typing process that editors and proofreaders failed to catch.
When the writer means to enter the wrong term, the error is referred to be a typo. The majority of the time it is spelt wrongly. It's possible for a word to be incomplete, to have an extra letter, or to be missing a letter, which can occasionally result in the creation of a new term with a completely different meaning. A typographical error in material that has been written or printed.
Thus, correct option is: a
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Josh is hiking Glacier National Park. He has now hiked a total of
17
km
17 km17, start text, space, k, m, end text and is
2
km
2 km2, start text, space, k, m, end text short of being
1
2
2
1
start fraction, 1, divided by, 2, end fraction of the way done with his hike.
Write an equation to determine the total length in kilometers
(
ℎ
)
(h)left parenthesis, h, right parenthesis of Josh's hike.
In a case whereby Josh is hiking Glacier National Park and has now hiked a total of 17 km, total distance that Josh will travel is 38 km.
How can we know the total distance travel?The concept that will be used here is the using of model for simplification of expression. we can write the equation that models the problem since Josh was able to hiked 17 km, and this can be seen to have been done 2 km away from being 1/2 done.
An the model can appear as 17 + 2 = (1/2)h
where h =length of the hike.
then we can solve for h,
17 + 2 = (1/2)h
19 =0.5h
h = 38 km
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The properly written question:
Josh is hiking Glacier National Park. He has now hiked a total of 17 \text{ km}17 km17, space, k, m and is 2 \text{ km}2 km2, space, k, m short of being \dfrac12 2 1 start fraction, 1, divided by, 2, end fraction of the way done with his hike.
What is the equation of the line that passes through the point
(-4,3) and has a slope of -3/4?
Answer:
y = -3/4x + 6
Step-by-step explanation:
In order to write an equation of the line in slope-intercept form, we first have to look at the equation:
y = mx + b
We have m, the slope, which is -3/4, and we have our y and x values, so in order to find b, we need to plug the other values in and solve for b
(-4,3)
y = 3
x = -4
m = -3/4
y = mx + b
(3) = [tex](\frac{-3}{4} )[/tex](-4) + b
3 = -3 + b
6 = b
So, equation of the line in slope-intercept form that passes through point (-4,3) and has a slope of -3/4, is y = -3/4x + 6
I hope this helps! :)
a project is in the execution phase. based on the originally approved blueprint, 1,000 products were developed. the project team randomly chooses 100 products to evaluate against the quality plan. what is the project team undertaking?
The project team is conducting a quality check of randomly selected products against the quality plan.
What is probability ?
Probability is a branch of mathematics that deals with the likelihood of events occurring. It is a number between 0 and 1 that represents the chance of an event happening. An event with a probability of 0 cannot happen, while an event with a probability of 1 is certain to happen.
The project team is undertaking quality control activities. Specifically, they are conducting a quality check by evaluating 100 randomly selected products against the quality plan. This is done to ensure that the products meet the required standards and specifications outlined in the quality plan, and that they are fit for their intended use. Quality control is an ongoing process that is performed throughout the project to identify and correct any defects or issues in the products before they are delivered to the customer.
The project team is conducting a quality check of randomly selected products against the quality plan.
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Which two functions meet the following criteria?
• The y-intercepts have a difference of 3.
• The slopes are both negative.
The first and fourth functions agrees that have y-intercepts have a difference of 3 and the slopes are both negative.
What is Slope of Line?The slope of the line is the ratio of the rise to the run, or rise divided by the run. It describes the steepness of line in the coordinate plane.
The slope intercept form of a line is y=mx+b, where m is slope and b is the y intercept.
The slope of line passing through two points (x₁, y₁) and (x₂, y₂) is
m=y₂-y₁/x₂-x₁
Let us find the slope of first graph
m=-3+2/2=-1
-1=-1(-2)+b
-1=2+b
b=-3
The first function is y=-1x-3
Second function is y=4x-6
Third function is y=4x-1
The fourth function is y=-3x-3
Hence, the first and fourth functions agrees that have y-intercepts have a difference of 3 and the slopes are both negative.
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What is the value of y in this triangle?
Answer:64
Step-by-step explanation: You add 79 and 37 then subtract the sum of the two numbers from 180
I need help, please!!!
You can use a compass and set its angle such that it the radius of the circle that it will draw is less than that of WX's length but longer than its half. Use it to make 4 arcs.
Making 4 arcs (2 arcs up and down from W and 2 arcs up and down from X which intersect the previous two arcs) with the circle of radius smaller than the length of WX will give two points on a perpendicular bisector.
How to find the perpendicular bisector of a line segment with the help of a compass and a straightedge?
The construction steps are as follows:
Let the line segment to be bisected(divided into two equal parts) by a perpendicular line(that perpendicular bisecting line is called the perpendicular bisector of the given line segment) be WX
Take a compass and set its radius length smaller than the length of WX and longer than half of WX
Put the tip of the compass on W and make an arc upside of WX
Now make an arc downside of WX
Repeat the above two steps but now with the tip being on X such that two new arcs intersect the previous two arcs.
Use a straightedge and join both the points of intersection of arcs.
The obtained line is the perpendicular bisector of the line segment WX
Using the above method, we get the perpendicular bisector of WX shown in the below-attached figure.
Thus,
Making 4 arcs (2 arcs up and down from W and 2 arcs up and down from X which intersect the previous two arcs) with a circle of radius smaller than the length of WX will give two points on a perpendicular bisector.
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You can use a compass and set its angle such - 1
(2x + 4) ( x- 4)
I need help
need to be 20 character long so the answer is 2x²+12x-16 the answer is C
You depoit $120 in an invetment account that earn 6. 4% annual interet compounded quarterly. Write a function that repreent the balance y (in dollar) of the invetment account after t year
A function that represents the balance y (in dollars) of the investment account after t year is y = $120 × (1 + 0.064/4)^(4t).
The balance of an investment account is the sum of all deposits and withdrawals to/from an investment account, considering the manager's compensation calculation.
After the trading interval ends and compensation is paid out, the account balance will equal the equity.
Let y be the investment account balance (in dollars) after t years. Then,
y = $120 × (1 + 0.064/4)^(4t)
Where the interest rate is 6.4% and is compounded quarterly.
So the interest rate per quarter is 0.064/4.
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Which of the following is an equation of a curve that intersects at right angles every curve of the family y = 1/x + k where k takes all real values? a)y= -x b)y= -x^2 c)y= -x^3/3 d)y=x^3/3 e)y=ln x
The equation of a curve which intersects at right angles every curve of the family y = 1 / x + k is: y = x^3 / 3. The correct option is D.
The given equation:
y = 1/x + k.
And since y’ = –1 / x^2
So, the desired curve satisfies:
y’ = x^2
From the given equation we get:
dy / dx = –1 / x^2
any suitable function would have the negative reciprocal slope, so:
df / dx = x^2 / 1 = x^2
So, f(x) = x^3 / 3
Hence, the equation that intersects at right angles of y = 1 / x + k is y = x^3 / 3.
What is the intersection of a curve?Generally, an intersection curve consists of the common points of two transversally intersecting surfaces, which means that at any common point the surface normal are not parallel. This restriction excludes cases in which the surfaces are touching or have surface parts in common.
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two of the vertices of a regular octahedron are to be chosen at random. what is the probability that they will be the endpoints of an edge of the octahedron? express your answer as a common fraction.
In an octahedron, there is a 12/15 = 4/5 chance that two randomly selected vertices will serve as the endpoints of an edge
The term "octahedron" comes from the Greek word which means "8 faced." A polyhedron with 8 faces, 12 edges, and 6 vertices is called an octahedron. Four edges meet at each vertex. One of the five platonic solids with faces that reflect equilateral triangles
Few properties of an octahedron
The scatterplot contains data points, pairing average monthly temperature (x) and monthly energy cost (y).
Using the least-squares regression method, which is the line of best fit?
line a
line b
line c
line d
Answer:
i think line b is the best fit
Step-by-step explanation:
hii friend
The expression -350 +16.6m represents a summering that begins at a depth of 350 feet below sea level and ascended at a rate of 16.6 ft./min. what was the depth of the submarine after nine minutes 
Answer:
Step-by-step explanation:
After nine minutes, the depth of the submarine will be -334.4 ft. below sea level. This is calculated by taking the starting depth of -350 ft. and adding the amount of ascent in nine minutes (9 minutes x 16.6 ft./min. = 149.4 ft.). So the result would be -350 + 149.4 = -334.4 ft.
What is absolute value form?
Absolute value is a mathematical term used to describe the distance between a number and zero on a number line. It is written in algebraic form as |x|.
The absolute value of a number is always positive, even if the number itself is negative. For example, the absolute value of -5 is 5, and the absolute value of 5 is also 5.
When graphed on a number line, the absolute value of a number is the distance between that number and zero. Positive numbers are found on the right side of the number line, and negative numbers are found on the left side. The absolute value of a number is the same regardless of which side of the number line it is located.
Absolute value can be used to compare the distance between two numbers on a number line. For example, the absolute value of 6 minus the absolute value of 3 is equal to the absolute value of 3 minus the absolute value of 6. This is because the distance between the two numbers is the same regardless of the order of subtraction.
Absolute value can also be used to solve equations.
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Pavel uses a piece of cardboard to create a box. The polynomial function V(x) = x^4 − 42x^3 + 352x^2 + 2,688x gives the volume in cubic centimeters of the box in terms of its length, x. If Pavel wants the box to have a volume of 64,800 cm3, what must be the length rounded to the nearest tenth of a centimeter?
PLEASE ITS FOR A TEST
Answer:
To find the length of the box that will give a volume of 64,800 cm^3, we need to find the value of x that makes V(x) equal to 64,800. We can do this by setting V(x) equal to 64,800 and solving for x:
V(x) = x^4 − 42x^3 + 352x^2 + 2,688x = 64,800
x^4 − 42x^3 + 352x^2 + 2,688x - 64,800 = 0
This is a polynomial equation, and we can use techniques like factoring or synthetic division to solve for x. However, in this case, the polynomial is quite large and difficult to factor, so we can use a numerical method like the bisection method or the Newton-Raphson method to find an approximate value for x.
Using the bisection method, we can start by guessing a range of possible values for x, such as x = 50 to x = 100, and then repeatedly narrowing down the range until we find a value that makes V(x) = 64,800.
Using the Newton-Raphson method, we can start by guessing an initial value for x and then repeatedly updating the guess using the formula x(n+1) = x(n) - f(x(n))/f'(x(n)), where f(x) is the polynomial function and f'(x) is its derivative, until we find a value that makes V(x) = 64,800.
Both methods are likely to give an approximate value for x, which is around 94.3cm.
PLEASE HELP WITH EXPLANATION
A line passes through the point (4, -11) and has a slope of 3/4. Write the equation of the line in standard form.
Answer:
The standard form of the equation of a line is:
y = mx + b
Where m is the slope of the line and (x,y) is a point on the line. We know that the line passes through the point (4, -11) and has a slope of 3/4.
We can use the point-slope form to find the equation of the line:
y - y1 = m(x - x1)
Where (x1, y1) is the point on the line and m is the slope.
Substituting in the given information we get:
y - (-11) = (3/4)(x - 4)
Simplifying the equation we get
y = (3/4)x + (33/4)
This is the equation of the line in standard form.
A car is 5.5 ft long. A truck is 15% longer than the car .How long is the truck
The truck is 6.325 feet long.
What is Percentage?Percentage is defined as the parts of a number per fraction of 100. We have to divide a number with it's whole and then multiply with 100 to calculate the percentage of any number.
So the percentage actually means a part per 100.
Percentage is usually denoted by the symbol '%'.
Given that,
A car is 5.5 ft long. A truck is 15% longer than the car.
Length of car = 5.5 feet
Length of truck = 5.5 + (15% × 5.5)
= 5.5 + [(15/100) × 5.5]
= 5.5 + (0.15 × 5.5)
= 5.5 + 0.825
= 6.325 feet
Hence the length of the truck is 6.325 feet.
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let n be a randomly selected integer from 1 to 40. find the indicated probability. 1. n is prime given that it is odd
The probability of a randomly selected integer from 1 to 40 being prime, given that it is odd, is 18/40.
What is Probability?Probability is the measure of how likely an event is to occur. It is expressed as a number between 0 and 1, where 0 means the event will never happen, and 1 means the event is certain to happen. Probability is used to make predictions or calculated decisions about the outcome of a random event. Probability is used in many areas of life, from gambling and finance to science and engineering.
This is because there are 18 prime numbers between 1 and 40 that are odd: 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, and 41. Thus, the probability of a randomly selected integer from 1 to 40 being prime, given that it is odd, is 18/40.
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Show your work to receive full credit. Find the solution to the system of equations.
3x+6y=18
X-12y=31
The solution to the system of equations for 3x+6y=18 and X-12y=31 are:
X=37/7 and Y=25/14
A system of equations is a set of one or more equations involving a number of variables.
A system of equations is also known as a set of simultaneous or equation systems.
Now, consider the given equations:
3x+6y=18--------(1)
X-12y=31---------(2)
the equation can be rewritten as 3x+6y-18=0, by taking the common number in the equation we get:
x+2y-6=0 as x+2y=6----(3)
To solve the equations add them (2)+(3)
X-12y=31
X+2y=6
changing the signs we get
14y=25
y=25/14
Now substitute y value equation(3)
X+2(25/14)=6
7X+25=42
7X=37
X=37/7
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Prove Theorem 3 as follows: Given an m % n matrix A, an element in Col A has the form Ax for some x in Rn. Let Ax and Aw represent any two vectors in Col A. a. Explain why the zero vector is in Col A. b. Show that the vector Ax C Aw is in Col A. c. Given a scalar c, show that c.Ax/ is in Col A
This proof shows that the zero vector is in Col A, the vector Ax C Aw is in Col A, and c.Ax/ is in Col A, given a scalar c. This proves Theorem 3, which states that an element in Col A has the form Ax for some x in Rn.
a. The zero vector is in Col A because it is the result of multiplying the zero vector in Rn by matrix A. Therefore, A(0) = 0, which is the zero vector in Col A.
b. To show that the vector Ax C Aw is in Col A, we need to show that Ax C Aw can be written in the form A(x + w) for some vectors x and w in Rn. Since Ax and Aw are in Col A, they can be written as A(x) and A(w) for some vectors x and w in Rn. Therefore, Ax C Aw = A(x + w). Thus, the vector Ax C Aw is in Col A.
c. Given a scalar c, we need to show that c.Ax/ is in Col A. We can rewrite c.Ax/ as cA(x). Since A(x) is in Col A, then cA(x) is also in Col A. Therefore, c.Ax/ is in Col A.
This proof shows that the zero vector is in Col A, the vector Ax C Aw is in Col A, and c.Ax/ is in Col A, given a scalar c. This proves Theorem 3, which states that an element in Col A has the form Ax for some x in Rn.
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what is happening when oneplus() is called? in other words, what exactly does the function receive as an argument? why isn't the value of the variable in main() altered?
Therefore ,as a result it cannot be altered because oneplus() function doesn't allow it to altered.
Describe Function.Quantities and their variants, equations , surrounding structures, formations and their positions, and locations where they may found are all included variable in the study of mathematics. The link between a collection of inputs, each of which has a corresponding output, is referred to as a "function." A function is a dynamic relationship between inputs and outputs in which each input produces a single, unique result. Each function has a designated area and only needs a tiny area, or scope.
Here,
Given :
oneplus() function
The function receives as an argument that twoplus() function is better than oneplus() .
The value of variable in main() isn't altered as it cannot be altered because oneplus() function doesn't allow it to altered.
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Select the correct answer.
James wants to estimate the absolute age of an animal fossil. However, test results show that the fossil doesn't contain any atoms of carbon-14.
What can James conclude about the lack of carbon-147
James can conclude about lack of carbon-14 is ; ( E ) Without carbon-14, James can use relative dating to estimate the age of the fossil.
What is relative dating?Relative dating, while it will not give an exact age, can estimate the age of the fossil. James could take a look at the relative order of past events and estimate the age of the fossil that way.
It is important to know that all animals have carbon-14. Carbon 14 is in the air in carbon dioxide molecules, which animals produce through cellular respiration.
James can utilize relative dating, which can be used as a substitute to determine the age of fossils in the absence of Carbon-14, which is essential for Carbon dating, as Carbon-14 is not present in the animal fossils he is studying.
A scientific method of identifying an object's age in relation to another is called relative dating ( i.e. determining the relative order of events ).
We may thus draw the conclusion that James can determine the age of the fossil using relative dating in the absence of carbon-14.
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Complete question:
9) a 6 ft tall man walks at the rate of 5 ft/sec toward a street light that is 16 ft above the ground. a. at what rate is the length of his shadow changing when he is 10 ft from the base of the light?
When he is 10 feet from the base of the light, the rate at which the tip of his shadow moves is 10ft/s, and when he is 10 feet from the base of the light, the rate at which the length of his shadow changes is 4ft/s.
Given, the height of a man = 6 feet
Height of light = 15 feet
Rate of walk by man, dx/dt = 5 feet per second.
a) we have to find the rate at which the tip of his shadow is moving when he is 10 feet from the base of the light.
By using ratio of similar triangles,
15/y = 6/(y - x)
On cross multiplication,
15(y - x) = 6y
15y - 15x = 6y
15y - 6y = 15x
9y = 15x
Dividing by 3 on both sides,
3y = 5x
On differentiating both sides with respect to t,
3(dy/dt) = 5(dx/dt)
dy/dt = (5/3)(dx/dt)
dy/dt = (5/3)(6)
dy/dt = 30/3
dy/dt = 10 ft/s
Therefore, the rate at which the tip of his shadow is changing is 10 ft/s.
b) we have to find the rate at which the length of his shadow is changing when he is 10 feet from the base of the light.
Length of shadow, BD = y - x
Rate of change of shadow is calculated by differentiating length with respect to time.
d(BD)/dt = dy/dt - dx/dt
d(BD)/dt = 10 - 6
= 4 ft/s
Therefore, the rate at which the length of his shadow is changing is 4 ft/s.
Thus, when he is 10 feet from the base of the light, the rate at which the tip of his shadow moves is 10ft/s, and when he is 10 feet from the base of the light, the rate at which the length of his shadow changes is 4ft/s.
Complete question:
A man 6 feet tall walks at a rate of 5 feet per second away from a light that is 15 feet above the ground. (a) When he is 10 feet from the base of the light, at what rate is the tip of his shadow moving? (b) When he is 10 feet from the base of the light, at what rate is the length of his shadow changing?
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you are treating a 50-year-old man that was involved in a fire. he suffered 25% 2nd-3rd degree burns to the anterior chest, neck and face. he has singed nasal hairs, and you identify stridor on your primary survey. pulse oximetry is 88% on a 100% non-rebreather mask. a burn center is 45 miles away. the next most appropriate step prior to transfer is:
A 100% non-rebreather mask has a pulse oximetry reading of 88%. There is a burn centre 45 miles distant. the best course of action to do after transferring a serious burn side.
A 50-year-old man who was injured in a fire is being treated by you. He sustained 25% 2nd–3rd degree burns to his face, neck, and anterior chest. He has burned nasal hairs, and your initial survey reveals stridor.
Any damage that exceeds 10% in size should be treated in a similar manner, although significant burns are classified as those that encompass 25% or more of the total body surface area. Rapid evaluation is essential. Any blaze can be managed using the general strategy for a significant burn. The most crucial things are to take a thorough history.
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What is the simplest expression equivalent to 5(d+1)
Answer:
5d + 5
Step-by-step explanation:
5(d+1)
5d + 5
Find a unit vector normal to the surface cos(xy) = ez − 2 at the point (1,π,0), and then find the equation of the plane tangent to the surface at this point.
The equation of the plane tangent to the surface at the point (1,π,0) is:
-sin(π)x + y/ √2 + z/ √2 = -sin(π) + π/ √2
To find a unit normal vector to the surface cos(xy) = e^z - 2 at the point (1,π,0), we need to find the gradient of the surface at that point. The gradient of the surface is given by:
∇f = <f_x, f_y, f_z> = < -ysin(xy), xsin(xy), cos(xy)>
So, the gradient of the surface at the point (1,π,0) is:
< -π*sin(π), cos(π), cos(π)>
To make it a unit vector we divide by the magnitude of the vector
< -π*sin(π), cos(π), cos(π)> = (π^2 + cos^2(π) + cos^2(π))^1/2
< -π*sin(π) / √π^2 + cos^2(π) + cos^2(π), cos(π) / √π^2 + cos^2(π) + cos^2(π), cos(π) / √π^2 + cos^2(π) + cos^2(π)>
The unit normal vector is
< -sin(π), 1/ √2, 1/ √2>
To find the equation of the plane tangent to the surface at this point we need to find a point on the plane and the normal vector.
We know one point on the plane is (1,π,0) and the normal vector is < -sin(π), 1/ √2, 1/ √2>
The equation of the plane is of the form:
ax + by + cz = d
Where (a, b, c) is the normal vector and (x, y, z) are the coordinates of any point on the plane.
so, the equation of the plane tangent to the surface at the point (1,π,0) is:
-sin(π)x + y/ √2 + z/ √2 = d
We can find d by substituting the point (1,π,0) into the equation
-sin(π) * 1 + π/ √2 + 0 = d
d = -sin(π) + π/ √2
so the equation of the plane tangent to the surface at the point (1,π,0) is:
-sin(π)x + y/ √2 + z/ √2 = -sin(π) + π/ √2
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Eva has xx dimes and yy quarters. She has at most 18 coins worth a minimum of $3 combined. Solve this system of inequalities graphically and determine one possible solution.
The system of inequality for Eva saving is 0.10x + 0.25y ≥ 3 and the graph of the inequality is illustrated below.
The term in equality in math is known as a relationship between two expressions or values that are not equal to each other
Here we have given that Eva has x dimes and y quarters and here we also know that she has at most 18 coins worth a minimum of $3 combined.
Then the inequality is written as,
=> x+y≤18
As we all know the that dimes are equal to 0.10 dollar and one quarter is equal to 0.25 dollar, then the inequality is rewritten as,
=> 0.10x+0.25y ≥ 3
When we plot the graph from the inequality then we get the graph like the following.
Through the graph we have identified that Eva could have 6 dimes and 10 quarters.
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