Consider the surface given by
2x^2+5y^2+z^2=4.
The surface is sliced by planes of the form x=a, y=b or z=c for values of a, b, c given below. How do I match the resulting slices (in other words, the corresponding traces) with their correct plots?
-- Also the slices are:
1. z= 1.5
2. x= 1
3. z=0
4. y=0
The student can match each slice of the surface 2x^2+5y^2+z^2=4 with its correct plot by substituting the slice values into the equation, resulting in a set of new equations each representing a different conic section centered at the origin.
Explanation:To understand the shapes or plots of the resulting slices when the surface given by 2x^2+5y^2+z^2=4 is sliced by planes of the form x=a, y=b or z=c, you must substitute values of a, b, and c into the equation of the surface to reveal new equations describing the slices.
Let's take z=1.5 as example. Substituting z with 1.5 into the equation, we get 2x^2+5y^2+(1.5)^2=4. This simplifies to 2x^2+5y^2=2.25. This is the equation for an ellipse centered at the origin on the xy plane.Substituting x=1 into the equation gives us 2*(1)^2+5y^2+z^2=4. This simplifies to 5y^2+z^2=2, another ellipse but centered at the origin on yz plane.Substituting z=0, gives us the equation 2x^2+5y^2=4. This is the equation of an ellipse in the xy plane centered at the origin.Finally, substituting y=0 into the equation results in 2x^2+z^2=4. This is the equation of a circle in the xz plane centered at the origin.By comparing these resulting equations with the standard forms of conic sections (circle, ellipse), you can match them with their correct plots.
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PETS Becky wants to buy some fish for her aquarium. She has $20 to spend and the fish cost $2.50 each. Write and solve an inequality to find how many fish Becky can afford.
The inequality 2.5x ≤ 20 represents the given situation, and Becky can afford at most eight fish.
What is inequality?Inequality is defined as mathematical statements that have a minimum of two terms containing variables or numbers that are not equal.
Let x be the number of fish Becky can afford.
We can write an inequality to represent the situation using the cost of the fish and the amount of money Becky has:
2.5x ≤ 20
To solve this inequality, we'll start by isolating the variable x on one side of the inequality. To do that, we'll divide both sides of the inequality by 2.5:
x ≤ 8
This inequality tells us that Becky can afford at most 8 fish.
To check:
20/2.5 = 8 fish
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which set of values could be the side lengths of a 30-60-90 triangle?
A. {4,4/3,8/3}
B. {4,4/3,8}
C. {4,4/2,8}
D. {4,4/2,8/2}
On the first day of the year, Diego had $700 in his savings account and started spending $35 a week. His brother Juan had $450 and started saving $15 a week. After how many weeks will the brothers have the same amount? What will that amount be?
Help !
Factor completely and then place the factors in the proper location on the grid.
4y2 + 25y + 6
Answer:
factored form of given equation [tex]4y^2+25y+6[/tex] is [tex](4y+1)(y+6)[/tex]
Step-by-step explanation:
Given equation [tex]4y^2+25y+6[/tex]
We have to write the given equation in factors form and then represent the factors on grid.
Consider the given equation [tex]4y^2+25y+6[/tex]
25y can be written as 24y + y , we get
[tex]\Rightarrow 4y^2+24y+y+6[/tex]
Taking 4y common from first two term and 1 common from last two term, we get,
[tex]\Rightarrow 4y(y+6)+1(y+6)[/tex]
[tex]\Rightarrow (4y+1)(y+6)[/tex]
Thus, factored form of given equation [tex]4y^2+25y+6[/tex] is [tex](4y+1)(y+6)[/tex]
On grid it is shown as shown in attachment below.
simplify
(10)/(5b+4)+(6)/(2b-3)
A.-10b-54/(5b+4)(2b-3)
B. 16/7b+1
C. 16/(5b+4)(2b-3)
D. 50b-6/(5b+4)(2b-3)
A baker bought some flour. He used to 2/5 of the flour to make bread and used the rest to make batches of muffins. If he used 16 pounds of flour making bread and 2/3 pound for each batch of muffins how many batches of muffins did he make
Solve log x − 1 16 = 4.
Accounts Payable had a normal starting balance of $800. There were debit postings of $600 and credit postings of $300 during the month. The ending balance is a
A. $500 credit.
B. $1,000 debit.
C. $500 debit.
D. $1,000 credit
Answer:
The correct answer is most definitely A. $ 500 credit
Step-by-step explanation:
I am 100% Positive
Dominic, Ralf and Peter have just eaten a HUGE Christmas meal. Dominic now weighs half as much as Ralph, and Peter weighs three times as much as Dominic. Together they weigh 720 pounds. How much does Dominic weigh?
What is the equation of a line that is parallel to 2x+3y=3 and passes through the point (3,−4)?
W hich of the following are you not likely to see on a graph? dependent variable, units, independent variable, prediction ...?
Answer: Fourth option is correct.
Step-by-step explanation:
On graph, we can display dependent variables, units, independent variables , because they can be expressed in numbers easily.
Whereas prediction is not competent every time to get expressed with numerical terms.
Hence, prediction is not likely to see on the graph.
Thus, Fourth option is correct.
Which of the following are properties of the incenter of a triangle? Choose all that apply.
A. The incenter is where all of the bisectors of the angles of the triangle meet.
B. The incenter of an obtuse triangle lies on the outside of the triangle.
C. The incenter is equidistant from each vertex of the triangle.
D. The incenter of a triangle is always inside it.
A & D
A. The incenter is where all of the bisectors of the angles of the triangle meet.
D. The incenter of a triangle is always inside it.
Answer:
A. The incenter is where all of the bisectors of the angles of the triangle meet.
C. The incenter is equidistant from each vertex of the triangle.
D. The incenter of a triangle is always inside it.
Step-by-step explanation:
Which national legislature has themost members?
A certain chain of ice cream stores sells 28 different flavors, and a customer can order a single-, double- , or triple-scoop cone. suppose on a multiple-scoop cone that the order of the flavors matter and that the flavors can be repeated.how many possible cones are there? ...?
There are 22,764 possible cones.
Explanation:To calculate the number of possible cones, we need to consider the number of flavors and the number of scoops. Since a customer can order a single-, double-, or triple-scoop cone, we will consider each case separately.
For a single-scoop cone, the customer can choose one flavor out of the 28 available flavors. Therefore, there are 28 possible single-scoop cones.
For a double-scoop cone, the customer can choose two flavors for the two scoops. Since the order of the flavors matters and repetition is allowed, we can think of this as selecting two flavors with replacement. Using the formula n^r, where n is the number of flavors and r is the number of scoops, there are a total of 28^2 = 784 possible double-scoop cones.
For a triple-scoop cone, the customer can choose three flavors for the three scoops. Again, using the formula n^r, there are a total of 28^3 = 21,952 possible triple-scoop cones.
Therefore, the total number of possible cones is 28 + 784 + 21,952 = 22,764.
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1. Which is an example of an activity with a moderate amount of physical activity?
a.) cross-country skiing
b.) biking up steep-hill terrains
c.) playing a game of soccer
d.) skating
2. Which could be considered a vigorous physical activity?
a.) surfing
b.) dancing
c.) playing doubles tennis
d.) chopping wood
3. Which activity provides a low level of physical exercise?
a.) raking leaves
b.) walking the dog
c.) dancing
d.) washing dishes
Activities that provide moderate, vigorous, or low exercise levels can be determined by their intensity and duration. Skating involves moderate physical activity, surfing can be considered a vigorous activity, and walking the dog provides a low level of physical exercise.
Explanation:The level of physical activity involved in various activities usually depends on the intensity and duration of the actions involved. An example of an activity involving a moderate amount of physical activity could be d.) skating, considering the balance, coordination, and movement involved.
A vigorous physical activity, on the other hand, is characterized by increased heartbeat and breathing. Based on this, a.) surfing could be categorized as a vigorous activity as it involves intense body workout and body balance. Lastly, an activity that provides a low level of physical exercise involves less effort and fewer calories burned. A good example of this could be b.) walking the dog, as this activity mostly involves casual walking.
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How do you fine arccot(-sqrt(3))?
Answer:The answer is be And i’m Strongly positive about this because i just got it right!
Step-by-step explanation:
m ∠CAD = 0.3(m(GE) - m(CD))
True or False
Answer:
False
You’re welcome ;)
A piece of paper is cut and then folded into rectangular prism as shown below.
Which side is the bottom, and which side is on the left of the rectangular prism?
A. C is on the bottom, B is on the left
B. B is on the bottom, C is on the left
C. A is on the bottom, E is on the left
D. B is on the bottom, E is on the left
Answer: B is on bottom, C is on the left
Step-by-step explanation:
A is on top and B is opposite of A. Therefore, it's on bottom and C is on the left as E is on the right.
The bottom of the rectangular prism is side C, and the left side is side B.
Explanation:To determine which side is the bottom and which side is on the left of the rectangular prism, we need to visualize how the paper was cut and folded. Let's assume that the original piece of paper had the letters A, B, C, D, E, and F on it. After folding, the side with the letter C will be the bottom of the rectangular prism, and the side with the letter B will be on the left. So, the correct answer is A. C is on the bottom, B is on the left.
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Which of the following is an example of why irrational numbers are 'not' closed under addition?
√4 + √4 = 2 + 2 = 4, and 4 is not irrantonal
1/2 + 1/2 = 1, and 1 is not irrational
√10 + (-√10) = 0, and 0 is not irrational
-3 + 3 = 0, and 0 is not irrational
Answer:
Step-by-step explanation:
its answer C !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
A bag contains
10
marbles:
4
are green,
2
are red, and
4
are blue. Linda chooses a marble at random, and without putting it back, chooses another one at random. What is the probability that both marbles she chooses are blue? Write your answer as a fraction in simplest form.
Final answer:
The probability that both marbles chosen by Linda are blue is 2/15, calculated by multiplying the probability of selecting a blue marble on each draw without replacement.
Explanation:
To calculate the probability that Linda selects two blue marbles in a row without replacement, we need to consider the number of blue marbles and the total number of marbles in the bag during each draw. Initially, there are 10 marbles in total with 4 blue marbles. The probability of drawing a blue marble on the first draw is therefore 4/10.
Upon successfully drawing a blue marble the first time, the marble is not replaced, meaning there are now only 9 marbles left with 3 being blue. The probability of drawing a second blue marble is now 3/9, which simplifies to 1/3.
To find the total probability of both events occurring in sequence (both draws resulting in blue marbles), we multiply the probabilities of each individual event occurring:
(4/10) × (3/9) = (2/5) × (1/3) = 2/15.
Therefore, the probability that both marbles Linda chooses are blue is 2/15.
Select all ratios equivalent to 20:4
4:20, 2:10, 15:3, 1:2
Final answer:
The only ratio equivalent to 20:4 from the given choices is 15:3 because, when simplified, both ratios reduce to 5:1.
Explanation:
To determine which ratios are equivalent to 20:4, we need to find ratios that can be simplified or scaled to form the same relationship. An equivalent ratio maintains the proportion when both terms are multiplied or divided by the same number.
First, the given ratio of 20:4 can be simplified by dividing both terms by 4, which gives us 5:1. Now, we can compare this to the choices provided:
4:20 is not equivalent because when simplified (divided by 4), it gives 1:5, which is the inverse of 5:1.2:10 simplifies to 1:5 (dividing by 2), also not equivalent for the same reason.15:3 simplifies to 5:1 (dividing both terms by 3), which is equivalent to 20:4.1:2 is already in simplest form and is not equivalent to 5:1 or 20:4.Therefore, the only ratio equivalent to 20:4 given in the choices is 15:3.
I need help finding the slope for AB, BC, CD and DA
What is the difference between slope on a table and slope on a graph
The difference between slope on a table and slope on a graph is shown below:
The slope on a table refers to the rate of change between two points represented in a table of values.
It is calculated by finding the ratio of the change in y-values to the change in x-values between two points.
The slope on a table is determined by taking the difference in y-values and dividing it by the difference in x-values.
On the other hand, the slope on a graph refers to the steepness or incline of a line that connects two points on a graph.
It is calculated by the ratio of the vertical change (rise) to the horizontal change (run) between two points on the graph.
While both the slope on a table and the slope on a graph represent the rate of change, they are determined differently.
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Rick combines 8 atoms of hydrogen and 4 atoms of oxygen to make 4 molecules of water
A giant salmon skier uses skies that are one sixth her height. if she is 174 cm tall how long are her skies?
The expression in the figure below represent the measures of two angle.Find the value of x . f || g . The diagram is not to scale.
What is the equation in point slope form of the line that passes through the point (–2, 4)(–2, 4) and has a slope of 5?
If f(x) = integral of 1/ (sqrt of t^3 +2)dt, then f'1 = ?
I'll write the equation with teh equation thing also ...?
Is the line through points P(–8, –10) and Q(–5, –12) perpendicular to the line through points R(9, –6) and S(17, –5)? Explain.
...?
Answer: No, the line through points P(–8, –10) and Q(–5, –12) is not perpendicular to the line through points R(9, –6) and S(17, –5).
Step-by-step explanation:
Two lines are called perpendicular to each other if the product of their slope is -1.
Since, the slope of a line having end points [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex] is,
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]
Thus, the slope of line Joining points P(–8, –10) and Q(–5, –12),
[tex]m_1=\frac{-12+10}{-5+8}=\frac{-2}{3}=-\frac{2}{3}[/tex]
While, The slope of line Joining points R(9, –6) and S(17, –5),
[tex]m_2=\frac{-5+6}{17-9}=\frac{1}{8}[/tex]
Since,
[tex]m_1\times m_2=-\frac{2}{3}\times \frac{1}{8}=-\frac{1}{12}\neq -1[/tex]
Thus, the line through points P(–8, –10) and Q(–5, –12) is not perpendicular to the line through points R(9, –6) and S(17, –5).