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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The following curve passes through (3,1). Use the local linearization of the curve to find the approximate value of y at x=2.8. ...?
d/dx (2 x^2 y + y = 2x + 13)
4xy + 2x^2 y' + y' = 2
4xy + y'(2x^2 + 1) = 2
y' = (2- 4xy)/(2x^2 +1)
ow we can use this in a linear equation for a slope
Ty = -5x/8 +5(3)/8 +8/8
= -5x/8 +(15+8)/8
= -5x/8 +23/8
this will gives us an approximation at x=2.8 now
ANSWER:
y ≈ (-10/19)*(2.8 - 3) + 1 = 1 2/19 ≈ 1.105
STEP-BY-STEP EXPLANATION:
y = (2x+13)/(2x^2+1)
y' = ((2x^2+1)*(2) - (2x+13)(4x)) / (2x^2+1)^2
at x=3, this is
y'(3) = (19*2 - 19*12)/19^2 = -10/19
So, your linearization is
y ≈ (-10/19)*(x-3) + 1
At x=2.8, this is
y ≈ (-10/19)*(2.8 - 3) + 1 = 1 2/19 ≈ 1.105
Use linear approximation to estimate 15^.25 ...?
Can someone answer the questions on the sheet for me please?
Solve the inequality. Graph the solutions. h – 2 < –1
Use the relationships in the diagram below to write an equation and solve for X
What multiplies to make 12 and adds up to 16
D=20-1.95c how would I work this out correctly
640, 160, 40, 10, ...
Which correctly describe the graph of the geometric sequence? Check all that apply.
The graph will show exponential growth.
The graph will appear linear.
The domain will be the set of natural numbers.
The range will be the set of natural numbers.
The graph will show exponential decay.
The graph will show exponential decay and The domain will be the set of natural numbers.
Option C and D will apply.
What is a Geometric Sequence ?A geometric sequence is a sequence of numbers obtained by either multiplying or dividing by the same value.
The geometric sequence given is
640, 160, 40, 10, ...
Each number is divided by 4
So the nth term will be
[tex]\rm T_n = a_1 r^{n-1}[/tex]
where [tex]\rm a_1 \; is \; the \; first \; term[/tex]
and r is the common ratio
r =(1/4) for this sequence
The function is
[tex]\rm T_n = 640(\dfrac {1}{4})^{n-1}[/tex]
As from the function it can be understood , That The graph will show exponential decay and The domain will be the set of natural numbers.
Option C and D will apply.
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The sequence is a geometric sequence showing exponential decay with a factor of 0.25 (divisible by 4). The graph will show exponential decay and not appear linear. The domain is the set of natural numbers, while the range consists of specific values from the sequence, not all natural numbers.
Explanation:The sequence given is 640, 160, 40, 10, ..., which is a geometric sequence. We can determine this because each term is obtained by multiplying the previous term by a constant factor.
In this case, each term is divided by 4 to get the next term (160 is 640 divided by 4, 40 is 160 divided by 4, and so on). Therefore, the common ratio r is ¼ or 0.25, which is less than 1.
Now, let’s evaluate the statements provided:
The graph will show exponential decay because the ratio is between 0 and 1, which means the sequence is getting smaller.The graph will not show exponential growth since the terms are decreasing. Exponential growth would require the terms to get larger as the sequence progresses.The graph will not appear linear because the rate of decrease is not constant in terms of subtraction, but rather in division by a factor.The domain of a sequence typically consists of the set of natural numbers since it represents the position of each term in the sequence.The range will not be the set of natural numbers because the terms do not include all natural numbers but rather specific values determined by the geometric sequence.So, the correct statements are that the graph will show exponential decay and the domain will be the set of natural numbers.
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In the function y=1/2x^2 , what effect does the number 1/2 have on the graph, as compared to the graph of the function y=x^2 ?
A. It shrinks the graph vertically to 1/2 its original height.
B. It stretches the graph vertically by a factor of 2.
C. It stretches the graph horizontally by a factor of 2.
D. It shrinks the graph horizontally to 1/2 its original width.
In the function y=1/2x^2 , what effect does the number 1/2 have on the graph, as compared to the graph of the function y=x^2 ?
A. It shrinks the graph vertically to 1/2 its original height.
B. It stretches the graph vertically by a factor of 2.
C. It stretches the graph horizontally by a factor of 2.
D. It shrinks the graph horizontally to 1/2 its original width.
Answer:
D isn't the correct answer. It's "It shrinks the graph vertically to 1/2 its original height."
Step-by-step explanation:
I'm not sure why though this is right because I graphed it, and I don't see how that could be the right answer.
Answer:
Option A - It shrinks the graph vertically to 1/2 its original height.
Step-by-step explanation:
Given : In the function [tex]y=\frac{1}{2} x^2[/tex]
To find : What effect does the number [tex]\frac{1}{2}[/tex] have on the graph, as compared to the graph of the function [tex]y=x^2[/tex] ?
Solution :
The parent function is [tex]y=x^2[/tex]
We have given that [tex]\frac{1}{2}[/tex] number is multiply to the parent function.
When the unit is multiply to the function gives you vertical stretch or compression
i.e, f(x)→ bf(x), o<b<1 then the function is vertically compressed.
[tex]y=\frac{1}{2} x^2[/tex] As [tex]0<\frac{1}{2}<1[/tex] means there is vertical compression or shrinks.
Therefore, Option A is correct.
It shrinks the graph vertically to 1/2 its original height.
The LCM of 50, 120, and 225 is 5. true or false?
Answer:
Its false
Step-by-step explanation:
well first i pt the answer in and it came out correct.
Is the coordinate (-2,-4) a solution to the equation y= 3x-2.
You invest $2,000 in an account that is compounded annually at an interest rate of 5%. You never withdraw money from the account. How much money will be in the account after 4 years?
Answer:
A=2000(1+0.05)^4=2,431.01
Step-by-step explanation:
Guys i need help. My niece has come over my house and she need help with this question any help?
Loves from KIM.
A ladder that is 21 feet long is propped against a building. The bottom of the ladder was placed 4 feet from the base of the building. How high up on the building does the ladder reach? Round the answer to the nearest tenth of a foot.
4.1 feet
17.0 feet
20.6 feet
21.4 feet
Answer:
C
Step-by-step explanation:
I took test on Edg
please help with this #15
Kathleen and Arnob both run from the park entrance along a loop. Kathleen starts walking from the park entrance and gets a 5-mile head start on Arnob. The graph shows how far they have both traveled.
How many minutes does it take Arnob to catch up to Kathleen?
a. 9.8
b. 10
c. 73.5
d. 75
For this case, the first thing we must do is define variables.
We have then:
x: time in minutes
y: distance traveled.
We then have the following equations:
For Kathleen:
[tex] y = (\frac{1}{15}) x + 5
[/tex]
For Arnob:
[tex] y = (\frac{2}{15}) x
[/tex]
By the time Arnob reaches Kathleen we have:
[tex] (\frac{1}{15}) x + 5 = (\frac{2}{15}) x
[/tex]
From here, we clear the value of x.
We have then:
[tex] (\frac{2}{15}) x - (\frac{1}{15}) x = 5
[/tex]
[tex] (\frac{1}{15}) x = 5
x = (15) * (5)
x = 75 min
[/tex]
Answer:
it takes Arnob to catch up to Kathleen 75 minutes:
d. 75
Triangle LMN is congruent to triangle HIJ. Angle L measures 35 degrees angle M measures 65 degrees and angle H measures 2x + 10 degrees. Find the value of x.
Answer: The value of x is 12.5°.
Step-by-step explanation:
Since we have given that
ΔLMN ≅ ΔHIJ
So, According to "Congruency rules":
∠L = ∠H -------------------------------------(1)
∠M = ∠I
∠N = ∠J
∠M = 65° , ∠L = 35° and ∠H = (2x+10)°
From eq(1), we get that
[tex]2x+10=35^\circ\\\\2x=35-10\\\\2x=25\\\\x=\dfrac{25}{2}\\\\x=12.5^\circ[/tex]
Hence, The value of x is 12.5°.
What is 57 divided by 4241
The result of dividing 4241 by 57 is approximately 74.40.
To divide 4241 by 57, we perform the division as follows:
74
____________
57 | 4241
- 3996
_______
245
- 228
______
170
- 171
______
-1
The quotient is 74 with a remainder of 1.
Therefore, [tex]\( \frac{4241}{57} = 74 \)[/tex].40 with a remainder of 1.
Complete question:
What is 4241 divided by 57?
The number of students at marita's school decreased to 98% of last year's number currently there are 1170 students how many students were there last year round to the nearest whole number
There were about 1194 students at Marita's school last year.
To find the number of students last year when the current number is 1170 and represents 98% of last year's number, you can set up a simple equation.
Let "x" represent the number of students last year.
According to the given information, the current number of students is 98% of last year's number, which can be expressed as:
1170 = 0.98x.
To find the value of "x," you need to divide 1170 by 0.98:
[tex]\(x = \frac{1170}{0.98} = 1193.877\).[/tex]
Rounding to the nearest whole number, last year's number of students was approximately 1194.
So, there were about 1194 students at Marita's school last year.
A bacteria culture begins with 15 bacteria which double in amount at the end of every hour. How many bacteria are grown during the 12th hour?
Which ordered pairs in the form (x,z) are solution to the equation 3x-4y?
Part 1 : When solving systems of equations, how do you determine what method to use?
Part 2 : Choose 1 system of equations from the choices below. Then, solve the system and post your solution, showing your steps so that other students can see which method you chose.
–y + 3x = 6
y = –6x + 12
6x – 4y = 54
–9x + 2y = –69
2y = x + 1
–2x – y = 7
...?
To solve systems of equations, select a method based on the system's setup; using substitution, we solve the given system and find the solution to be (2, 0).
Explanation:When solving systems of equations, one must choose the method that best fits the problem's constraints. Methods include substitution, elimination, and graphing. The method selected often depends on how the equations are presented and which method allows for the most straightforward calculation.
Choosing the system –y + 3x = 6 and y = –6x + 12, we can solve it using substitution since the second equation is already solved for y:
Substitute the expression for y from the second equation into the first.So –(–6x + 12) + 3x = 6.Simplify to get 6x – 12 + 3x = 6.Combine like terms to get 9x – 12 = 6.Add 12 to both sides to get 9x = 18.Divide by 9 to find x = 2.Plug x back into the second equation to get y = –6(2) + 12, hence y = 0.Our solution is (x, y) = (2, 0).
evaluate 3X^2-14X-49/X-7
the quotient of the equation is __X+__
Answer:
[tex]3x+7[/tex]
Step-by-step explanation:
[tex]\frac{3x^2-14x-49}{x-7}[/tex]
before dividing this fraction , lets factor the numerator
[tex]3x^2-14x-49[/tex]
Product is -49 and sum is -14, lets break the middle term using factors
[tex](3x^2+7x)+ (-21x-49)[/tex]
Take out GCF from each group
[tex]x(3x+7)-7(3x+7)[/tex]
[tex](3x+7)(x-7)[/tex]
Now we replace the factors in the numerator
[tex]\frac{(3x+7)(x-7)}{x-7}[/tex]
We have (x-7) at the top and bottom , so we cancel it out
[tex]3x+7[/tex]
To calculate the unit price of an item, divide the total number of units by the total price.
True or False?
Answer:
Its really false!!!!!
Step-by-step explanation:
Under a dilation, a figure is enlarged and its orientation is preserved. Choose the statement that best describes the dilation.
A.
The image is along the same ray as the preimage but is farther from the center of dilation.
B.
The image is along the opposite ray from the preimage but is farther from the center of dilation.
C.
The image is along the same ray as the preimage but is closer to the center of dilation.
D.
The image is along the opposite ray from the preimage but is closer to the center of dilation.
Answer: C) The image is along the same ray as the preimage but is closer to the center of dilation.
In 0.57 which is the part and which is the whole
What percent of 150 is 135?
find the median for the given set of data.
0.6, 1.1, 0.87, 2, 0.87, 1.23
a) 0.87
b)0.985
c)1.1
a ball bounces from a height of 2 metres and returns to 80% of its previous height on each bounce. find the total distance travelled by the ball until it stops bouncing a ball bounces from a height of 2 metres and returns to 80% of its previous height on each bounce. find the total distance travelled by the ball until it stops bouncing
The distance traveled by the ball until it stops bouncing is:
18 meters
Step-by-step explanation:It is given that:
a ball bounces from a height of 2 meters and returns to 80% of its previous height on each bounce.
This means that the distance traveled by the ball is the distance it travels by going down as well as coming up on bouncing.
and is given as follows:
[tex]\text{Total Distance}=2+0.8\times 2\ up+0.8\times 2\ down+(0.8)^2\times 2\ up+(0.8)^2\times 2\ down+.....\\\\\text{Total distance}=2+4\times (0.8)+4\times (0.8)^2+4\times (0.8)^3+....\\\\\text{Total distance}=2+4\times [0.8+(0.8)^2+(0.8)^3+......]\\\\\text{Total distance}=2+4\times (\dfrac{0.8}{1-0.8})[/tex]
Since, the formula of infinite geometric progression is:
[tex]\sum_{n=1}^{\infty} ar^{n-1}=\dfrac{a}{1-r}[/tex]
i.e.
[tex]\text{Total distance}=2+4\times (\dfrac{0.8}{0.2})\\\\\text{Total distance}=2+4\times 4\\\\\text{Total distance}=2+16\\\\\text{Total distance}=18\ \text{meters}[/tex]
Lisa ate 1/3 of pizza. Kate ate 4/12 of same pizza. What fraction did they eat altogether
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