I hope this helps.
Answer:-
∴x−3y−4z=0
Explanation:
First we rearrange the equation of the surface into the form f(x,y,z)=0
x2+2z2=y2
∴x2−y2+2z2=0
And so we have our function:
f(x,y,z)=x2−y2+2z2
In order to find the normal at any particular point in vector space we use the Del, or gradient operator:
∇f(x,y,z)=∂f∂xˆi+∂f∂yˆj+∂f∂zˆk
remember when partially differentiating that we differentiate wrt the variable in question whilst treating the other variables as constant. And so:
∇f=(∂∂x(x2−y2+2z2))ˆi+
(∂∂y(x2−y2+2z2))ˆj+
(∂∂z(x2−y2+2z2))ˆk
=2xˆi−2yˆj+4zˆk
So for the particular point (1,3,−2) the normal vector to the surface is given by:
∇f(1,3,−2)=2ˆi−6ˆj−8ˆk
So the tangent plane to the surface x2+2z2=y2 has this normal vector and it also passes though the point (1,3,−2). It will therefore have a vector equation of the form:
→r⋅→n=→a⋅→n
Where →r=⎛⎜⎝xyz⎞⎟⎠; →n=⎛⎜⎝2−6−8⎞⎟⎠, is the normal vector and a is any point in the plane
Hence, the tangent plane equation is:
⎛⎜⎝xyz⎞⎟⎠⋅⎛⎜⎝2−6−8⎞⎟⎠=⎛⎜⎝13−2⎞⎟⎠⋅⎛⎜⎝2−6−8⎞⎟⎠
∴(x)(2)+(y)(−6)+(z)(−2)=(1)(2)+(3)(−6)+(−2)(−8)
∴2x−6y−8z=2−18+16
∴2x−6y−8z=0
∴x−3y−4z=0
NEED HELP ASAP…..plz help
The answer is B) y = 4x
Explanation: If you substitute each number in the x column for the variable x, and then multiple that number by 4, you'll get the number in the y column to the right.
For example:
y = 4x --> y = 4 (2) --> y = 8
I hope this helped. :)
May I please receive help?
Answer:
it depends on the choices
Step-by-step explanation:
E Which could be the dimensions of a rectangular prism whose surface area is greater than 140 square feet? Select three options. 6 feet by 2 feet by 3 feet 6 feet by 5 feet by 4 feet 7 feet by 6 feet by 4 feet 8 feet by 3 feet by 7 feet 8 feet by 4 feet by 3 feet
Answer:
6feet by 5feet by 4feet
7feet by 6feet by 4feet
8feet by 3feet by 7feet
Sarah has only $180 to spend on her birthday party. If she had to pay $100 for the room and each guest cost $6
for food, how many people can she invite without going over her budget?
Answer:
She can invite 13 people.
Step-by-step explanation:
Because Sarah has to pay $100 for the room, we can subtract.
$180-$100=$80.
Now that she has $80 left, we can see how many times $6 can go into $80.
$6x14=84.
This number is four more than $80, so Sarah can not invite 14 people.
But, if we do $6x13, we get $78.
$78 does not past $80 and is really close, Sarah can invite 13 people.
Final Answer: Sarah can invite 13 people without going over her budget.
I hope this helps and have a wonderful day! ;0
Answer:
13
Step-by-step explanation:
180-100 = 80
80 divided by 6 = 13.333
the two-way table shows information about the subjects studied
Answer:
a) 62
b) 31/45
Step-by-step explanation:
a) The table tells you there are 42 males, and 20 more females that study biology.
42 +20 = 62 . . . are male or study biology or both
__
b) Of the total of 90 people, 62 are male or study biology (or both). The probability that any person is in that category is ...
62/90 = 31/45 = P(male or biology)
A horse's mane grows at the rate of 6 over 5 centimeters per month.
How many months will it take the horse's mane to grow 24 over 10 centimeters?
Explain your answer using words, and show your work using division of fractions.
Answer:
It will take 2 months for the' mane to grow 24/10 centimeters, because 24/10 divided by 6/5 = 24/10 x 5/6 would be 2 months.
Step-by-step explanation:
Hope this helps, have a good day/night :)
It will take 4/2 months or 2 months for the horse's mane to grow 24/10 centimeters.
What is a linear equation?It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.
If in the linear equation, one variable is present, then the equation is known as the linear equation in one variable.
We have:
A horse's mane grows at the rate of 6 over 5 centimeters per month.
Let x be a number of months.
(6/5)x = 24/10
6x = 12
x = 12/6 = 4/2 or
x = 2 months
Thus, it will take 4/2 months or 2 months for the horse's mane to grow 24/10 centimeters.
Learn more about the linear equation here:
brainly.com/question/11897796
#SPJ2
What is equivalent to -2/5x=-4
A. -20
B. 1
C. -10
D. -8
E. X= -8/5
Answer:
10
Step-by-step explanation:
Multiply each side by the reciprocal, -5/2
x = -4 * -5/2
x = 20/2
x = 10
x over 2 +2= 15 two step equations
Answer:
[tex]\boxed{\boxed{\sf x=84}}[/tex]
Step-by-step explanation:
[tex]\sf \cfrac{x}{6} +2=16[/tex]
Multiply both sides of the equation by 6:
[tex]\sf x+12=96[/tex]
Subtract 12 from both sides:
[tex]\sf x=96-12[/tex]
Subtract 12 from 96:
[tex]\sf x=84[/tex]
_________________________________
Answer:
[tex] \sf \: \longmapsto\frac{x}{6} + 2 = 16[/tex]
[tex]\sf \: \longmapsto\frac{x}{6} = 16 - 2[/tex]
[tex]\sf \: \longmapsto \frac{x}{6} = 14[/tex]
[tex]\sf \: \longmapsto \: x = 14 \times 6[/tex]
[tex]\sf \: \longmapsto \: x = 84[/tex]
Step-by-step explanation:
[tex]\fbox {\fbox {\fbox {\fbox{ \pink{HeavenMistress}}}}}[/tex]
A car moving at a constant speed passed a timing device at t = 0. After 8 seconds, the car has
traveled 648 ft. Write a linear function rule to model the distance in feet d the car has traveled any
number of seconds t after passing the timing device.
The linear function rule is d =
Answer:answer d
Step-by-step explanation:
i just did the test
An 8 ounce steak costs $12.80. How much would a 32 ounce steak cost?
Answer:
12.80 divided by 8 = 1.60
1.60 x 32 = 51.20
Step-by-step explanation:
A bag contains
80
balls.
The ratio of red to blue balls is
3
:
7
Find how many red and blue balls there are.
Answer:
24 red balls 56 blue balls
Step-by-step explanation:
We can use the ratio as percentages
30% of 80 is 24 red balls, and then we do 80-24=56 to calculate blue balls
Help me pls right now I give brainliest
Answer:
4 + (2 x 3)^2
Step-by-step explanation:
4 + 6^2
4 + 36
40
Consider the equation 5/3v +4 + 1/3v = 8. What is the resulting equation after the first step in the equation?
Answer:
See below
Step-by-step explanation:
[tex]\frac{5}{3}v+4+\frac{1}{3}v=8[/tex]
[tex]2v+4=8[/tex] <-- Resulting equation after first step
[tex]2v=4[/tex]
[tex]v=2[/tex] <-- Actual solution
Hurry plz!!! graph y= 5/3x - 9
Answer:
This is what it would look like! Hope this helps!
Which binomial is a factor of 100x2 – 49?
a
O 10x + 7
O 25% - 7
O 25x + 49
O 203 – 49
-
Answer:
Step-by-step explanation:
What you have here is called "the difference of two squares"
Difference means subtraction and both 100x2 and 49 are perfect squares.
The factored form of 100x2-49 is
(10x+7)(10x-7)
Because 10x times 10x is 100x2 and 7 times 7 is 49
One factor has a + and
One factor has a -
It is a pattern worth memorizing!
So 10x + 7 is the factor you're looking for.
What is the slope of the line that contains these points?
Slope:
Answer:
-4
Step-by-step explanation:
Slope formula:
m=y2-y1/x2-x1
I will use (-1,10) and (1,2)
2-10/1-(-1)
Which is
-8/2
Divide:
-4
Thus the slope is -4
Hope this helps!
1234567891011121314151617181920
Answer:
What's this question? Oh my gosh!
estimate the line of best fit using two points on the line
Answer:
[tex]y=-8x+80[/tex]
Step-by-step explanation:
[tex]Slope=\frac{y_2-y_1}{x_2-x_1}=\frac{32-64}{6-2}=\frac{-32}{4}=-8[/tex]
[tex]y=mx+b[/tex]
[tex]y=-8x+b[/tex]
[tex]64=-8(2)+b[/tex]
[tex]64=-16+b[/tex]
[tex]80=b[/tex]
Therefore, the estimated line of best fit is [tex]y=-8x+80[/tex]
There are 6 triangles and 4 circles. What is the
simplest ratio of circles to total shapes?
Answer:
4/10
Step-by-step explanation:
4:10
as there are 4 circles, and 10 total (6 + 4)
simplify by diving by 2.
therefore the answer is,
2:5
(I guess, this could be simplified further, but it wouldn't be a whole number).
Juliet needs to rewrite 3 (x 2) = 6 y in slope-intercept form so she can easily graph it. Which step would be correct to start the process? She could combine the x and 2 to get 3 (2 x) = 6 y. She could divide both sides by 3 to get x 2 = 2 y. She could distribute the 3 to get 3 x 2 = 6 y. She could subtract the 6y to get Negative 6 y = 3 (x 2).
The step that would be correct to start the process is she could distribute the 3 to get 3x+2=6y
Note that the standard equation of a line in slope-intercept form is expressed as y = mx + b
m is the slopeb is the y-interceptGiven the function 3(x+2)=6y, for Juliet to write in slope-intercept form, the best approach is to first divide both equations by 6 as shown:
[tex]3(x+2)=6y \\\frac{3(x+2)}{6} =\frac{6y}{6} \\\frac{x+2}{6}=y[/tex]
Swap sides
[tex]y=\frac{x+2}{6}\\y=\frac{1}{6}x +\frac{1}{3}[/tex]
She could as well distribute the 3 over x + 2 to have:
3(x + 2) = 6y
3x + 3(2) = 6y
3x + 6 = 6y
Hence based on the option, the step that would be correct to start the process is she could distribute the 3 to get 3x+2=6y
Learn more on distributive law here: https://brainly.com/question/25224410
Answer:
Its C
Nevermind Its Not its A or B
Step-by-step explanation:
:)
The cost of an anti-virus software package is $65 for the first year and $10 for each annual renewal. If the independent variable is the number of annual renewals and the dependent variable is the total amount paid, what is the slope and y-intercept of the graph of the equation representing this situation?
Answer:
slope $10/renewaly-intercept $65Step-by-step explanation:
The slope is the cost of a renewal: $10.
The y-intercept is the initial cost: $65.
How many terms are in the expression 3xy+2x+1
Answer:
4
Step-by-step explanation:
In universal algebra and mathematical logic, a term algebra is a freely generated algebraic structure over a given signature. For example, in a signature consisting of a single binary operation, the term algebra over a set X of variables is exactly the free magma generated by X
Please help! If possible please show your work. Thank you in advance!! :D
Answer:
(-4)³ = -64-64Step-by-step explanation:
The first step in solving the equation is to cube both sides:
(∛x)³ = (-4)³ . . . . . = (-4)(-4)(-4) = 16(-4) = -64
x = -64 . . . . . simplified
__
We're not sure what "checking" is supposed to involve here. Usually, one would check the answer by seeing if a true statement is made when the answer is put into the original equation.
∛(-64) = -4 . . . true
Many calculators will not compute √(-64) because they compute roots using logarithms. The log of a negative number is not defined.
So, the way one would check this is to cube both sides, which is how we got the answer in the first place. We expect the same result from doing the same operation again, so it isn't really a check.
Muhammad needs at least 6 feet of yarn to make a scarf. If Muhammad has 2 yards and 3 inches of yarn, and there are 3 feet or 36 inches in 1 yard, will he be able to make a scarf?
Answer:
Muhammad will be able to make the scarf
Step-by-step explanation:
If he needs 6 feet of yarn and he has got 2 yards witch are 3 feet each multiply 3 feet by 2 and you get 6 yards and then add the 3 inches left, he's got 6 feet 3 inches
Question 7 high school geometry.
[tex]\huge \bf༆ Answer ༄[/tex]
In the given figure, The marked angles forms a pair of co - interior angles [ because lines l and m are parallel ]
therefore,
[tex] \sf12x - 8 + 104 = 180[/tex][tex] \sf12x + 96 = 180[/tex][tex] \sf12x = 180 - 96[/tex][tex] \sf12x = 84[/tex][tex] \sf x = 84 \div 12[/tex][tex] \sf x = 7[/tex]Hence, the value of x is ~ 7
75 percent of the sutdents in a school went on a field trip. If 285 students went on the trip, how any students are in the school
Answer:
380
Step-by-step explanation:
285 / x = 75 / 100
Cross multiply 28500 = 75x
Divide by 75 380
plz help ppl keep putting links
Answer:
∠DAB=140
∠BAC=60
∠EBF=40
∠ACB=80
∠BCG=100
Step-by-step explanation:
how to find the length of a triangle with angles
Answer:
1. The Pythagorean Theorem, a2+b2=c2, a 2 + b 2 = c 2 , is used to find the length of any side of a right triangle.
2. In a right triangle, one of the angles has a value of 90 degrees.
3. The longest side of a right triangle is called the hypotenuse, and it is the side that is opposite the 90 degree angle.
Step-by-step explanation:
e. Find the slope of the line that passes through the points (1, 3) and (9,7),
Answer:
0.5
Step-by-step explanation:
→ Find the difference in y
7 - 3 = 4
→ Find the difference in x
9 - 1 = 8
→ Divide the results
4 ÷ 8 = 0.5
Answer:
The slope is 1/2 (m=1/2)
Step-by-step explanation:
Use the slope formula: [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex] to solve for the slope. y2 is 7, y1 is 3, x2 is 1, x1 is 9. [tex]\frac{7-3}{9-1}=\frac{4}{8} = \frac{1}{2}[/tex]
What is the equation of the line that passes through the point (8,-4) and has a slope of 3?
Answer: The equation of a line that passes through the point (8,-4) and has a slope of 3 is y = 3x - 28.
Explanation:
y = -4, x = 8
By putting above values in equation (i)
-4 = 3 (8) + b
-4 = 24 + b
-28 = b
b = -28
y = 3x - 28