Answer: equation of the tangent plane is z = 1
Step-by-step explanation:
Given equation
z = e^(-x²-y²) at point (0,0,1)
now let z = f(x,y)
Δf(x,y) = [ fx, fy ]
= (-2xe^(-x²-y²)), (-2ye^(-x²-y²))
now
Δf (0,0) = [ 0, 0 ] = [ a, b ]
equation of the tangent plane therefore will be
z - z₀ = a(x-x₀) + b(y-y₀)
z - 1 = 0(x-0) + 0(y-0)
z - 1 = 0 + 0
z = 1
Therefore equation of the tangent plane is z = 1
Prove the statement using the ε, δ definition of a limit. lim x → 1 4 + 2x 3 = 2
Given ε > 0, we need δ ---Select--- such that if 0 < |x − 3| < δ, then 2 + 1 3 x − 3 ---Select--- . But 2 + 1 3 x − 3 < ε ⇔ 1 3 x − 1 < ε ⇔ 1 3 |x − 3| < ε ⇔ |x − 3| < ---Select--- . So if we choose δ = ---Select--- then 0 < |x − 3| < δ ⇒ 2 + 1 3 x − 3 < ε. Thus, lim x → 3 2 + 1 3 x = 3 by the definition of a limit.
You want to prove
[tex]\displaystyle\lim_{x\to1}\frac{4+2x}3=2[/tex]
By the definition of the limit, this means that for any [tex]\varepsilon>0[/tex], we can find [tex]\delta>0[/tex] such that
[tex]|x-1|<\delta\implies\left|\dfrac{4+2x}3-2\right|<\varepsilon[/tex].
In order to get the inequality we want, we need to have
[tex]\left|\dfrac{4+2x}3-2\right|=\left|\dfrac{2x-2}3\right|=\dfrac23|x-1|<\varepsilon\implies|x-1|<\dfrac{3\varepsilon}2[/tex]
so we can pick [tex]\delta=\frac{3\varepsilon}2[/tex].
So here's the proof: Let [tex]\varepsilon>0[/tex] be given, and let [tex]\delta=\frac{3\varepsilon}2[/tex]. Then
[tex]|x-1|<\delta=\dfrac{3\varepsilon}2[/tex]
[tex]\implies\dfrac23|x-1|<\varepsilon[/tex]
[tex]\implies\left|\dfrac{2x-2}3\right|=\left|\dfrac{2x+4}3-1\right|<\varepsilon[/tex]
as required.
Carries first three children were boys. If she has more children, they will all be boys. Is this deductive or inductive reasoning?
Answer:
Inductive reasoning
Step-by-step explanation:
Inductive reasoning is when you make a false assumption based on previous knowledge you had before. The previous fact will often be referring to just a certain amount/set of things.
Deductive reasoning is when you have previous knowledge and you make a claim that is correct based on the knowledge before. The previous fact will often be referring to a whole set of things, not limited to a certain number.
The fact here is that Carrie's first three children were boys. This doesn't necessarily mean all of her upcoming children will be boys. So this is inductive reasoning.
Hope this helped!
Answer:
inductive
Step-by-step explanation:
Inductive
I NEED HELP ASAP please
Answer:
A
Step-by-step explanation:
Draw a figure to represent the following information: T
is between S and U, ST = 7x, SU = 45, and TU = 5x –
3.
Answer:
ST = 28 unit
TU = 17 units
Step-by-step explanation:
Given:
ST = 7x
SU = 45
TU = 5x – 3
Find:
Each value
Computation:
SU = ST + TU
45 = 7x + 5x - 3
48 = 12x
x = 4
So,
ST = 7x
ST = 7(4)
ST = 28 unit
TU = 5x – 3
TU = 5(4) – 3
TU = 17 units
There are 40 nickels in a roll. If you have 150 rolls of nickels, how many nickels do you have?
You would have 6,000 nickels. Multiply 40 by 150
There are 6000 Nickels in 150 rolls of Nickle.
To find out the total number of nickels you have, you need to multiply the number of nickels in a single roll by the number of rolls.
Given that there are 40 nickels in a roll and you have 150 rolls..
So, the total number of nickels can be calculated as:
= 40 nickels/roll x 150 rolls
= 6000 nickels.
Therefore, you have 6000 nickels.
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How much shorter is the handle than the top of the screwdriver?
Answer:
Hey There! Here's Ur Answer
Step-by-step explanation:
one at their standard length of 45-3/4 inches, the other two inches shorter.
Happy to Help!
The red blood cell counts (in millions of cells per microliter) for a population of adult males can be approximated by a normal distribution, with a mean of 5.2 million cells per microliter and a standard deviation of 0.5 million cells per microliter. What is the minimum red blood cell count that can be in the top 24% of counts? What is the maximum red blood cell count that can be in the bottom 15% of counts? can somebody help me?
Answer:
5.55 million cells per microliter
4.68 million cells per microliter
Step-by-step explanation:
First, use a chart or calculator to find the z-score for reach percentage.
P(Z > z) = 0.24
P(Z < z) = 1 − 0.24 = 0.76
z = 0.706
Next, use definition of z-score to find the value.
z = (x − μ) / σ
0.706 = (x − 5.2) / 0.5
x = 5.55
Repeat for the other percentage.
P(Z < z) = 0.15
z = -1.036
z = (x − μ) / σ
-1.036 = (x − 5.2) / 0.5
x = 4.68
Which number is IRRATIONAL?
Answer:
A
Step-by-step explanation:
because no square root in in 12
Answer:
[tex]\sqrt{12}[/tex]
If a square root is not a perfect square, then it is an irrational number
[tex]ANSWER =\\\sqrt{12} \\\\=2\sqrt{3}[/tex]
Step-by-step explanation:
How to find measurement of degree?
Answer:
It's 30 degrees. YSX and QSL are verticals so they are equal. Then QSL AND MLP are corresponding so they are too equal. So then yeah.
Answer:
30°
Step-by-step explanation:
It’s important to note the angle relationships.
We have two parallel lines intersecting one line. This means that each of the angles formed by one line will be equal to the angles formed by the other.
Using this info, we can tell that XYZ and MLP are alternate exterior angles, since they are formed by two parallel lines.
Alternate exterior angles are equal: since we know XYZ is 30°, MLP must be 30°.
Hope this helped!
If A and B are 4 * 6 matrices and C is a 7 * 4 matrix, which of the following are defined?
1. CA.2. B^T * C^T.3. AC.4. A-B.5. B-C.6. B^T.
Answer:
1. CA is defined
2. B^T * C^T defined
3. AC is NOT defined
4. A - B is defined
5. B - C is NOT defined
6. B^T is defined
Hence, 1,2,4, and 6 are defined
Step-by-step explanation:
Order of the matrices:
Matrix A is a (4 × 6) matrix
Matrix B is a (4 × 6) matrix
Matrix C is a (7 × 4) matrix
To determine which are defined
1. CA
CA means product of Matrix C and Matrix A
To determine the product of two matrices, the number of columns in the first matrix must be equal to the number of rows in the second matrix. For example, given that matrix X is a (m × n) matrix, matrix Y is a (n × k) matrix and matrix Z is (k × n) matrix. From the definition above,
XY can be determined because number of columns in X equals number of rows in Y
XZ cannot be determine because number of columns in X is not equal to the number of rows in Z.
YZ can be determined because number of columns in Y equals number of rows in Z
(NOTE: A matrix of order (m × n) means the matrix has m rows and n columns)
Hence, for CA
Matrix C is a (7 × 4) matrix
Matrix A is a (4 × 6) matrix
Number of columns in C equals number of rows in A, hence CA is defined
2. B^T * C^T
B^T means transpose of matrix B
Transpose of a matrix is defined as a new matrix whose rows are the same as the columns of the original matrix and whose columns are the rows of the original matrix. Hence, for a matrix of order (m × k), the transpose of the matrix will have an order (k × m).
Hence,
Matrix B is a (4 × 6) matrix
∴B^T gives a matrix of order (6 × 4)
Matrix C is a (7 × 4) matrix
∴ C^T gives a matrix of order (4 × 7)
Since the number of columns in B^T equals the number of rows in C^T, then B^T * C^T defined
3. AC
Matrix A is a (4 × 6) matrix
Matrix C is a (7 × 4) matrix
The number of columns in A is NOT equal to the number of rows in C, hence AC is NOT defined
4. A - B
To find the difference between two matrices, the matrices must have the same order.
Matrix A is a (4 × 6) matrix
Matrix B is a (4 × 6) matrix
Since matrices A and B have the same order [(4 × 6)], hence A - B is defined
5. B - C
Matrix B is a (4 × 6) matrix
Matrix C is a (7 × 4) matrix
Since matrices B and C are of different orders [(4 × 6) and (7 × 4) respectively], then B - C is NOT defined
6. B^T
B^T means the transpose of matrix B
Matrix B is a (4 × 6) matrix
From the above definition
B^T gives a (6 × 4) matrix
Hence, B^T is defined
three subtracted from twice a number ?
please someone help me, i will give brainliest
Answer:
Both of them are the same measure: 45 degrees.
Step-by-step explanation:
You plug in 15 for the xin both of the equations they give.
3(15) +17=45
75-2(15)=45
if jeff had 10 cookies and sam ate 10 how many are left?
Answer:
0
Step-by-step explanation:
10-10=0
A company recently replaced its 9-oz cup of yogurt with a 7-oz cup and reduced the suggested retail price from 87 cents to 75 cents. Was the price per ounce reduced by the same percent as the size of the cup? If not, find the price difference per ounce in terms of a percent.
Answer:
Question 1
Was the price per ounce reduced by the same percent as the size of the cup? No it's not the same
Question 2
If not, find the price difference per ounce in terms of a percent.
13.8%
Step-by-step explanation:
The first yoghurt cup size = 9 oz
The second and recent yoghurt cup size = 7 oz
The difference in ounces = 9 oz - 7 oz
= 2 oz
Converting this difference to percentage
= 2 oz/ 9 oz × 100%
= 22.222222222%
The percent reduction in cup size is approximately
22.2%.
The first retail price per ounce = 87 cents
The second and recent retail price per ounce =75 cents
The difference in prices = 87 cents - 75 cents
= 12 cents
Converting this difference to percentage
= 12 cents / 87 cents × 100%
= 13.793103448%
The percent reduction in yoghurt price per ounce is approximately
13.8%.
Question 1
Was the price per ounce reduced by the same percent as the size of the cup?
From the above calculation,
Percent reduction in price per ounce =
13.8%
Percent reduction in the size of the cup = 22.2%
13.8% ≠ 22.2%
Therefore, it is not the same
Question 2
If not, find the price difference per ounce in terms of a percent.
Therefore, the price difference per ounce in terms of percent is
13.793103448%.
Approximately ≈ 13.8%
SOME ONE HELP ME PLZ FAST it's already late
Question Example Step by Step Calculate the minimum and maximum possible areas. Round your answers to the nearest whole square unit. Sara wants to paint a wall. The length and width of the wall are 3 meters and 1.8 meters, respectively. The minimum possible area is about m2. The maximum possible area is about m?
Answer:
4
Step-by-step explanation:
Help pls what is the answer to this 3(n+1)=5.4 Solve for n.
Answer:
N = 0.8
Step-by-step explanation:
3(n + 1) = 5.4
3n + 3 = 5.4
- 3 = -3
3n = 2.4
3n/3 = 2.4/3
N = 0.8
tristan wants to build a square garden in his backyard. if the garden is going to be 64 ft squared how many feet of material will he need for the perimeter of the garden?
Answer:
32 ft
Step-by-step explanation:
First Tristan must determine the length of one side of his square garden. Sine A = x^2, where x is the length of one side, and since 64 ft^2 = x^2, we can find the length x by taking the square root of both sides: 8 ft = x.
Now the length of the material enclosing the garden is the perimeter, P.
For a square, P = 4x.
Therefore, in this case, P = 4(8 ft) = 32 ft
Find the least whole number that can replace ? To make the statement true
? ÷9>700
Answer:
6301.
Step-by-step explanation:
First we find the integer such that ? / 9 = 700.
? = 700 * 9 = 6300.
Therefore the least whole number for ? / 9 > 700 should be 6301.
Find all points on the x-axis that are 14 units from the point (6,-7) All points on the x-axis that are 14 units from the point (6, -7) are Simplify your answer. Type an ordered pair. Use a comma to separate answers as needed.)
Answer: [tex](6+7\sqrt{3},0)\text{ and }(6-7\sqrt{3},0)[/tex] are the required points.
or (18.124,0) and ( -6.124,0) are the required points.
Step-by-step explanation:
Let (x,0) be the point on x -axis that are 14 units from the point (6,-7) .
Then by distance formula , we have
[tex]\sqrt{(x-6)^2+(0-(-7))^2}=14\ \ \ [\ \because distance=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}][/tex]
Taking square on both the sides , we get
[tex](x-6)^2+7^2=14^2\\\\\Rightarrow\ x^2+6^2-2(6)x+49=196\\\\\Rightarrow\ x^2+36-12x=147\\\\\Rightarrow\ x^2-12x=111\\\\\Rightarrow\ x^2-12x-111=0[/tex]
Using quadratic formula : [tex]x=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]
[tex]x=\dfrac{12\pm\sqrt{(-12)^2-4(1)(-111)}}{2}\\\\\Rightarrow\ x=\dfrac{12\pm\sqrt{144+444}}{2}\\\\\Rightarrow\ x=\dfrac{12\pm\sqrt{588}}{2}\\\\\Rightarrow\ x=\dfrac{12\pm\sqrt{2^2\times7^2\times3}}{2}\\\\\Rightarrow\ x=\dfrac{12\pm14\sqrt{3}}{2}\\\\\Rightarrow\ x=6\pm7\sqrt{3}[/tex]
so, [tex](6+7\sqrt{3},0)\text{ and }(6-7\sqrt{3},0)[/tex] are the required points.
since [tex]\sqrt{3}=1.732[/tex]
so, [tex](6+7(1.732),0)\text{ and }(6-7(1.732),0)[/tex] are the required points.
i.e. (18.124,0) and ( -6.124,0) are the required points.
7/9 as a decimal please
Answer:
0.77777778
Step-by-step explanation:
...
Hi there!
~
[tex]\frac{7}{9} = 0.77777778[/tex]
Hope this helped you!
Which of the following lines is parallel to x = 8?
a. 3y = 16
b. x = 7
c. х = y
d y = 8
Answer:
d. y = 8
Step-by-step explanation:
The given line is of the form ...
y = constant
A parallel line must be of the same form. The matching answer is ...
y = 8
Help immediate... What are the like terms and to simplify fully. -7y^2-6-2-6x+x
Answer:
the fully simplified expression is: [tex]-7y^2+7x-8[/tex]
Step-by-step explanation:
The like terms are:
-6 and -2, which combined give -8
and 6 x and x, which combine give 7 x
So the simplified form of this is:
[tex]-7y^2+7x-8[/tex]
Suppose you have a credit card debt of $4,000. Last month the bank charged you $40 interest on the debt. The solution to the equation 40= 4000/12r represents the annual interest rate (r) on the credit card. Find the annual interest rate on the credit card.
Answer:
12%
Step-by-step explanation:
As per the given formula:
40= 4000/12rr = 40*12/4000r = 0.12 0.12*100% = 12%Interest rate is 12%
6.009 in expanded form
Answer:
6.009 = (6 x 1) . (0/10) + (0/100) + (9/1000)
Step-by-step explanation:
evaluate the expression when p= 12 and m =15;p-m
2. "three times the sum of a number and 7”.
Answer:
3 * (7 + n)
Step-by-step explanation:
Three times - '3 *'
The sum of a number and 7 - '(7 + n)'
"Three times the sum of a number and 7” would be '3 * (7 + n)'.
Hope this helps.
The required equation is 3*(n + 7).
It is required to find the equation.
What is equation?An equation is a mathematical statement that is made up of two expressions connected by an equal sign. Equation, statement of equality between two expressions consisting of variables and/or numbers.
Given:
Let the number be n.
The sum of a number and 7 is n + 7
Three times the sum of a number and 7 is
3*(n + 7).
Therefore, the required equation is 3*(n + 7).
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Write these numbers in order of size,
smallest first:
a 8810 m, 8.9 km, 8901 m, 8.821 km,
8812 m, 8.8 km
Answer:8.8 km, 8810 m, 8812 m, 8.821 km, 8.9 km, 8901 m
Step-by-step explanation:
8810 m, 8.9 km, 8901 m, 8.821 km, 8812 m, 8.8 km
which mean
8810 m, 8900 m, 8901 m, 8821 m, 8812 m, 8800 m
arrange accordingly
8800 km, 8810 m, 8812 m, 8821 m, 8900 m, 8901 m
convert back
8.8 km, 8810 m, 8812 m, 8.821 km, 8.9 km, 8901 m
Answer:
8.8km , 8810m , 8812m , 8.821km , 8.9km , 8901m
Step-by-step explanation:
1km = 1000m
Convert values in km to m by multiplying them by 1000
8.8km × 1000 = 8800m
8.821km × 1000 = 8821m
8.9km × 1000 = 8900m
If a student gets an A on a final exam, then the student will pass the course.
The student gets an A on the final exam.
Answer: PERIOD
Step-by-step explanation:
Get good grades on your assignments and the student will pass the course with an A.
When Barbara started her trip, the odometer read 13,487.8. When she ended the trip, it read
14,108.6. Barbara's car gets 22 miles per gallon. Her tank was full at the beginning of the
trip. When she filled the tank, it cost her $88.04. How many gallons did Barb use, and what
price did she pay per gallon of gas on this fill-up?
HELP ASAP PLEASE
Answer:
28.2 gal
$3.12/gal
Step-by-step explanation:
Length of trip:
14,108.6 mi - 13,487.8 mi = 620.8 mi
(620.8 mi)/(22 mpg) = 28.218 gal
She used 28.2 gallons.
price per gallon = $88.04/(28.218 gal) = $3.12/gal
What is
2+2?
I been trying to figure it out, but I’m stuck on this question
Answer:
4
Step-by-step explanation: