Answer:
[tex]y = 5[/tex].
Or, equivalently:
[tex]\begin{aligned}\begin{bmatrix}0 \\ -3 \\ 0\end{bmatrix} \left(\begin{bmatrix}x \\ y \\ z\end{bmatrix} - \begin{bmatrix}1 \\ 5 \\ -3\end{bmatrix}\right) = 0\end{aligned}[/tex].
Step-by-step explanation:
Every plane in [tex]\mathbb{R}^{3}[/tex] could be represented with a vector equation of the form [tex]\vec{n}\, (\vec{r} - \vec{r}_{0}) = 0[/tex], where:
[tex]\vec{n}[/tex] is a vector normal to the plane (a normal vector), and [tex]\vec{r}_{0}[/tex] is the position vector of a point in the plane.Notice that in this question, the coordinates (and hence the position vectors) of the points in this plane are already given. For example, the position vector of the point [tex](1,\, 5,\, -3)[/tex] is the vector:
[tex]\begin{aligned}\vec{r}_{0} = \begin{bmatrix}1 \\ 5 \\ -3\end{bmatrix}\end{aligned}[/tex].
Specifically in [tex]\mathbb{R}^{3}[/tex], normal vectors of a plane could be found by:
finding two distinct directions parallel to that plane, and taking the cross product between the two directions.Subtracting position vectors of points in this plane from each other would give directions that are parallel to this plane:
[tex]\begin{aligned}\begin{bmatrix}2 \\ 5 \\ -3\end{bmatrix} - \begin{bmatrix}1 \\ 5 \\ -3\end{bmatrix} = \begin{bmatrix}1 \\ 0 \\ 0\end{bmatrix}\end{aligned}[/tex].
[tex]\begin{aligned}\begin{bmatrix}3 \\ 5 \\ 2\end{bmatrix} - \begin{bmatrix}1 \\ 5 \\ -3\end{bmatrix} = \begin{bmatrix}2 \\ 0 \\ 5\end{bmatrix}\end{aligned}[/tex].
The cross product between these two vectors in [tex]\mathbb{R}^{3}[/tex] would be:
[tex]\begin{aligned} \vec{n} = \begin{bmatrix}1 \\ 0 \\ 0\end{bmatrix} \times \begin{bmatrix}2 \\ 0 \\ 5\end{bmatrix} = & \begin{bmatrix}0 \times 5 - 0 \times 0 \\ 0 \times 2 - 1 \times 5\\ 1 \times 0 - 0 \times 2\end{bmatrix} = \begin{bmatrix}0 \\ -3 \\ 0\end{bmatrix}\end{aligned}[/tex].
(Note that the cross product between other directions parallel to the plane might give other normal vectors that are parallel to the one in this example.)
Using the position vector of the point [tex](1,\, 5,\, -3)[/tex] as [tex]\vec{r}_{0}[/tex], one possible vector equation for this plane would be:
[tex]\begin{aligned}\begin{bmatrix}0 \\ -3 \\ 0\end{bmatrix} \left(\begin{bmatrix}x \\ y \\ z\end{bmatrix} - \begin{bmatrix}1 \\ 5 \\ -3\end{bmatrix}\right) = 0\end{aligned}[/tex].
Expand the dot product and simplify to obtain a scalar equation for this plane:
[tex]\begin{aligned}\begin{bmatrix}0 \\ -3 \\ 0\end{bmatrix} \begin{bmatrix}x - 1 \\ y - 5 \\ z - (-3)\end{bmatrix} = 0\end{aligned}[/tex].
[tex]0\, (x - 1) + (-3)\, (y - 5) + 0\, (z - (-3)) = 0[/tex].
[tex](-3)\, (y - 5) = 0[/tex].
[tex]y = 5[/tex].
help me pleaseeeeeeeeeeeeeeeeee
Answer:
Step-by-step explanation:
Volume
V = w h l
V = 2*15*13
V = 390 ft^3
-------------------------
Surface area
SA = b*h
SA = 15*13
SA = 195
-------------------------
b) Surface area
C) Volume
Whats the difference between 16x + 5 and 4x + 5
If xy + 1/(xy) = 2 , then what does (x^2)(y^2) + 1/((x^2)(y^2)) = ?
Show all work.
Show any graphical support.
Explain what happened with both the math work and the graph(s).
Think about what happened.
Would it happen with more terms or the next function in the sequence?
Why or why not? Explain.
The value of the expression will be [tex](xy)^2+\dfrac{1}{(xy)^2}=2[/tex]
What is an expression?Expression in maths is defined as the collection of the numbers variables and functions by using signs like addition, subtraction, multiplication and division.
Given that:-
The value of the expression is [tex]xy+\dfrac{1}{xy}=2[/tex]
So we need to find [tex](xy)^2+\dfrac{1}{(xy)^2}=?[/tex]
The value of the expression will be calculated as:-
[tex]xy+\dfrac{1}{xy}=2[/tex]
Squaring the above equation.
[tex](xy)^2+\dfrac{1}{(xy^2)}+2\times (xy)^2\times \dfrac{1}{(xy^2)}=4[/tex]
[tex](xy)^2+\dfrac{1}{(xy^2)}=2[/tex]
Again squaring the above expression.
[tex](xy)^4+\dfrac{1}{(xy^4)}+2\times (xy)^4\times \dfrac{1}{(xy^4)}=4[/tex]
[tex](xy)^4+\dfrac{1}{(xy^4)}=2[/tex]
Hence the value of the expression will be [tex](xy)^2+\dfrac{1}{(xy)^2}=2[/tex]
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Kenosha is having a lunch with 4 of her friends at a fancy restaurant. The bill total is $175.50 if a 20% tip is added onto the total how much each person need to contribute
Answer:
$8.78
Step-by-step explanation:
first you need to find 20% of $175.50
which is 35.10
then you divide 35.10 by 4 leaving you with 8.78
please mark brainliest
The table displays the scores of students on a recent exam. Find the mean of the
scores to the nearest 10th.
Score Number of Students
65
5
70
6
75
8
80
2
85
9
90
1
95
6
100
3
Answer:
43.75, or 43.8 to the nearest 10th
Step-by-step explanation:
The mean is the mathematical average of a set of two or more numbers. Summing the numbers in a set and dividing by the total number gives you the arithmetic mean.
The total of your numbers is 700.
There are 16 numbers.
700 divided by 16 is 43.75
The prime factorisation of √169 is?
Answer:
Square root of 169 by Prime factorization is 13×13
Answer:
13*13
Hope this helped!
solve by completing the square
Step-by-step explanation:
answer is in the picture above
calculate the value of:
1+3+5+....+43
17 Which numbers make the comparison true? 27,768 Select the two correct answers. A 27,759 8 28.744 26,773 27,568 E 27,836
Answer:
B and D
Step-by-step explanation:
hope it helps in some way possible
Using the Data Set {125, 6, 133, 129, 125}, find the standard deviation:
what is the area of a circle with 5cm radius
Answer:
Step-by-step explanation:
The formula to calculate the area of a circle is
[tex]A =\pi r^2[/tex]
This means that if [tex]r = 5 "cm"[/tex], the area is
[tex]A = 5^2\pi " cm"^2 = 25 \pi " cm"^2 =(estimation) 78.539816 " cm"^2[/tex]
Answer:
See below
Step-by-step explanation:
We are given that a circle has a radius of 5 cm
We want to find the area of this circle
The area of a circle is given as [tex]\pi r^{2}[/tex], where r is the radius
As stated above, the radius of this circle is 5; ergo, r =5
We can substitute 5 as r in the formula
A = [tex]\pi r^{2}[/tex]
A = [tex]\pi (5)^{2}[/tex]
Raise 5 to the 2nd power
A = π * 25
A = 25π cm²
If you need your answer in terms of pi (or as an exact answer), the answer would be 25π cm² (don't forget your units!)
However, if your system wants pi approximated, see below:
If your system wants pi to be used as 3.14, then multiply 25 by 3.14; 25 * 3.14 = 78.5 cm²
If your system wants pi to be used as 22/7, then multiply 25 by 22/7; 25 * 22/7 ≈ 78.57 cm²
which inequality is represented by this graph?
Answer:
the answer is A for the shaded region
Select the correct answer.
What is the range of this absolute value function?
y
-10
-10.
-8
9
N-
N
A
-6
-8
-10
10
Is (-3, 1) a solution to this system of inequalities?
5x + 5y ≤ -19
10x 16y < 1
yes or no
Answer:
No
Step-by-step explanation:
5(-3)= -15
5(1)= 5
-15+5=-10
-10 is greater than -19 not less than or equal too.
Hope this helps!
a=2,b=1 and c=4.What is 3ac-a+2b
Step-by-step explanation:
a = 2
b = 1
c = 4
Question:[tex]3ac - a + 2b[/tex]
= Solution ,
= 3 × 2 × 4 - 2 + 2 × 1
= 24 - 2 + 2
= 24 + 2 - 2
= 26 - 2
= 24
hence the answer is 24....
First try was incorrect
Ivy is making fasnacht (deep-fried German doughnuts) to sell the
Tuesday before Ash Wednesday, her bakery's biggest fasnacht day of
the calendar year. She has 6 pounds of butter and her recipe calls for
1
2
cup of butter per 1.5 dozen fasnacht. If 1 pound of butter is 2 cups,
then how many cups of butter will Ivy have left over after making 30
Answer:
3 cups of butter ivy will have left over
e demand for a certain product is random. It has been estimated that the monthly demand of the product has a normal distribution with a mend of 390units. The unit price of product is ETB 25. Ordering cost is ETB 40 per order and inventory carrying cost is estimated to be 35 percent per year. Calculate economic order quantity (EOQ). 10. Given the data below, what is the simple linear regression
The economic order quantity of the product with the demand of 390 units is 1392.86 units.
What is an economic order quantity?This refers to an inventory management technique that helps make efficient inventory management decisions.
The formula for economic order quantity is [tex]\sqrt{2 * D * S / H}[/tex]
Given data
Demand = 390 units.
Unit price of product is ETB 25.
Ordering cost is ETB 40 per order
inventory carrying cost is estimated to be 35 percent per yer
EOQ = [tex]\sqrt{2*390*25/40*0.35}}[/tex]
EOQ = 19,500 / 14
EOQ = 1392.85714286
EOQ = 1392.86 units
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Which of the following could be the center of a circle that includes the points (-5, 2) and (-3, 6)?
A. (0, 2)
B. (0, -2)
C. (2, 2)
D. (2, 1)
The center of a circle that includes the points (-5, 2) and (-3, 6) could be (a) (0,2)
How to determine the center of the circle?The points are given as:
(-5, 2) and (-3, 6)
The equation of a circle is represented as:
[tex](x -a)^2 + (y - b)^2 = r^2[/tex]
Where:
Points = (x,y)Center = (a,b)Radius = rSubstitute both points in the above equation
[tex](-5 + a)^2 + (2 - b)^2 = r^2[/tex]
[tex](- 3+ a)^2 + (6 - b)^2 = r^2[/tex]
The radii are equal.
So, we have:
[tex](-5 + a)^2 + (2 - b)^2 = (- 3+ a)^2 + (6 - b)^2[/tex]
Expand the equations
[tex]25 -10a + a^2 + 4 - 4b + b^2 = 9 - 6a + a^2 + 36 - 12b + b^2[/tex]
Evaluate the like terms
[tex]25 -10a + 4 - 4b = 9 - 6a + 36 - 12b[/tex]
Collect like terms
6a -10a - 4b + 12b = 9 + 36 - 25 - 4
Evaluate
-4a + 8b = 16
Divide through by - 4
a - 2b = -4
Next, we test the options:
Option (a) (a,b) = (0,2)
Substitute these values in the equation
0 - 2*2 = -4
Evaluate
-4 = -4
Both sides of the equation are the same
Hence, the center of a circle that includes the points (-5, 2) and (-3, 6) could be (a) (0,2)
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Which of the following figures has a circumference that is closest to 121 inches?
A
a circle with a diameter of 38.5 inches
B
a circle with a diameter of 19.3 inches
C
a circle with a radius of 38.5 inches
D
a circle with a radius of 6.2 inches
Answer:
A.
Step-by-step explanation:
C = 2πr = πd
A. C = π(38.5 in.) = 120.95 in.
First guess: Answer: A.
5 points
11 cm
I literally dont know what to do
Find the area.
14 in
6.8 in
Answer:
95.2Step-by-step explanation:
It nearly confused me, but I got the entire thing in my brain.
Given equation:
14 * 6.8Solve:
Transfer:6.8 ⇒ 68Solve:14 * 68= 952Transfer a decimal point to the right 1 space:952 → 95.2.Answer is 95.2.
Assuming Earth to be a sphere of radius 4000 miles, how many miles north of the Equator is City A, if it is 36° north from the Equator?
Answer:
2513 miles
Explanation:
[tex]\sf Length \ of \ arc = \dfrac{\theta}{360} * 2\pi r[/tex]
Here given:
∅ = 36°
radius = 4000 miles
Insert following:
[tex]\sf \rightarrow \dfrac{36}{360} * 2\pi (4000)[/tex]
[tex]\sf \rightarrow 800\pi \ \ \ (in \ terms \ of \ \pi )[/tex]
[tex]\sf \rightarrow 2513.3 \ \ (rounded \ to \ nearest \ tenth)[/tex]
[tex]\sf \rightarrow 2513 \ \ (rounded \ to \ nearest \ mile)[/tex]
How would you write 8^5 as a multiplication expression? A. 8 × 5 B. 8 × 8 × 8 × 8 × 8 C. 5 × 5 × 5 × 5 × 5 × 5 × 5 × 5
[tex]\huge\underline{\red{A}\blue{n}\pink{s}\purple{w}\orange{e}\green{r} -}[/tex]
if we ever face a number written in the form of [tex]\underline{x^{n}}[/tex]where x denotes the base and n denotes the exponent or power , we can expand it in the following way -
[tex] x^{n} = x \times x \times x \times.... x ( upto\: " n " \: times )[/tex]
therefore ,
[tex]8 {}^{5} = 8 \times 8 \times 8 \times 8 \times 8[/tex]
option ( B )
hope helpful -,-
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
[tex]\diamond\:\large\blue\textsf{\textbf{\underline{\underline{Question:-}}}}\:\diamond[/tex]
✶ How would you write [tex]\bold{8^5}[/tex] as a multiplication expression [tex]\textit{?}[/tex]
[tex]\diamond\large\blue\textsf{\textbf{\underline{\underline{Answer and How to solve:-}}}}\diamond[/tex]
✶ The exponent indicates how many times a certain number was multiplied by itself.
✶ In this case we have [tex]\bold{8^5}[/tex], so 8 was multiplied by itself five times.
So we conclude that [tex]\bold{8^5}[/tex] written as a multiplication expression looks as follows:-
[tex]\bigcirc\!\!\!\!\checkmark[/tex] 8•8•8•8•8
Good luck.- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
Calculate the diameter of the
circle.
- - -- - - - - - - - - - - - - - - - - - - - --
[tex]\diamond\large\blue\textsf{\textbf{\underline{Given question:-}}}[/tex]
[refer to attachment for question]
[tex]\diamond\large\blue\textsf{\textbf{\underline{\underline{Answer and how to solve:-}}}}[/tex]
Remember, the radius is exactly one-half of the diameter, so if we need to find the diameter, we multiply the radius times 2:-
r=6.5m
d=13m
r=9.1 ft
d=18.2 ft
Good luck with your studies.- - - - - - - - - - - - - - - - - - - - - - - - - - - - - -- - -
13 of 15
L
Find the x-intercepts of the parabola with
vertex (-1,-17) and y-intercept (0,-13).
Write your answer in this form: (*1,91),(X2,42).
Answer:
(√30 - 1, 0)(-√30 - 1, 0)Step-by-step explanation:
Making the equation of the parabola :
⇒ y = a(x - h)² + k
⇒ y = (x + 1)² - 17 - 13
⇒ y = (x + 1)² - 30
x-intercepts have y = 0 :
0 = (x + 1)² - 30(x + 1)² = 30Taking the square root on each side :
√(x + 1)² = √30x + 1 = ±√30x = ±√30 - 1The x-intercepts are :
(√30 - 1, 0)(-√30 - 1, 0)If x-1/-3=y-2/2k=z-3/2 and x-1/3k=y-5/4=z-6/-5 are perpendicular, find the value of k
Which of the following functions matches this graph?
X
-54-3 -2 -1
1 2 3 4 5
a. y = x²
b. y = 3x²
M Ca
a
7 M
T?
U
d.
y
11
--x
10
Answer:
x plus y is 44 to the 99th power
Step-by-step explanation:
What is the slope of the line that passes through the points(−8,2) and (-11, 3)? Write your answer in simplest form.
Answer: -1/3
Step-by-step explanation:
The formula is y2 - y1/ x2 - x1 . So the answer would be -1/3 bc 3 - 2 = 1 and -11 - (-8) = -3.
Each of the 7 cats Ik a pet store was weighed here are their eights in pounds
7,16,10,16,9,13,14 help me find the mean and median
Answer:
Below in bold.
Step-by-step explanation:
7,16,10,16,9,13,14
Arrange in ascending order:
7 9 10 13 14 16 16
The median = middle value
= 13 pounds.
Mean = (7+9+10+13+14+16+16)/7
= 12.14 pounds.