The length of the vector u*v has a maximum value of 16 and a minimum value of 0, and it is moving in a positive z-direction.
What is the maximum and minimum values of the length of the vector? in what direction does point?Generally, the equation for is mathematically given as
Consider the following vector:
[tex]\begin{aligned}\mathbf{v} &=0 \mathbf{i}+4 \mathbf{j}+0 \mathbf{k} \\&=\langle 0,4,0\}\end{aligned}[/tex]
Let us assume that u is a vector that has a length of four, that begins at the origin, and rotates in the x-y plane.
This vector creates a circle with the origin serving as the circle's center and a radius of 4.
So, the coordinates of u can be taken as,
[tex]u=(x\pm \sqrt{4^2-x^2 ,0})[/tex]
Here, 0 [tex]\leq[/tex]x [tex]\leq[/tex] 4.
Now, the cross product of the two vectors u and v is,
[tex]\begin{array}{ccc}\mathbf{i} & \mathbf{j} & \mathbf{k} \\x & \pm \sqrt{4-x^2} & 0 \\0 & 4 & 0\end{array}[/tex]
[tex]&=\mathbf{i}(0-0)-\mathbf{j}(0-0)+\mathbf{k}(4 x-0) \\&=4 x \mathbf{k}\end{aligned}[/tex]
The length of the vector u* v is,
[tex]\begin{aligned}|\mathbf{u} \times \mathbf{v}| &=\sqrt{(4 x)^2} \\&=4 x\end{aligned}[/tex]
Here, 0 <=x <= 4.
If x=4, then u*v is,
[tex]\begin{aligned}\mathbf{u} \times \mathbf{v}| &=4 \times 4 \\&=16 \\|\mathbf{u} \times \mathbf{v}| &=4 \times 0 \\&=0\end{aligned}[/tex]
In conclusion, As a result, the length of the vector u*v has a maximum value of 16 and a minimum value of 0, and it is moving in a positive z-direction.
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CQ
Let v = 4j and let u be a vector with length 4 that starts at the origin and rotates in the xy-plane. Find the maximum and minimum values of the length of the vector u
Determine whether the conclusion is based on inductive or deductive reasoning.Holly notices that every Saturday, her neighbor mows his lawn. Today is Saturday. Holly concludes her neighbor will mow his lawn.
Based on the explanation that is provided below, Holly's conclusion is based on inductive reasoning.
What is the difference between inductive and deductive reasoning?Inductive reasoning can be described as reasoning whose conclusion is based on a pattern of observations.
On the other hand, deductive reasoning refers to reasoning whose conclusion is based on a fact.
As Holly notices that every Saturday, her neighbor mows his lawn, this shows a pattern of observations.
This, therefore, implies that Holly's conclusion is based on inductive reasoning.
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a positive five-digit integer is in the form $ab,cba$; where $a$, $b$ and $c$ are each distinct digits. what is the greatest possible value of $ab,cba$ that is divisible by eleven?
The required positive five-digit integer of the form ab,cba; which should be divisible by 11 is 87,978
Explain the divisibility test of 11.
For a number to be divisible by 11, the difference between the sum of its odd digits (1st, 3rd, 5th...) and the sum of its even digits (2nd, 4th...) must be divisible by 11.
Calculation for the positive five-digit integer of the form ab,cba to be divisible by 11
Required 5 digit number is of the form, ab,cba
Using the divisibility test of 11, we get
(b + b) - (a + c + a) to be divisible by 11
i.e. 2b - (2a + c) to be divisible by 11
Replacing ab,cba using the greatest numbers, such as 7, 8 and 9 and checking its divisibility with 11
78,987 = 2*8 - (2*7 + 9) = 16 - (14 + 9) = 16 - 23 = -7 NO
87,978 = 2*7 - (2*8 + 9) = 14 - (16 + 9) = 14 - 25 = -11 YES
79,897 = 2*9 - (2*7 + 8) = 18 - (14 + 8) = 18 - 22 = -4 NO
97,879 = 2*7 - (2*9 + 8) = 14 - (18 + 8) = 14 - 26 = -12 NO
89,798 = 2*9 - (2*8 + 7) = 18 - (16 + 7) = 18 - 23 = -5 NO
98,789 = 2*8 - (2*9 + 7) = 16 - (18 + 7) = 16 - 25 = -9 NO
Thus, a positive 5-digit number is 87,978
Hence, the required positive five-digit integer of the form ab,cba; which should be divisible by 11 is 87,978
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A frame 2 inches wide surrounds a painting that is 18 inches wide and 14 inches tall. What is the area of the frame?
A 68 in²
B 84 in²
C 144 in²
D 252 in²
E 396 in²
The area of the frame is D. 252 in².
How to calculate the area?It should be noted that the frame 2 inches wide surrounds a painting that is 18 inches wide and 14 inches tall.
The area will be:
= Length × Width
= 18 × 14
= 252 in²
The area is 252 inches².
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Draw the line of reflection that reflects \triangle ABC△ABCtriangle, A, B, C onto \triangle A'B'C'△A
′
B
′
C
′
triangle, A, prime, B, prime, C, prime.
Thus, the equation of the line of reflection,
x=2 and x=4
When a point on a line segment divides it into two segments, the formula used to determine the coordinates of that point is known as the section formula.
It is given that,
A=(7,6)
A'=(-1,6),
B=(5,5)
and B'=(1,5),
As, the mid point of vertices of figure to the corresponding vertices of reflected figure should lie on reflected line.
Since, Δ ABC is reflected to Δ A'B'C' through this line,
Let, Q be the mid point of line AA', using section formula
Coordinate of Q = ((7-(-1))/2 , (6-6)/2 )
Q = (4,0)
and R be the mid point of line BB', using section formula
Coordinate of R = Q = ((5-1)/2 , (5-5)/2 )
Q = (2,0)
Q and R lies on the line of the reflection,
Thus, the equation of the line of reflection,
x=2 and x=4
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a bike wheel. the weight of a full steel bead tire is approximately 800 grams, while a lighter wheel weighs only 700 grams. what is the weight of each tire in pounds? there are 453.592 grams in one pound. round answers to 2 decimal places.
According to the given statement the weight of each tire in pounds:
For 800 grams = 1.76 pounds.
For 700 grams = 1.54 pounds.
What significance does the weight conversion of typical baking ingredients have?For dry substances, it's crucial to convert to weight. While most recipes
meant for home chefs express the components by volume, most recipes in industrial kitchens express essential ingredients by weight.
How are conversion factors used?A conversion factor is indeed a number that is used to multiply or divide one set of units into another. If a conversion is necessary, it must be carried out with the right conversion factor to produce a value that is identical. That example in the case, when translating between inches and feet, 12 inches equals one foot.
According to the given data:800 grams must be converted to pounds.
(1 pound =453.592 x= 800)
800 must be divided by 453.592 to get the number 1.763699. To round it up: 1.76
We now repeat this for 700.
1,5432 when 700 is divided by 453.592. Rounding that down, we get: 1.54
The given statement the weight of each tire in pounds:
For 800 grams = 1.76 pounds.
For 700 grams = 1.54 pounds
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A test has twenty questions
worth 100 points. Some
questions are worth three points,
some are worth eleven points.
How many three-point questions
are there? How many eleven
point questions are there?
There are 5 11 pointer questions and 15 3 pointer questions
We are given that total points of the test is 100
The test contains questions of two markings 3 points and 11 points
It is given that the total number of questions is 20
Let the number of three pointer questions be 'x' and the number of 11 pointer questions be 'y'
Thus total number of questions=x + y =20
Now the total sum of all the points comes to 100
Therefore,
3x+11y =100
x + y =20
x= 20-y
Now putting the value of x in the other question,
3(20-y) +11y =100
60-3y +11y=100
8y=100-60
8y=40
y=5
Thus x=20-y=20-5=15
Thus there are 5 11 pointer questions and 15 3 pointer questions
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dana walk 350 meter to school enevy day how many kio
Answer:
2.1
Step-by-step explanation:
If Mr. Smith's full recipe makes 10 cups
of chili and serves 15 people. What is the
serving size in cups?
7 of 107 of 10 items question ben went to the hardware store and bought 15 pieces of rope of equal length. the total length of the ropes was 326.7 meters. how long was each rope?
Answer:
The Correct answer is 21.78 meters
Step-by-step explanation:
Simply divide 326.7 ÷ 15 and it will leave you with 21.78
Can someone please help I will be giving Brainliest to whoever can answer :)
Match the questions with the graphs that are labeled A-H. (keep in mind that some questions might have the same answer)
1. A = {(x, y): y > x^2}
2. B = {(x, y): y ≥ x^2+ 3}
3. C = {(x, y): y ≤ 3x^2 + 2}
4. D = {(x, y): y ≥ 2x^2- 5x + 1}
The inequalities are matched with their correct graph respectively as follows:
D ⇒ {(x, y): y > x²}.G ⇒ {(x, y): y ≥ x²+ 3C ⇒ {(x, y): y ≤ 3x² + 2}A ⇒ {(x, y): y ≥ 2x² - 5x + 1}J ⇒ x²- 3x ≥ 0H ⇒ x² - 3x + 2 ≤ 0B ⇒ {(x, y): y ≤ 1 - x²} B ⇒ {(x, y): y ≥ -1}What is a graph?A graph can be defined as a type of chart that's commonly used to graphically represent data on both the horizontal and vertical lines of a cartesian coordinate, which are the x-axis and y-axis.
What is an inequality?An inequality can be defined as a mathematical relation that compares two (2) or more integers and variables in an equation based on any of the following arguments:
Less than (<).Greater than (>).Less than or equal to (≤).Greater than or equal to (≥).In Geometry, if the leading coefficient of a quadratic equation is greater than (>) zero, the parabolic curve would open upward while the parabolic curve would open downward when the leading coefficient of a quadratic equation is less than (<) zero.
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Complete Question:
Match the questions with the graphs that are labeled A-H. (keep in mind that some questions might have the same answer)
1. A = {(x, y): y > x^2}
2. B = {(x, y): y ≥ x^2+ 3}
3. C = {(x, y): y ≤ 3x^2 + 2}
4. D = {(x, y): y ≥ 2x^2- 5x + 1}
6. x^2- 3x ≥ 0
7. x^2- 3x + 2 ≤ 0
8. {(x, y): y ≤ 1 - x^2}
9. {(x, y): y ≥ -1}
Gabrielle is 7 years younger than Mikhail. The sum of their ages is 67. What is Mikhail‘a age
Answer:
Step-by-step explanation
Mikhail is 37
Gabrielle is 30
37+30= 67
Simplify 5 · P · 2.
A. 10P
B. 52P
C. 7P
Answer:
Step-by-step explanation:
5 x 2 = 10
Pretty sure this is right but I'm not 100 percent sure!
Answer: 10P ==> A
Step-by-step explanation:
5 · P · 2= 5 · 2 · P ==> Commutative property of multiplication
5 · 2 · P=
10 · P=10P ==> A
The table shows the numbers y of students absent from school x days after a flu outbreak.
Write a function that models the data.
Use the model to approximate the number of students absent 10 days after the outbreak.
A scatter plot is also referred to as scatter chart, scatter diagram or scattergram and it can be defined as a type of graph which is used for the graphical representation of the values of two (2) variables, with the resulting points showing any association (correlation) between the data set.
What is a quadratic function?A quadratic function can be defined as a mathematical expression (equation) that can be used to define and represent the relationship that exists between two or more variable on a graph.
In Mathematics, the standard form of a quadratic equation is given by;
ax² + bx + c = 0
By critically observing the graph (see attachment) which models the data in the given table, we can infer and logically deduce that the polynomial function is given by:
y = -0.4908x² + 5.8845x + 1.3572
For the number of students that are absent 10 days after the outbreak, we have:
y = -0.4908(10)² + 5.8845(10) + 1.3572
y = -0.4908(100) + 58.845 + 1.3572
y = -49.08 + 58.845 + 1.3572
y = 11.12 ≈ 11 students.
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(-1)⁵, 3`⁶, 3⁶, 5¹, 10°, 0.1
the 3⁶ is a negative exponent
What is this least to greatest?
The least to greatest will [ ( - 1 ) ^ 5 ] < [ 3 ^ ( - 6 ) < 0.1 < ( 10 ^ 0 ) < ( 5 ^ 1 ) < ( 3 ^ 6 ) .
( - 1 ) ^ 5 , 3 ^ ( - 6 ) , 3 ^ 6 , 5 ^ 1 , 10 ^ 0 , 0.1
Simplifying each of them
( - 1 ) ^ 5 = - 1
3 ^ ( - 6 ) = 0.001
3 ^ 6 = 729
5 ^ 1 = 5
10 ^ 0 = 1
0.1 = 0.1
Least to greatest = - 1 < 0.001 < 0.1 < 1 < 5 < 729
= [ ( - 1 ) ^ 5 ] < [ 3 ^ ( - 6 ) < 0.1 < ( 10 ^ 0 ) < ( 5 ^ 1 ) < ( 3 ^ 6 )
Hence , least to greatest will [ ( - 1 ) ^ 5 ] < [ 3 ^ ( - 6 ) < 0.1 < ( 10 ^ 0 ) < ( 5 ^ 1 ) < ( 3 ^ 6 ) .
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(-12c⁵) (3c⁴)
Sensitive fr
Simplify: (-12c⁵) (3c⁴)=36c⁹.
Simplification of (-12c^5) (3c^4) is -36c⁹.Given that
(-12c⁵) (3c⁴)To find
Simplification form of (-12c⁵) (3c⁴) = .........?So, according to the question
We have,
(-12c⁵) (3c⁴)To convert it in simplest form we have to use mathematically operations of powers.
= (-12c⁵) (3c⁴)
Now, separate the numerical and variable parts from equation
= (-12 ×3) c⁵× c⁴
Now, from using the mathematically operations of powers, to add powers, and multiply 12 with 3.
∵ [tex]a^m\times a^n = a^{m+n}[/tex]
∴[tex]c^5\times c^4 = c^{5+4}[/tex]
= (-36) c⁵⁺⁴
= (-36) c⁹
Simplification form of (-12c⁵) (3c⁴) = (-36) c⁹.
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Use prime factors to find the H.C. F and
L.C.M
-168 and 196
-150 and 180
(Refer to the table given below)
So,
LCM of 168 and 196: 1176LCM of 150 and 180: 900Then,
HCF of 168 and 196: 28HCF of 150 and 180: 30Therefore,
LCM of 168 and 196: 1176LCM of 150 and 180: 900HCF of 168 and 196: 28HCF of 150 and 180: 30Know more about LCM here:
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find y intercept when y=3x-1
Answer:
Y-intercept is -1
Step-by-step explanation:
Slope-intercept form:
y=mx+b
b=y-intercept
m=slope
y=3x-1
b=-1
Hope this helps!
Please mark as brainliest if correct!
A prize at an arcade costs 545 tickets. You have 435 tickets, and your friend has
690 tickets. Can you buy the prize when your friend gives you 1/6 of their tickets?
Explain.
NEED THIS DONE ASAP !! PLEASE
A: All real numbers greater than 0
B: All real numbers
C: All real numbers between -5 and 4
D : All real numbers greater than -2
Answer:
B: All real numbers
Step-by-step explanation:
Check the attached image for explanation.
Hope it helps.Find the surface area of that part of the plane 4x 5y z=74x 5y z=7 that lies inside the elliptic cylinder x225 y2100=1
Solve for [tex]z=f(x,y)[/tex] in the plane equation.
[tex]4x + 5y + z = 7 \implies f(x,y) = z = 7 - 4x - 5y[/tex]
Let [tex]E[/tex] be the set of points in the plane [tex]z=0[/tex] bounded by the ellipse [tex]\frac{x^2}{25}+\frac{y^2}{100}=1[/tex], i.e.
[tex]E = \left\{(x,y) ~:~ \dfrac{x^2}{25} + \dfrac{y^2}{100} \le 1\right\}[/tex]
Then the area of the plane bounded by the elliptic cylinder is
[tex]\displaystyle \iint_E dA = \iint_E \sqrt{1 + \left(\dfrac{\partial f}{\partial x}\right)^2 + \left(\frac{\partial f}{\partial y}\right)^2} \, dx \, dy \\\\ ~~~~~~~~ = \iint_E \sqrt{1 + (-4)^2 + (-5)^2} \, dx\, dy \\\\ ~~~~~~~~ = \sqrt{42} \iint_E dx \, dy[/tex]
which is simply √42 times the area of the ellipse in the plane [tex]z=0[/tex]. This ellipse has a minor axis of length 5 and a major axis of length 10, so its area is π•5•10 = 50π, and so the area of the plane in question is 50√42 π.
To confirm this result: In polar coordinates, with
[tex]\begin{cases}x(r,\theta) = 5r\cos(\theta) \\ y(r,\theta) = 10r\sin(\theta) \\ \frac{x^2}{25}+\frac{y^2}{100}=r^2\end{cases}[/tex]
the area element is
[tex]dA = \begin{vmatrix}\frac{\partial x}{\partial r}&\frac{\partial x}{\partial\theta} \\ \frac{\partial y}{\partial r} & \frac{\partial x}{\partial\theta}\end{vmatrix} \, dr \, d\theta \\\\ ~~~~~~~~ = \begin{vmatrix}5\cos(\theta)&-5r\sin(\theta)\\10\sin(\theta)&10r\cos(\theta)\end{vmatrix} \, dr \, d\theta \\\\ ~~~~~~~~ = \left(50r\cos^2(\theta)+50r\sin^2(\theta)\right)\,dr\,d\theta \\\\ ~~~~~~~~ = 50r \, dr \, d\theta[/tex]
The ellipse can be parameterized by
[tex]E = \left\{(r,\theta) ~:~ 0\le\theta\le2\pi \text{ and } 0\le r\le1\right\}[/tex]
so that the integral for the area of the ellipse in the plane [tex]z=0[/tex] is
[tex]\displaystyle \iint_E dA = \int_0^{2\pi} \int_0^1 50r \, dr \, d\theta \\\\ ~~~~~~~~ = 100\pi \int_0^1 r \, dr \\\\ ~~~~~~~~ = 100\pi\left(\frac12-0\right) = 50\pi[/tex]
kurt busch won the daytona 500 (mile) race with a rate of 143.187 mph in 2017. find his time to the nearest thousandth
The time taken to finish the race is 3.49 hours
Speed is defined as. The rate of change of position of an object in any direction. Speed is measured as the ratio of distance to the time in which the distance was covered.
Given,
The total distance = 500 miles
The speed = 143.187 mph
We know, Speed = Distance / Time
Time = Distance / Speed
Substitute the values
Time = [tex]\frac{500}{143.187}=3.49[/tex] hours
Hence, the time taken to finish the race is 3.49 hours
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I have a math question, try not to get it wrong
Answer: c
Step-by-step explanation: it is a rational number because it repeats
The screenshot has the question If you help within next Hour I will make you brainlest and get 50 points
Answer:
2,689
Step-by-step explanation:
you got the first two right it's the last that is wrong
you need to do 2,407-(-282) the two negative make it a positive so add them together and you get 2,689.
since 1900, the percentage of americans over the age of 65 has while the percentage of americans under the age of 18 has .
The percentage of Americans over the age of 65 has increased while the percentage of Americans under the age of 18 has decreased .
What happened to the population in America?The United Stats of America is one of the countries that is known to have a very good health care system. This implies that, there has ben a very huge improvement in the health care of the population of the United States.
As a result of this improvement in the healthcare of the people of the United States, the percentage of Americans over the age of 65 has increased while the percentage of Americans under the age of 18 has decreased .
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If there are 6 family members in your family and they are all going to skate
4 hours each, it would cost $
Answer: 24c
Step-by-step explanation:
c = cost
6x4=24
24 times the amount it costs per hour c
24c
help me please
(2a+3)(3a-4)
Answer: 6[tex]a^{2}[/tex]+a-12
Step-by-step explanation:
First, you want to distribute (2a+3)(3a-4) ---> 2a(3a-4) + 3a(3a-4)
That will get you 6[tex]a^{2}[/tex]-8a+9a-12
Next, you will want to combine like terms to get 6[tex]a^{2}[/tex]+a-12
Since you cannot simplify that any further, 6[tex]a^{2}[/tex]+a-12 is your answer.
If the points A, B, and C are clinear with B between A and C, and if AC = 21 and AB = 7, what is the
length of line segment BC?
BC=
Answer: BC=14
Subtract AC by AB. Just learned this in Geomatry.
Create a function that has been:
Shifted right 3 units
Shifted up 2 units
Reflected about the x-axis
A function that has been transformed by the given transformations is y = -f(x - 3) + 2
How to create a function that has been transformed?The transformation are given as:
Shifted right 3 unitsShifted up 2 unitsReflected about the x-axisLet the equation of the parent function be
y = f(x)
So, we have the following transformations
Shifted right 3 units
The transformation rule is
(x, y) = (x - 3, y)
So, we have:
y = f(x - 3)
Shifted up 2 units
The transformation rule is
(x, y) = (x, y + 2)
So, we have:
y = f(x - 3) + 2
Reflected about the x-axis
The transformation rule is
(x, y) = (x, -y)
So, we have:
y = -f(x - 3) + 2
Hence, a function that has been transformed by the given transformations is y = -f(x - 3) + 2
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Jenny sells earrings and bracelets on Etsy. The earrings cost $5 a pair and bracelets cost $12. If Jenny made 20 pieces on Saturday for $156. How many of each type of jewelry did she make?
1. 10 earrings and 7 bracelets
2. 7 earrings and 10 bracelets
3. 12 earrings and 8 bracelets
4. 8 earrings and 12 bracelets
She makes 12 earrings and 8 bracelets of each type of jewelry. (option 3 is correct.)
Jenny sells earrings and bracelets on Etsy
The cost of a pair of earrings = $5
The cost of bracelets = $12.
If Jenny made 20 pieces on Saturday for the cost of $156.
Each type of jewelry made by Jenny is
Let she made X pair of earrings
Y number of bracelet
Then the linear equation will be
$5X +$12Y = $156
by using the given values in option we get the answer
X = 12
Y = 8
She makes 12 earrings and 8 bracelets of each type of jewelry. (option 3 is correct.)
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Solve for x, given the equation square root of x plus 9 − 4 = 1. (2 points)
Answer:
x = 16
Step-by-step explanation: