12/√3 is the direction of the vector v .
What does a basic math vector mean?
A thing with both magnitude and direction is called a vector.
A vector can be visualized geometrically as a directed line segment, where the direction is indicated by an arrow and the length of the segment equals the magnitude of the vector.
Normalize (make length 1) the vector v = <1, 1, -1>.
||v|| = √(1^2 + 1^2 + (-1)^2) = √3.
So, the unit vector u is given by u = v/||v|| = <1, 1, -1>/√3.
To find the rate of change of the potential in the direction of the vector v, you should calculate the ∇f(6, 6, 5) and multiply by u.
=<df/dx, df/dy, df/dz>*u
= <4x-3y+yz, -3x+xz, xy> {at (6, 6, 5)} * u
= <36, 12, 36> · <1, 1, -1>/√3
= 12/√3.
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The complete question is -
Suppose that over a certain region of space the electrical potential V is given by the following equation. V(x, y, z) = 2x2 − 3xy + xyz (a) Find the rate of change of the potential at P(6, 6, 5) in the direction of the vector v = i + j − k.
Express cos U as a fraction in simplest terms.
T
6
U
84
S
Answer:
cosU = [tex]\frac{3}{4}[/tex]
Step-by-step explanation:
cosU = [tex]\frac{adjacent}{hypotenuse}[/tex] = [tex]\frac{TU}{ST}[/tex] = [tex]\frac{6}{8}[/tex] = [tex]\frac{3}{4}[/tex]
Write each sequence as a function. {1,3,5,7,9,…}
1. Which line has a slope of 1, and which has a slope of 2?
2. Use a ruler to help you graph a line whose slope is 1/3. Albee this line a
Answer:
I can't answer unit I know what lines you're talking about, can you insert an image or graph of the questions?
Step-by-step explanation:
The total cost of fencing a square park at rupees 20 per meter are rupees
2880. Find the side of the square park.
The side of square park, whose fencing costed Rs 2880 is 36m.
What is a square?
A quadrilateral with four equal sides is called a square. There are numerous items in our environment that have a square shape. Equal sides and internal angles that are both 90 degrees distinguish each square shape. Let's find out more about a square's characteristics, mathematics, and design.
We know perimeter of a square of side 'a' is 4a
Therefore, the cost of fencing a square park at Rs 20/meter would be equal to
= Rs(20*4a)
= Rs 80a
Given, the cost of fencing = Rs 2880
Thus, 80a = 2880
⇒ a = 2880/80
⇒ a = 36
Thus, the side of square park, whose fencing costed Rs 2880 is 36m
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For the following, find the arc length:
(Use pi=3.14 and round your final answer to the hundredths.)
X=
[tex]\textit{arc's length}\\\\ x = r\theta ~~ \begin{cases} r=radius\\ \theta =\stackrel{radians}{angle}\\[-0.5em] \hrulefill\\ r=10\\ \theta =\frac{\pi }{3} \end{cases}\implies x=10\cdot \cfrac{\pi }{3}\implies x\approx 10.47[/tex]
Given values for x and y to be -3 and 1, evaluate the following ordered triples
-5x - 4y + 2z = -5
-4x + 2y3z = 38
2x + 3y + 4z = -35
The system of linear equation have an ordered triple of (x, y, z) are (-3, 1, -8)
Evaluating Linear EquationTo evaluate an algebraic expression, you have to substitute a number for each variable and perform the arithmetic operations.
In the question given, we have a system of linear equations where the value of x and y are given.
-5x - 4y + 2z = -5 ...eq(i)
-4x + 2y + 3z = 38 ...eq(ii)
2z + 3y + 4z = -35 ...eq(ii)
Since we have the value two variables (x, y) which are (-3, 1), we can substitute it in any of the equation to find the value of z.
Taking eq(i)
-5x - 4y + 2z = -5
-5(-3) - 4(1) + 2z = -5
15 - 4 + 2z = -5
11 + 2z = -5
2z = -5 - 11
2z = - 16
z = -8
The ordered triple are (-3, 1, -8)
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Jason is a high school basketball player. He made some free throws (worth one point each) and some two-point shots in a particular game. Jason made a total of 13 photos altogether and scored a total of 20 points. Write a system of equations that could be used to determine the number of free throws Jason made and the number of two-point shots he made. Define the variables that you use to write the system.
Answer:
Let x be the number of free throws Jason made, and y be the number of two point shots he made.
The system of equations will be
x+ 2y = 20x+2y=20
x + y = 13x+y=13
Solving these using elimination method we get,
x + 2y = 20x+2y=20
----------------------------
y = 7y=7
x = 6⇒x=6
The number of free throws Jason made are 6, and the number of two point shots he made are 7.
Deshaun wants to attend a college that will cost $25,600 for the first year. His uncle gave him a special gift of $2500 to use toward the cost. Deshaun plans to attend the college in 7 years. How much must Deshaun save each month to have enough for the first-year cost?
Deshaun must save the amount of $275 each month to have enough for the first-year cost.
As per the given question, we have
The first-year cost of college = $25,600
The gift cost = $2500
The amount left to pay will be:
⇒ first-year cost - gift cost
⇒25,600 - 2,500 = 23100
The months left till college = 7 × 12 = 84
So, he would have to save per month :
⇒ 23,100/84
Apply the division operation, and we get
⇒ 275
Thus, he must save the amount of $275 each month to have enough for the first-year cost.
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Which equation represents the linear relationship between the x-values and the y- values in the table
The equation of a line that represents the table is y = 6x - 5.
What are lines and their slopes?We know lines have various types of equations, the general type is
Ax + By + c = 0, and the equation of a line in slope-intercept form is
y = mx + b.
Where slope = m and b = y-intercept.
the slope is the rate of change of the y-axis with respect to the x-axis and the y-intercept is the (0,b) where the line intersects the y-axis at x = 0.
To obtain the linear equation first we need slope(m) = (y₂ - y₁)/(x₂ - x₁)
= (1 + 11)/(1 + 1) = 12/2 = 6.
Now, we'll take any one of these coordinate points and construct an equation in slope-intercept form,
- 11 = 6(-1) + b.
- 11 = - 6 + b.
b = - 5.
∴ y = 6x - 5 is our equation.
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Brett bought a house five years ago for $150,000. At that time he borrowed $140,000 from his bank. The house is now worth $162,000. The current value of his mortgage must be no higher than ________ for him to request termination of his PMI policy.
$126,360.
Once his equity has increased to 22% of the current market value, he can request that PMI be cancelled. He may request termination of PMI when his mortgage balance reaches $126,360 {$162,000 × (1 − 0.22)}.
The current value of his mortgage must be no higher than $126,360 for him to request termination of his PMI policy.
What is mortgage value?
The appraised value of the property used to determine the mortgage value is determined by a reputable firm. It might not match the purchase-sale value. The mortgage value, which serves as the Bank's guarantee, is the benchmark used in the mortgage application and arrangement process.
Given:
Brett bought a house five years ago for $150,000.
At that time he borrowed $140,000 from his bank.
The house is now worth $162,000.
Once his equity has increased to 22% of the current market value he can request that PMI be canceled.
He may request termination of request when his mortgage balance reaches
162,000(1 - 0.22) = 162,000(0.78) = 126,360.
Hence, the current value of his mortgage must be no higher than $126,360 for him to request termination of his PMI policy.
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Sasha put $3,500 into a savings account that earns 2.3% annual compound
interest If she makes no other deposits or withdrawals, what will her balance be after 12 years ? Round to the nearest cent. SHOW ALL WORK TO RECEIVE CREDIT.
Sasha's balance after 12 years, if she makes no other deposits or withdrawals would be $ 4, 598. 07
How to find the balance ?Sasha's balance after 12 years will be the future value of her savings after 12 years at a rate of 2. 3% per year.
This future value can be found by the formula :
Amount after 12 years = Amount deposited by Sasha x ( 1 + annual compound interest ) ^ number of years
= 3, 500 x ( 1 + 2 .3 % ) ¹²
= 3, 500 x 1.3137344983996021269289886802331
= $ 4, 598. 07
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A Circle Has An Equation of (x - 5)^2 + (y - 1)^2 = 30. What Is The Center And Radius Of The Circle?
the center of the circle is at (5, 1) and the radius is approximately 5.48 units.
Why it is and what is perimeter of a circle?
The standard equation of a circle with center (a,b) and radius r is:
(x - a)²2 + (y - b)²2 = r²2
Comparing this equation to the given equation, we can see that the center of the circle is (5, 1) and the radius is the square root of 30. Therefore, the center of the circle is at (5, 1) and the radius is approximately 5.48 units.
The perimeter of a circle is also known as its circumference, and it can be calculated using the formula:
C = 2πr
where C is the circumference, r is the radius of the circle, and π (pi) is a mathematical constant approximately equal to 3.14159.
Alternatively, you can also use the formula:
C = πd
where d is the diameter of the circle.
So if you know the radius or diameter of a circle, you can use either of these formulas to calculate its circumference (perimeter).
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Two numbers when multiplied equals 63 if one number is x and the other number is greater than x by 2
a) represent the information given in equation form
b) express as a quadratic equation
c) solve the quadratic equation to find possible values of x
d) if told that the two numbers are positive numbers what are the values of the two original numbers?
The values of the two original numbers are 7 and 9.
Two numbers when multiplied equal 63 if one number is x and the other number is greater than x by 2.
As per the given phrase, the information given in equation form is as
x × (x + 2) = 63
It expresses as a quadratic equation:
x² + 2x - 63 = 0
Solve the quadratic equation to find possible values of x
x² + 9x - 7x - 63 = 0
x(x + 9) - 7(x + 9) = 0
(x + 9)(x - 7) = 0
(x + 9) = 0 and (x - 7) = 0
x = -9 and x = 7
Since we were told that the two numbers are positive numbers so take x = 7.
Thus, the values of the two original numbers are 7 and 9.
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What is the complete factorization of the polynomial below?
x³+3x²-x-3
O A. (x-1)(x-1)(x+3)
O B. (x+1)(x-1)(x+3)
OC. (x + 1)(x-1)(x-3)
O D. (x-1)(x-1)(x-3)
The piecewise function h(x) is shown on the graph.
7
S
5
3
N
-7-6-5-4-3-2-1₁
-2-
7 ? 9 9 9 7
-6
23 4 5 6 7 X
What is the value of h(2)?
O-2
O -1
0
3
The value of the piecewise function h(x) at x = 2 is (b) -1
How to evaluate the piecewise functionFrom the question, we have the following parameters that can be used in our computation:
Part 1:
h(x) = x cubed for x less than negative 3
Part 2:
h(x) = 2 times x squared minus 9 for negative 3 is less than or equal to x which is less than 4,
Part 3
h(x) = 5 times x plus 4, for x greater than or equal to 4
When the above statements are represented properly, we have the following equations
Part 1: h(x) = x³ for x < -3
Part 2: h(x) = 2x² - 9 for -3 ≤ x < 4
Part 3: h(x) = 5x + 4, for x ≥ 4
To calculate the function h(2), we use the domain -3 ≤ x < 4
So, we have the following function
h(x) = 2x² - 9
Substitute the known values in the above equation, so, we have the following representation
h(2) = 2(2)² - 9
Evaluate the expression
h(2) = -1
Hence, the value is (b) -1
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Complete question
The piecewise function h(x) is shown on the graph.
the function is defined by part 1, which is x cubed for x less than negative 3, part 2, which is 2 times x squared minus 9 for negative 3 is less than or equal to x which is less than 4, and part 3 which is 5 times x plus 4, for x greater than or equal to 4
What is the value of h(2)?
Help I need a formula to know what I am doing
Answer:
2((2x+2)+3x)=124 units
Step-by-step explanation:
We know that the formula for perimeter is 2(b+h) and since we know this, we just substitute the values for this and solve.
help needed proportional relationship easy
Find the z* values based on a standard normal distribution for an 86% confidence interval for a proportion, for a 78% confidence interval for a mean.
The z values are-
confidence interval 86 % = 1.0confidence interval 78% = 0.8Describe the term confidence interval?The likelihood that a parameter might fall between two values near the mean is shown by a confidence interval.Confidence intervals quantify when certain or uncertain a survey method is.They are also utilized in regression analysis and hypothesis testing.P-values and confidence intervals are commonly used by statisticians to determine statistical significance.They are often built with 95% or 99% confidence levels.Although they are related, confidence level and confidence interval are not the same thing.Obtain the z values from the t-distribution table for 0.86 and 0.78 confidence interval.
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Find the equation of the line passing through pl7, -2) and (5, 3).
The equation of the line passing through (7, -2) and (5, 3) is 5x + 2y - 31 = 0.
What is two point equation form?
The equation of a line in the coordinate plane can be expressed in two point form. Depending on the facts at hand, there are different ways to find a line's equation. One of the ways is the two-point form. When two locations along a line are known, this is used to determine the equation of the line. Slope intercept form, intercept form, point slope form, and others are crucial ways to describe a line equation.The equation of the line passing through two points is
(y - y₁) / (y₂ - y₁) = (x - x₁) / (x₂ - x₁)
Here, (x₁,y₁) ∈ (7, -2)
(x₂, y₂) ∈ (5, 3).
y - (-2) / 3 -(-2) = x - 7/ 5 - 7
(y + 2) / 5 = x-7 / -2
-2y - 4 = 5x - 35
5x + 2y - 31 = 0
Hence, the equation of the line passing through (7, -2) and (5, 3) is 5x + 2y - 31 = 0.
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write an equation of the passing through point p that is perpendicular to the given line .
p(3,1) y= 1/3x -5
Answer:
y = -3x + 10
Step-by-step explanation:
slope of perpendicular line = -3
y-1 = -3(x-3)
y-1 = -3x + 9
y = -3x + 9 + 1
y = -3x + 10
Given that f(x)= 2x+8 g(x)= 5x-2/4 and h(x)= 2x+6/x
find
a) g[f(0)]
b) f(-5)
c) f[h(3)]
d) h°f(x)
e) h⁻¹(x)
The values of the functions g[f(0)]b) f(-5), f[h(3)], h°f(x) and h⁻¹(x) are 9.5, -2, 16, (4x+22)/x and 6/(x-2) respectively
How to find the g[f(0)] of the function?
A function is a relationship between inputs where each input is related to exactly one output
Given: f(x)= 2x+8, g(x)= 5x-2/4 and h(x)= 2x+6/x
(a) g[f(0)]
Substitute x = 0 into f(x)= 2x+8 to get f(0)
f(0) = 2(0)+8 =8
g[f(0)] = g(8)
Substitute x = 8 into g(x)= 5x-2/4 to get g[f(0)]
g[f(0)] = g(8)
g[f(0)] = 5x-2/4
g[f(0)] = 5(8)-2/4 = 9.5
b) f(-5)
Substitute x = -5 into f(x)= 2x+8 to get f(-5)
f(x)= 2x+8
f(-5)= 2(-5)+8 = -2
c) f[h(3)]
h(x)= 2x+6/x
h(3) = 2(3)+6/3 = 4
f[h(3)] = f[4]
f[4] = 2(4)+8 = 16
f[h(3)] = 16
d) h°f(x)
h°f(x) = h(2x+8)
Since h(x)= 2x+6/x
h°f(x) = 2(2x+8) +6/x
h°f(x) = 4x+16+6/x = (4x+22)/x
e) h⁻¹(x)
h(x)= 2x+6/x
Let y = 2x+6/x
x = 6/(y-2)
x = h⁻¹(y)
h⁻¹(x) = 6/(x-2)
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How would this two triangles be called
TU ≅ QV, UV ≅ RS , and ST ≅ QR.
The triangles ΔSTU and ΔRQV are congruent triangles
What are congruent triangles?Two triangles are congruent if the three sides of one triangle are congruent to the three sides of the other triangle.
The parameters from the diagram includes;
Side [tex]\overline{TU}[/tex] in triangle ΔSTU is congruent to side [tex]\overline{QV}[/tex] in triangle ΔRQV
Segment [tex]\overline{UV}[/tex] is congruent to segment [tex]\overline{RS}[/tex]
[tex]\overline{UV}[/tex] ≅ [tex]\overline{RS}[/tex]
[tex]\overline{UV}[/tex] = [tex]\overline{RS}[/tex] By definition of congruency
Side [tex]\overline{ST}[/tex] in triangle ΔSTU is congruent to side [tex]\overline{QR}[/tex] in triangle ΔRQV
Segment [tex]\overline{RU}[/tex] is congruent to segment [tex]\overline{UR}[/tex], by reflexive property
[tex]\overline{RV}[/tex] = [tex]\overline{RU}[/tex] + [tex]\overline{UV}[/tex] by segment addition postulate
Similarly, [tex]\overline{SU}[/tex] = [tex]\overline{RU}[/tex] + [tex]\overline{RS}[/tex]
Therefore; [tex]\overline{SU}[/tex] = [tex]\overline{RU}[/tex] + [tex]\overline{UV}[/tex] (by substitution property)
[tex]\overline{RV}[/tex] = [tex]\overline{SU}[/tex] by substitution property
[tex]\overline{RV}[/tex] ≅ [tex]\overline{SU}[/tex] by definition of congruency
The three sides of the triangle ΔSTU are congruent to the three sides of the triangle ΔRQV, therefore;
The triangles ΔSTU and ΔRQV are congruent by Side-Side-Side, SSS, congruency postulate
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Please help, I don't understand this.
Answer:
-0.3
Step-by-step explanation:
just sum -0.66x and 0.36x
Answer: -21
Step-by-step explanation:
To begin, we can combine like terms, -0.66 and 0.36 are coefficients with the same variable.
This gives us -0.66x+0.36x= -0.30x, and the equation becomes -0.30x=6.3.
Next, we can simply solve for x by dividing 6.3 by -0.30, and that gives us x=-21.
Find the missing angles
m∠1=
m∠2=
m∠3=
m∠4=
m∠5=
Answer:
m1= 35
m2= 65
m3= 29
m4= 115
m5=65
Amanda is the manager of Gladrags. She just got a new shipment of jeans and is pricing them for the store to make money. Her invoice for the jeans
states that the jeans cost her store $20 per pair. Amanda marks the jeans up to sell for $55 per pair. Find the percent of change.
O 175% increase
O 175% decrease
O 17.5% increase
O 17.5% decrease
To find the percent of change, we need to calculate the difference between the original price and the new price, and then divide this difference by the original price and multiply by 100%.
The difference between the original price of $20 and the new price of $55 is $55 - $20 = $35.
The percent of change is: ($35/$20) * 100% = 1.75 * 100% = 175%
Since the new price is higher than the original price, this is an increase. Therefore, the percent of change is a 175% increase. The correct answer is therefore
O 175% increase.
Simplify and write the answer
(3x²y⁴)³
Answer:
27x^6y^12
Step-by-step explanation:
3^3×x^2(3)×y^4(3)
=27^6y^12
Find how long it takes a person to drive 260 miles on a highway if she merges onto a highway at 7 p.m. and drives nonstop with her cruise control set on 80 mph.
The time taken by the person to cover 260 miles will be 3 hours and 15 minutes.
What is speed?Speed is defined as the ratio of the time distance travelled by the body to the time taken by the body to cover the distance. Speed is the ratio of the distance travelled by time. The unit of speed in miles per hour.
Given that a person to drive 260 miles on a highway if she merges onto a highway at 7 p.m. and drives nonstop with her cruise control set at 80 mph.
The amount of time taken by the person to cover the distance of 260 miles with a speed of 80mph is,
Speed = Distance / Time
Time = Distance / Speed
Time = 260 / 80
Time = 3.25 or 3 hours 15 minutes
Therefore, the time taken by the person to cover 260 miles will be 3 hours and 15 minutes.
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To copy an angle using only a compass and a straightedge begin by marking the angle. Then draw a ray from the vertex which will be one of the legs of the new angle. What is the next step in the construction
Next step is to Mark off your new arc with this new width by positioning the compass point on the reference line where the previous arc crossed it.
Steps to be followed while measuring an exact angle using compass and straight edge are:
If a reference line is not given, draw one using a straightedge.Add a dot as the reference line's starting point.Position the compass's point at the vertex of the ABC angle (vertex at pointSwing the arc so that the pencil crosses BOTH rays (sides) of the angle. Holding the compass point at the starting point (dot) on the reference line, swing an arc that will cross the reference line and rise above the reference line without adjusting the compass's size. Return to the supplied angle ABC and determine the span (width) of the arc between the points at which it crosses one side of the angle and the other. Mark off your new arc with this new width by positioning the compass point on the reference line where the previous arc crossed it. Join this new intersection point to the reference line's starting point. Mark the duplicate.
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A coffeehouse charges a flat rate, r, for each hour a customer wants to use the Internet. write an equation to express the total cost, c, to use the Internet at the coffeehouse for t hours.
The equation to express the total cost, c, to use the Internet at the coffeehouse for t hours is c = rt.
How to illustrate the equation?An equation is the statement that illustrates the variables given. In this case, two or more components are taken into consideration to describe the scenario.
In this case, the coffeehouse charges a flat rate, r, for each hour a customer wants to use the Internet. An equation to express the total cost, c, to use the Internet at the coffeehouse for t hours.
The equation will be:
c = r(t)
c = rt
where c = cost
t = number of hours
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Based on the definition advocated by the class reading, which of the following would be an example of fake news? A New York Times reporter isn't very good at her job, and ends up publishing an article containing several important factual errors A popular web-based news site publishes an op-ed that is hopelessly biased and poorly argued The Onion publishes a satirical, comedic story making fun of President Trump. Nothing in the story is remotely true. In order to increase applications, GSU knowingly creates and disseminates a false but realistic-looking news article talking about how great the parking situation here on campus is Your uncle writes a long blog post repeating rumors he heard online that Kim Kardashian is actually a lizard person sent here by an alien race to destroy humanity.
The Onion publishes a satirical, comedic story making fun of President Trump. Nothing in the story is remotely true
False information is presented as fake news. This is bogus news since the onion published a satirical fictional report about President Trumb. GSU fabricates false, deceptive information, often known as false news. False news is not defined as news that has factual inaccuracies.
GSU intentionally produces and disseminates a phony but plausible-looking news item touting the excellent parking situation on campus in an effort to boost applicants.
The term "fake news" describes news sources that pose as authentic while actually being false. It frequently aims to make money from advertising or to harm someone's or an organisation's reputation.
By purposefully fabricating and spreading a bogus but plausible-looking news article claiming how excellent the parking situation is on campus, GSU hopes to increase the number of applications. Which is false information that will cause people to come forward with job applications.
The Onion publishes a satirical, comedic story making fun of President Trump. Nothing in the story is remotely true
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