Answer: We know that the center of the ellipse is the midpoint of the line segment joining the foci. So, the center is ((15+3)/2, (-2-2)/2) = (9, -2).
The distance between the foci is 2c, where c is the distance between the center and each focus. So, 2c = 15 - 3 = 12, which means c = 6.
The distance between the center and each co-vertex is b. So, b = 10 - (-2) = 12.
The semi-major axis is a, which is the distance from the center to a vertex. Since we have the co-vertices, we can use the Pythagorean theorem to find a:
a^2 = b^2 - c^2
a^2 = 12^2 - 6^2
a^2 = 108
a = sqrt(108) = 6*sqrt(3)
Therefore, the equation of the ellipse is:
(x - 9)^2 / (6*sqrt(3))^2 + (y + 2)^2 / 12^2 = 1
Simplifying, we get:
(x - 9)^2 / 72 + (y + 2)^2 / 144 = 1
So, the equation of the ellipse is (x - 9)^2 / 72 + (y + 2)^2 / 144 = 1.
Enjoy!!!!!!!!!!!!!!!!!!!!!!
Samir bought three pounds of strawberries for $12.00. What is the price, in dollars
per ounce of strawberries?
1 pound = 16 ounces
Before you try that problem, answer the question below.
How many ounces of strawberries did Samir buy?
A printing company bought a machine for $86.000. it's estimated life is 10 years with residual value of $6,000, Using the straight-line method, what's the book value of the machine at the end of year2?
Hence, at the end οf year 2, the machine's bοοk value is $70,000.
Examples οf residual value what?Example οf Calculating Residual Value fοr a Business-Owned Vehicle. Hence, if the cοrpοratiοn sells the car after 6 years, 60% οf the οriginal cοst οf the car is depreciated οver 6 years, and the residual value is 40%. Remaining Value Befοre Tax is anοther name fοr this value.
The cοst οf an asset is evenly dispersed acrοss the asset's useful life with the straight-line technique οf depreciatiοn. Cοmpute the annual depreciatiοn cοsts and deduct it frοm the machine's οriginal cοst tο arrive at the machine's bοοk value at the end οf year twο.
Yοu can cοmpute the yearly depreciatiοn expense as fοllοws:
Cοst οf Asset - Residual Value / Useful Life = Depreciatiοn Cοsts
Inputting the values prοvided yields:
Depreciatiοn Expense = ($86,000 - $6,000) / 10 = $8,000 per year
The machine's οriginal cοst must be subtracted frοm the bοοk value at the end οf year twο in οrder tο determine the machine's value:
Bοοk Value at End οf Year 2 = Cοst οf Asset - (Depreciatiοn Expense x Number οf Years)
Bοοk Value at End οf Year 2 = $86,000 - ($8,000 x 2) = $70,000
Thus, the machine's bοοk value at the end οf year twο is $70,000.
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each square in the grid below has area 1. find the area of the irregular quadrilateral below. [asy] size( 200 ) ; int xmax
The required area of the irregular quadrilateral as given in the attached diagram is equal to 37.5 square units.
In the attached diagram,
Area of each square grid is equal to 1 square units.
Area of the irregular quadrilateral
= Area of the triangle A + Area of the triangle B + Area of the triangle C + Area of the rectangle D ___(1)
Area of triangle A = ( 1/2 ) × Base × height
= ( 1/2 ) × 4 × 8
= 16 square units
Area of triangle B = ( 1/2 ) × Base × height
= ( 1/2 ) × 5 × 5
= 12.5 square units
Area of triangle C = ( 1/2 ) × Base × height
= ( 1/2 ) × 3 × 4
= 6 square units
Area of rectangle D = length × width
= 3 × 1
= 3 square units
Substitute all the values in (1 ) we have,
Area of the irregular quadrilateral
= 16 + 12.5 + 6 + 3
= 37.5 square units.
Therefore, the area of irregular quadrilateral is equal to 37.5 square units.
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The above question is incomplete, the complete question is:
Each square in the grid below has area 1. Find the area of the irregular quadrilateral below.
Diagram is attached.
Part y Wa g on, Inc., provides musical entertainment at weddings, dances, and various other functions. The company performs adjusting entries monthly but prepares closing entries annually on December 31. The company recently hired Jack Armstrong as its new accountant. Jack’s first assignment was to p re p are an income statement, a statement of retained earnings, and a balance sheet usin g an adjusted trial balance given to him by his predecessor, dated December 31, the current year.
From the ad j usted trial balance, Jack p re p ared the followin g set of financial statements.
Preparation of a Corrected set of Financial Statements :
Income Statements :
PARTY WAGON .INC
INCOME STATEMENT
FOR THE YEAR ENDED DECEMBER 31
CURRENT YEAR
Party Revenue Earned
156,000
Total Revenue
156,000
Expenses :
Insurance Expenses
2,160
Office Rent Expense
14,400
Supplies Expense
1,440
Salary Expense
90,000
Repair and Maintainence expense
2,400
Travel Expense
7,200
Miscellaneous Expense
4,320
Interest Expense
5,280
Depreciation - Van
9,600
Depreciation -Music and Equipment
8,400
Total Expenses
145,200
Income Before Income Tax
10,800
Less : Income Tax Expense
2,400
Net Income
8,400
How to explain the financial statementJack included balance sheet accounts in the income statement, therefore the corrected income statement consisting of revenue and expenses accounts is provided above.
Statement of Retained Earnings :
Retained Earnings (As per adjusted trial balance) 18,000
Add : Net Income 8,400
Less : Dividends (1,200)
Retained Earnings Dec 31, Current Year 25,200
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PLEASE HELP ME!!! Type the correct answer in each box. Use T for true and F for false.
Complete the truth table for the contrapositive of a conditional statement.
р
T
T
LL
LL
q
T
F
T
LL
P→q
T
F
T
T
~9~p
The answer will of given mathematical logic will be T F T T F respectivelly.
What fundamental ideas underlie mathematical logic?A negation, conjunction, and disjunction are the fundamental mathematical logics. The symbols for negation, conjunction, and disjunction in mathematical logic are "," "," and "v," respectively.
What is the purpose of mathematical logic?Logical proofs frequently employ mathematical logic. Proofs are legitimate arguments that establish the veracity of mathematical assertions. A series of statements make up an argument. The conclusion is the last assertion, and the premises are all the statements that came before it (or hypothesis).
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The complete truth table is shown in the below diagram.
≈ q → ≈ p: True False True True
Define the conditional statement for contrapositive?The contrapositive of a conditional statement is a new conditional statement that is formed by negating both the hypothesis (the "if" part) and the conclusion (the "then" part) of the original statement, and switching their positions. The truth table for the contrapositive of a conditional statement has the same number of rows as the truth table for the original statement.
For example, if the original statement is "If it is raining, then the ground is wet", then the contrapositive would be "If the ground is not wet, then it is not raining."
According to the given table the contrapositive of a conditional statement q and p is defines as;
True
False
True
True
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find any critical numbers of the function.
Answer:
(2, -4)
Step-by-step explanation:
[tex]{ \sf{f(x) = {x}^{3} - {3x}^{2} }} \\ { \sf{ {f}^{l}(x) = {3x}^{2} - 6x }} \\ \\ { \sf{0 = x(3x - 6)}} \\ { \sf{0 = 3x - 6}} \: \: \: \: \: \\ { \sf{3x = 6}} \\ { \sf{x = 2}}[/tex]
For x = 2
[tex]{ \sf{f(2) = {2}^{3} - 3 {(2)}^{2} }} \\ { \sf{f(2) = 8 - 12}} \\ { \sf{f(2) = - 4}}[/tex]
Point is (2, -4)
Let g(x) = 3x^2 - 2x + 4. Evaluate g(5)
Answer:
g(5)=69
Step-by-step explanation:
g(5)=3(5)^2-2(5)+4
g(5)=75-10+4
g(5)=69
Roberto must make his costume for the school play. He needs a piece of fabric that is 2 2/3 yards long and 1 1/2 yard wide. What is the area of the piece of fabric Roberto needs?
Roberto needs 4 square yards of fabric to make his costume.
What is improper fraction?A fraction that has the numerator higher than or equal to the denominator is said to be inappropriate. For instance, the fraction 7/3 is incorrect since 7 is bigger than 3. Mixed numbers, which combine a whole number and a correct fraction, can be created from improper fractions.
Given that, piece of fabric that is 2 2/3 yards long and 1 1/2 yard wide.
Convert the length from a mixed number to an improper fraction:
2 2/3 = (2 x 3 + 2)/3 = 8/3
1 1/2 = 3/2
The area of the rectangle is:
Area = Length x Width
Substituting the values we have:
Area = (8/3) x (3/2) = 4
Hence, Roberto needs 4 square yards of fabric to make his costume.
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8. The diagram shows the triangle PQR. In the diagram, all the angles are in degrees. RP = RQ Find the value of y. Show clear algebraic working. P= 2x + 10, R=y, Q= X + 15
The value of y in the given isosceles triangle is 140°.
What is isosceles triangle?A triangle with two equal edges is said to be isosceles. Also equal are the two angles that face the two identical sides. In other terms, an isosceles triangle is a triangle with two sides that are the same length.
If the sides AB and AC of a triangle ABC are equivalent, then the triangle ABC is an isosceles triangle with B = C. "If the two sides of a triangle are congruent, then the angle opposite to them is also congruent," states the theorem that explains the isosceles triangle.
What is an angle?An angle is a shape created by two lines that share an endpoint and are referred to as the angle's sides and vertex, respectively. Angles created by two beams are in the plane where the rays are located. The meeting of two surfaces also creates angles.
In the given question,
∠P=∠Q
2x+10=x+15
x=5
Therefore,
∠P=2(5)+10=20°
∠Q=5+15= 20°
∠P+∠Q+∠R= 180°
20+20+∠R= 180°
∠R= 140°
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can you find the value of constant k?
k=?
The constant k that makes f(x) continuous everywhere is k = 49/41.
What is a continuous function?If a function's limit at a given position exists and is the same as the function's value there, the function is said to be continuous at that location. If a function is continuous over its whole domain, then it is continuous everywhere. As the name implies, a continuous function is one whose graph is continuous throughout without any pauses or leaps. To put it another way, we say that a function is continuous if we can draw the curve (graph) of the function without ever picking up the pencil.
For f(x) to be continuous everywhere, it must be continuous at x = 7.
Using the left limit we have:
k(7)² = 49k
Using the right limit we have:
(7x + k) = 49 + k
Setting the limits equal we have:
49k = 49 + k = 8k
49k = 8k + 49
41k = 49
k = 49/41
Hence, the constant k that makes f(x) continuous everywhere is k = 49/41.
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OBFW Publishers
Joy Milne of Perth, UK, smelled a "subtle musky odor" on her husband Les that she had never smelled before. At first, Joy
thought maybe the smell was from Les's sweat after long hours of work. But when Les was diagnosed with Parkinson's 6 years
later, Joy suspected the odor might be a result of the disease. Scientists were intrigued by Joy's claim and designed an
experiment to test her ability to "smell Parkinson's." Joy was presented with 12 shirts, each worn by a different person, some of
whom had Parkinson's and some of whom did not. The shirts were given to Joy in random order, and she had to decide whether
each shirt was worn by a Parkinson's patient or not. Joy identified 11 of the 12 shirts correctly. If we assume that Joy was just
guessing, she would have probability 1/2 of correctly identifying each shirt.
(a) Find the probability that Joy would identify at least 11 shirts correctly by random guessing.
Round your answer to 4 decimal places.
Leave your answer in decimal form.
about us
careers
the probability of indentifying at least 11 shirts correctly by random guessing is 0.0002
What is Probability?The ratio of favaourable outcomes to all possible outcomes of an event is known as the probability. The total number of positive results for an experiment with 'n' outcomes can be represented by the symbol x. The probability of an occurrence can be calculated using the following formula.
Probability(Event) = Positive Results/Total Results = x/n
Total no.of event=12
the probability that Joy will identify at least 11 shirts correctly by random guessing=
P(X≥11)=P(X=11)+P(X=12)
=¹²C₁₁(½)¹(½)¹¹+¹²C₁₂×(½)¹²(½)⁰
=12×½×(1/2)¹¹+(½)¹²
=0.00024414062≈0.0002
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Question 4
Let us assume an original starting value of $4 trillion in 2033, but that the actual rate of
decline after 2033 was 10% greater than the 7.6% rate. (Notice that this refers to a 10%
relative increase over the 7.6% rate of decline that was originally estimated in the
lesson, and not an absolute increase of 10 percentage points.) In the questions below,
consider how this would affect the estimated value of the funds in 2038?
What is the new estimated value of the trust funds in 2038? Round to the nearest
The new estimated value of the trust funds in 2038 would be $2.5 trillion.
What is funds?Funds are resources of monetary value that can be used to acquire goods, services, or to meet financial obligations. They are usually obtained through the sale of goods and services or by borrowing. Funds can come from a variety of sources, including individuals, businesses, governments, and other organizations. Funds can be used to purchase assets such as stocks, bonds, real estate, or other forms of investments.
This is because a 10% relative increase over the original estimated 7.6% rate of decline means that the actual rate of decline is 8.36% (7.6% x 1.10 = 8.36%). Applying this rate to the original starting value of $4 trillion, the value of the trust funds in 2038 would be $4 trillion x 0.9164 (which is the equivalent of 1 - 0.0836) = $2.5 trillion.
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The new estimated value of the trust funds in 2038 would be $2.4 trillion.
What is trust fund?A trust fund is a legal arrangement in which a person or organization (the trustor) transfers assets to another person or organization (the trustee) to be managed and distributed for the benefit of a third party (the beneficiary). The trustor sets out a set of instructions (the trust deed) on how the trust funds should be handled, managed, and distributed. The trustee is legally bound to abide by these instructions, and is responsible for the management and distribution of the trust funds according to the trust deed. Trust funds can be used for a variety of purposes, such as providing for a beneficiary's education, medical care, or retirement.
This is because a 10% increase in the rate of decline would result in a rate of decline of 8.36% (7.6% plus 10% of 7.6%).
Using this new rate of decline, the value of the trust funds in 2038 would be $4 trillion multiplied by (1 - 0.0836)⁵,
which is equal to $2.4 trillion.
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Can someone pls help me it would mean so much to me
Answer: y = 3x-2 (for first question)
Step-by-step explanation:
Equation of the line: y = mx+c. For A, it passes through (0, -2) and has a gradient of 3. So, you substitute the values inside the equation.
x = 0
y = -2
m = 3
-2 = 0+c
c= -2
ans: y = 3x-2
Use the same method to complete the rest of the questions. GL
Note: I am just a student, if I get this wrong I hope someone corrects me, thanks
In need of help, if you could number and explain that would be awesome
The difference between the two formulas is that nPr takes order into account, while nCr does not. To determine which formula to use, consider whether order matters in the problem. If order matters, use nPr. If order does not matter, use nCr.
What are the possible outcomes of probability?a) An example of an application problem that uses nPr could be the following: In how many ways can a committee of 3 people be chosen from a group of 7 if the order of selection matters?
b) An example of an application problem that uses nCr could be the following: In how many ways can a committee of 3 people be chosen from a group of 7 if the order of selection does not matter?
c) The formula for nPr is n!/(n-r)!, where n is the total number of items and r is the number of items being selected in a specific order. The formula for nCr is n!/r!(n-r)!, where n is the total number of items and r is the number of items being selected without regard to order.
a) The tree diagram for the problem is:
H T
/ \ / \
H T H T
/ \ / \ / \ / \
H T H T H T H T
b) The probability that all the coins will turn up heads is 1/8 or 0.125, since there is only one outcome out of the eight possible outcomes that satisfies this condition.
c) The probability that there will be at least one tails is 7/8 or 0.875, since there are seven outcomes out of the eight possible outcomes that satisfy this condition (all except HHH).
Therefore, All the possible outcomes are: [tex]HHH, HHT, HTH, HTT, THH, THT, TTH, TTT.[/tex]
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2 bags of dog food. How many days will 3/4 last?
Answer:
3/4 of a bag of dog food will last 3 days.
Use the slope and y-intercept to identify the equation of this line.
Answer:
D. y = -2x
Step-by-step explanation:
slope = rise/run = 2/-1 = -2
y-intercept = (0,0)
y = mx + b
y = -2x + 0
y = -2x
explain integral calculus
Answer:
Integral
Step-by-step explanation:
explain integral calculus
calculate zeff for a valence electron in carbon using slater's rules. submit an answer to two decimal places.
The value of Zeff for a valence electron in carbon using slater's rule is equals to 3.60.
Effective nuclear charge (Zeff) for a valence electron in carbon using Slater's rules,
Consider the shielding effect of the inner electrons.
Slater's rules state that the effective nuclear charge felt by an electron in an atom = the actual nuclear charge minus the shielding constant for that electron.
The shielding constant for an electron in a particular shell is determined by summing the contributions of all the electrons in inner shells.
Slater assigned the following shielding constants for each shell,
Electrons in the same shell contribute 0.35
Electrons in the next inner shell contribute 0.85
Electrons in all inner shells beyond that contribute 1.00
Carbon has an atomic number of 6, so it has six electrons.
The first two electrons are in the inner shell, leaving four valence electrons in the outer shell.
Zeff for a valence electron in carbon,
Consider the contributions of the inner electrons.
Two electrons in the 1s orbital contribute
2× 0.35 = 0.70 to the shielding constant.
The two electrons in the 2s orbital contribute
2 × 0.85 = 1.70 to the shielding constant.
There are no electrons in the 2p orbitals,
This implies,
They do not contribute to the shielding constant.
Thus, the effective nuclear charge felt by a valence electron in carbon is,
Zeff
= 6 - 0.70 - 1.70
= 3.60
Rounding to two decimal places, we get,
Zeff = 3.60
Therefore, the Zeff for a valence electron in carbon is equals to 3.60.
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A statics class has 50 students and among those students, 35 are business majors and 7 like grilled cheese. Of the business majors, 3 like grilled cheese. Find the probability that a randomly selected statistic student is a business major or likes grilled cheese
The probability that a randomly selected statistics student is a business major or likes grilled cheese is 0.78.
What is probability?Probability is defined as the ratio of the number of favorable outcomes to the total number of outcomes in other words the probability is the number that shows the happening of the event.
Given that the statistics class has 50 students and among those students, 35 are business majors, and 7 like grilled cheese. Of the business majors, 3 like grilled cheese.
The probability will be calculated as:-
P(AUB) = P(A) + P(B) - P(AB)
[tex]P(AUB)=\dfrac{35}{50}+\dfrac{7}{50}-\dfrac{3}{50}[/tex]
[tex]P(AUB)=\dfrac{42-3}{50}[/tex]
[tex]P(AUB)=\dfrac{39}{50}[/tex]
P(AUB) = 0.78
Therefore the probability that a randomly selected statistics student is a business major or likes grilled cheese is 0.78.
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A contestant on a game show has a 1 in 6 chance of winning for each try at a certain game. Which probability models can be used to simulate the contestant’s chances of winning?
Select ALL of the models that can be used to simulate this event.
A) a fair six-sided number cube
B) a fair coin
C) a spinner with 7 equal sections
D) a spinner with 6 equal sections
E) a bag of 12 black chips and 60 red chips
Answer:
I'm pretty confident that the answer is E
THE FIRST ANSWER GETS BRAINLIEST AND FIVE STARS!
Parallelogram ABCD is a rhombus with measure EBC = 36. What is the measure of DAE?
picture below
Question 17 (2 points)
Suppose that 10% of Peloton bikes are defective and should be replaced. Peloton
offers one-year warranties on their new bikes, and should a customer use the bike in
the first year and discover the defect, the bike will be replaced. Peloton also knows
that 75% of customers use the bike in the first year. What is the probability a
customer will actually make a valid warranty claim?
0.075
0.10
0.175
0.75
The probability that a customer will actually make a valid warranty claim is 0.075.
What is Probability?A probability is a numerical representation of the likelihood or chance that a specific occurrence will take place. Both proportions ranging from 0 to 1 and percentages ranging from 0% to 100% can be used to describe probabilities.
According to question:The probability that a customer will make a valid warranty claim is the probability that the customer both uses the bike in the first year (which has a probability of 0.75) and discovers a defect (which has a probability of 0.10).
Using the multiplication rule of probability, the probability that both of these events occur is:
0.75 x 0.10 = 0.075
Therefore, the probability that a customer will actually make a valid warranty claim is 0.075.
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I need help with this
Angle PLE is measured at 90°. The options supplied do not contain the solution.
What measurement of an angle does not equal 90?The acute angle is defined as being less than 90 degrees. Right angles are 90 degrees in length. Angles that are obtuse have a greater angle than 90 degrees. Discover the various sorts of angles and examples of each.
As complementary angles, ZPLA and ZELA, we can infer that:
ZPLA + ZELA = 90°
Using the following expressions in place of ZPLA and ZELA, we obtain:
5x-2 + x+8 = 90
When we simplify the equation, we obtain:
6x + 6 = 90
6 is subtracted from both sides to yield:
6x = 84
Dividing by 6, we get:
x = 14
With the knowledge of x, we can determine the dimensions of ZPLA and ZELA:
ZPLA = 5x-2 = 5(14)-2 = 68°
ZELA = x+8 = 14+8 = 22°
Therefore, we can find the measure of angle PLE by subtracting the measures of ZPLA and ZELA from 180°:
PLE = 180 - ZPLA - ZELA
PLE = 180 - 68 - 22
PLE = 90
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I will mark you brainiest!
Are the two triangles on the coordinate plane congruent?
A) No
B) Yes
Answer:
No.
Step-by-step explanation:
Given two triangles on a coordinate plane, you can check whether they are congruent by using the distance formula to find the lengths of their sides. If three pairs of sides are congruent, then the triangles are congruent by the above theorem.
Over here, they aren't congruent by the SSS.
The profit (in thousands of dollars) from the expenditure of x thousand dollars on advertising is given by P(x)=1000+32x-2x2. Find the marginal profit at the following expenditures.
The marginal profit at the following expenditures for $8000 is 0 for $6000 is 8 for $12,000 is -16 and for $20,000 is -48.
When one more unit is produced and sold, a company or individual will make a profit known as marginal profit. The additional expense or profit made while manufacturing the next unit is referred to be marginal. Whereas marginal cost is the additional expense for manufacturing one extra unit, marginal product is the additional income received.
The difference between marginal cost and marginal product is known as marginal profit (also known as marginal revenue). Managers can utilise margin analysis to help them decide whether to increase output, reduce production, or halt production completely, a decision known as the shutdown point.
we have,
P(x)= 1000+32x - 2x²
Formula for derivative of function:
[tex]f'(x) = \lim_{h \to 0} \frac{f(x+h)-f(x)}{h}[/tex]
Finding the derivative,
P(x+h) = 1000 + 32(x+h) - 2(x+h)²
P(x+h) = -2x² -4xh - 2h² + 32x + 32h + 1000
P(x+h) - P(x) = h(-4x - 2h + 32)
P'(x) = -4x + 32
Finding derivatives for given values of x is,
P'(8) = -4(8) + 32 = 0
P'(6) = -4(6) + 32 = 8
P'(12) = -4(12) + 32 = -16
P'(20) = -4(20) + 32 = -48
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Complete question:
The profit (in thousands of dollars) from the expenditure of x thousand dollars on advertising is given by P(x)= 1000+32x - 2x². Find the marginal profit at the following expenditures.
a. $8000
b. $6000
c. $12,000
d. $20,000
Complete the process of solving the equation.
Fill in the missing term on each line. Simplify any fractions.
11w + 3 = 14
11w =
W =
Subtract 3 from both sides
Divide both sides by 11
Answer:
w = 1
Step-by-step explanation:
If we read the problem, we are given the instructional steps to solve this problem. Lets do it anyway without any help.
[tex]11w+3=14[/tex]
We, subtract 3 on both sides (3 - 3, 14 - 3)
[tex]11w=11[/tex]
Divide by 11w (11w/11w, 11/11w)
[tex]w=1[/tex]
WILL MARK AS BRAINLIEST!!!!!!!!!!!!
The point on the parabola y=x^2 that is closest to the point (9,1/2) is (______,______). The distance between the two points is ________.
Hint: Obtain an expression for the square of the distance and see where it is minimized. (you don't have to use the hint)
The point on the paraboIa y = x² that is cIosest to the point (9, 1/2) is approximateIy (2.2913, 5.2491). The distance between the two points is approximateIy 6.0291.
What is finding point on curve?CaIcuIus optimization probIems incIude the quest for the point on a curve that is cIosest to a given point. Finding the shortest path between two Iocations on a surface or figuring out how much materiaI is required to make a certain form are just two exampIes of its numerous practicaI uses.
Finding the greatest or Ieast vaIue of a function under specific constraints is a common task in optimization issues. These kinds of issues can be found in a variety of discipIines, such as engineering, economics, physics, and bioIogy. We can increase judgements and process effectiveness by finding soIutions to optimization difficuIties.
For the given paraboIa to fund the cIosest point to (9, 1/2) we use the distance formuIa:
d = √((x2 - x1)² + (y2 - y1)²)
Let, (x, x²), be a point on the paraboIa thus:
d = √((x - 9)² + (x² - 1/2)²)
The minimum distance is found using the derivative:
d' = (x - 9) + 2(x² - 1/2)(2x) = 0
4x³ - 4x - 17 = 0
x ≈ 2.2913
Substituting the vaIue of x we have:
d = √((2.219 - 9)² + ((2.219)² - 1/2)²)
d ≈ 6.0291
Hence, the point on the paraboIa y = x² that is cIosest to the point (9, 1/2) is approximateIy (2.2913, 5.2491). The distance between the two points is approximateIy 6.0291.
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The amount of money Sally earns in dollars, P, varies directly with the number, n, of necklaces she sells. When Sally sells 15 necklaces she earns $150.
Answer:
Equation: [tex]P=10n[/tex]
[tex]P=40[/tex] when n = 4
Step-by-step explanation:
Given
Direct Variation: P ∝ n
When n = 15, P = 150
Required
Determine the equation
Her earnings if she sold 4 necklaces
P ∝ n
Convert variation to equation
[tex]P=kn[/tex]
When P = 150, n = 15 (Substitute these values in the given equation)
[tex]150=k\times15[/tex]
Divide both sides by 15
[tex]\dfrac{150}{15} =\dfrac{k\times15}{15}[/tex]
[tex]10=k[/tex]
[tex]k=10[/tex]
Substitute k = 10 in [tex]P=kn[/tex]
[tex]P=10\times n[/tex]
[tex]P=10n[/tex] ------- Equation that relates P and n
When she sold 4 necklaces, n = 4
Substitute n = 4 in the formula above
[tex]P=10\times4[/tex]
[tex]P=40[/tex]
Find a vector x orthogonal to the row space of A, and a vector y orthogonal to column space, and a vector z orthogonal to the nullspace: A = [1 2 1 2 4 3 3 6 4].
A vector x orthogonal to the row space of A, and a vector y orthogonal to column space, and a vector z orthogonal to the null space. The orthogonal vector is :
A = [tex]\left[\begin{array}{ccc}1&2&1\\2&1&0\\1&-2&2\end{array}\right][/tex]
The orthogonal complement of the subspace V contains any vector perpendicular to V. This orthogonal subspace is denoted V⊥. (pronounced "V perp").
By this definition, null space is the orthogonal complement of row space. Every x perpendicular to the line satisfies Ax = 0 and lies in null space.
vice versa. If v is orthogonal to null space, it must be in row space. Otherwise, we can add this v as an extra row of the matrix without changing its null space. The rice space will become larger, breaking the rule of r+(n−r) = n.
The column space extent of A. These two vectors are the basis of col(A) , but they are not normalized.
In this case, the columns of A are already orthonormal, so you don't need to use the Gram-Schmidt procedure. To normalize a vector and then divide it by its norm:
[tex]\left[\begin{array}{ccc}1&2&1\\2&4&3\\3&6&4\end{array}\right][/tex]
and the vector after orthogonal process is:
[tex]\left[\begin{array}{ccc}1&2&1\\2&1&0\\1&-2&2\end{array}\right][/tex]
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write an algebraic expression to represent the phrase twelve dollars less than the original price. let p represent the unknown.
Answer:
p=O-12
Step-by-step explanation:
original price:O
12 less than O is "O-12"
therefore p=O-12