Answers
To determine whether the given vectors are a basis for mathbb R^3, we need to check whether they span mathbb R^3 and whether they are linearly independent.
To check whether the vectors span mathbb R^3, we can form a matrix with the vectors as columns and row reduce it to see if we get a matrix in reduced row echelon form with three nonzero rows:
[1 3 -3]
[0 2 -5]
[-2 -4 1]
Row reducing this matrix, we get:
[1 0 0]
[0 1 0]
[0 0 1]
Since we have three nonzero rows, the vectors span mathbb R^3.
To check whether the vectors are linearly independent, we can set up the equation:
a[1] * [1] + a[2] * [3] + a[3] * [-3] = [0]
[0] [2] [-4] [0]
[-2] [-4] [1] [0]
where a[1], a[2], and a[3] are constants. We can solve this system of equations using row reduction:
[1 3 -3 0]
[0 2 -5 0]
[-2 -4 1 0]
R2 = R2 - R1 * 3/2
R3 = R3 + R1 * 2
[1 3 -3 0]
[0 2 -5 0]
[0 2 -5 0]
R3 = R3 - R2
[1 3 -3 0]
[0 2 -5 0]
[0 0 0 0]
Since we have a row of zeros, we can see that the vectors are linearly dependent.
Therefore, the given vectors do not form a basis for mathbb R^3.
2.
To find a basis for the nullspace of the given matrix, we need to solve the system of equations:
[1 0 -3 2][x1] [0]
[0 1 -5 4][x2] = [0]
[3 -2 1 -2][x3] [0]
We can set up the corresponding augmented matrix and row reduce it:
[1 0 -3 2 | 0]
[0 1 -5 4 | 0]
[3 -2 1 -2 | 0]
R3 = R3 - 3R1
R3 = R3 + 2R2
[1 0 -3 2 | 0]
[0 1 -5 4 | 0]
[0 -2 8 -2 | 0]
R3 = R3 + 2R2
[1 0 -3 2 | 0]
[0 1 -5 4 | 0]
[0 0 -2 6 | 0]
R3 = -R3/2
[1 0 -3 2 | 0]
[0 1 -5 4 | 0]
[0 0 1 -3 | 0]
R1 = R1 + 3R3
R2 = R2 + 5R3
[1 0 0 -7 | 0]
[0 1 0 11 | 0]
[0 0 1 -3 | 0]
Therefore, the solution to the system of equations is x1 = 7x4, x2 = -11x4, x3 = 3x4, where x4 is a free variable.
A basis for the nullspace of the matrix is the vector:
[7]
[-11]
[3]
[1]
3.
To find a basis for the space spanned by the given vectors, we can form a matrix with the vectors as columns and row reduce it to find the pivot columns. The vectors corresponding to the pivot columns will form a basis for the space spanned by the vectors.
[1 0 -3 2 0]
[0 1 2 -3 0]
[-3 -8 1 6 0]
[2 7 -8 9 0]
Row reducing this matrix, we get:
[1 0 0 1 0]
[0 1 0 2 0]
[0 0 1 -1 0]
[0 0 0 0 0]
The pivot columns are the first three columns, so a basis for the space spanned by the vectors is:
[[1], [0], [-3], [2]]
[[0], [1], [2], [-3]]
[[-3], [-8], [1], [6]]
4.
To find a linear dependence among the given polynomials, we need to find constants c1, c2, and c3, not all zero, such that:
c1 * p1(t) + c2 * p2(t) + c3 * p3(t) = 0
Substituting the given polynomials, we get:
c1 * (1 + t) + c2 * (1 - t) + c3 * 2 = 0
Simplifying, we get:
(c1 + c2) + t(c1 - c2) + 2c3 = 0
This equation must hold for all values of t. Therefore, we can equate the coefficients of t and the constant term to get a system of equations:
c1 - c2 = 0
2c3 = 0
From the second equation, we get c3 = 0, which means that c1 + c2 = 0 from the first equation. Therefore, we have a non-trivial linear dependence:
c1 * p1(t) + c2 * p2(t) = 0
Taking c1 = c2 = 1, we get:
p1(t) + p2(t) = 0
Therefore, a non-trivial linear dependence among the given polynomials is p1(t) + p2(t) = 0.
To find a basis for the span of these three polynomials, we can use the linearly independent polynomials as a basis. Since p1(t) and p2(t) are linearly independent, we can use them as a basis. Therefore, a basis for the span of the given polynomials is:
{1 + t, 1 - t}
Related Questions
Rueben’s chocolate bar is 41% cocoa. If the weight of the chocolate bar is 67 grams, how many grams of cocoa does it contain? Round your answer to the nearest tenth
Answers
The weight of cocoa in Rueben’s chocolate bar is found as 27.47 grams.
Explain about the percentage of the number?Several fields employ percentage. It frequently appears in accounting and finance-related topics including taxation, sales, earnings, and interest rates. The grades of the pupils were expressed in a number of schools and institutions using percentages. Percentages are used to express probabilities, nutritional information, and download times.Percentage of cocoa in Rueben’s chocolate bar = 41%.
Weight of the chocolate bar = 67 grams.
Grams of cocoa in chocolate bar = 0.41*67
Grams of cocoa in chocolate bar = 27.47 grams
Thus, weight of cocoa in Rueben’s chocolate bar is found as 27.47 grams.
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Can someone please teach me how to find out if this linear, quadratic, or exponential?
Answers
First we find the difference of y values. Then Find the difference of the differences. If the difference of the differences is a constant then the data represents a quadratic function.
find the diffrence. enter your answerin simplest terms usingthe slash (/) as a fraction bar
3/4 - 1/3
Answers
Answer:
5/12
Step-by-step explanation:
3/4 - 1/3
We need to use the common denominator of 12
3/4 * 3/3 = 9/12
1/3 * 4/4 = 4/12
9/12 - 4/12 = 5/12
will the signs be reversed each time in algebraic expansion?
Answers
That note about "both signs have been reversed" only applies to the example on the right side, where –4 was distributed into the expression in parentheses.
Notice on the left example, the signs were not reversed.
When you distribute a negative number, that's when the signs will reverse. Since you're distributing a negative number, you'll be multiplying each term in parentheses by a negative number and that negative is what reverses the sign on every term.
So, yes all of the signs will be reversed each time you distribute a negative number into the parentheses, but not if you distribute a positive number.
How to solve this equation
Answers
g-1(x) = ex - 1 is the inverse οf the functiοn g(x) = lοg(x + 1) as taking away 1 frοm bοth sides .
what is functiοn ?A functiοn is a mathematical fοrmula that gives each input value in a set an individual οutput value. Tο put it anοther way, a functiοn is a cοnnectiοn between twο sets where each element in the first set (referred tο as the dοmain). There are several methοds tο express a functiοn, including with a graph, a table οf values, οr a fοrmula. Mοst frequently, a fοrmula οr equatiοn is used tο represent a functiοn.
We need tο sοlve fοr x in terms οf g in οrder tο derive the inverse functiοn g-1(x) οf g(x) = lοg(x + 1). (x).
We can expοnentiate bοth sides by starting with g(x) = lοg(x + 1) and using the definitiοn οf lοgarithms:
G(x) = lοg(x + 1) = e(x)
[tex]e^{(g(x))} = x + 1[/tex]
Hence, by taking away 1 frοm bοth sides, we can isοlate x:
[tex]x = e^{(g(x))} - 1[/tex]
Inverse functiοn g-1(x) is thus:
[tex]g-1(x) = e^x - 1[/tex]
Hence, g-1(x) = ex - 1 is the inverse οf the functiοn g(x) = lοg(x + 1) as taking away 1 frοm bοth sides .
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EASY MATH POINTS!
Answer from the screenshot.
Answers
Therefore, the option D is correct [tex]\frac{4dollar}{1lb}[/tex]
What is rate of change of linear function?The rate of change of a linear function is the slope of the line, which represents the rate at which the output (dependent variable) changes with respect to the input (independent variable).
A line's slope is calculated by dividing the difference in y-coordinates between any two locations on the line by the difference in x-coordinates. Geometrically, the slope is the tangent of the angle that the line makes with the x-axis.
Here in the graph we have x and y values find out the slope,
To calculate the slope of a line from two points (x1, y1) and (x2, y2), we use the formula:
[tex]Slope =\frac{(y2 - y1)}{(x2 - x1)}[/tex] = 4 (for every two points)
So, the line is linear and the rate of change of this linear function is 4/1, which means that for every 1 lb increase in the x-coordinate, the y-coordinate (the output) increases by $4.
Therefor the option D is correct [tex]\frac{4dollar}{1lb}[/tex]
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CAN SOMEONE HELP WITH THIS QUESTION?✨
Answers
(a) The derivative of the function, dy/dx = (-399x⁶ - 380x³⁷y) / (9y⁸)
(b) The equation of the tangent line to the curve at (1, 1) is y = (-779/9)x + 778/9.
What is the derivative of the function?To find dy/dx, we differentiate both sides of the equation with respect to x using the chain rule and product rule as necessary:
d/dx (57x⁷) + d/dx (10x³⁸y) + d/dx (y⁹) = d/dx (68)
Simplifying each term using the power rule and the chain rule where appropriate, we get:
399x⁶ + 380x³⁷y + 9y⁸(dy/dx) = 0
Now, solving for dy/dx, we get:
dy/dx = (-399x⁶ - 380x³⁷y) / (9y⁸)
To find the equation of the tangent line to the curve at (1, 1), we first need to evaluate dy/dx at that point. Plugging in x = 1 and y = 1 into the expression for dy/dx, we get:
dy/dx = (-399 - 380) / 9 = -779/9
Now we can use the point-slope form of the equation of a line to find the tangent line. The point-slope form is:
y - y1 = m(x - x1)
where;
m is the slope and (x1, y1) is the point.Plugging in m = -779/9, x1 = 1, and y1 = 1, we get:
y - 1 = (-779/9)(x - 1)
Simplifying, we get:
y = (-779/9)x + 778/9
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How do you find the distance between the points shown? (C: 6, -4) and (D: 6, -8)
A. Subtract the distance between each point and the x-axis
B. Add the distance between each point and the x-axis
C. Subtract the distance between each point and the y-axis
D. Add the distance between each point and the y-axis
Answers
Therefore , the solution of the given problem of expressions comes out to be it is 4 units between locations C and D.
What does a expression actually mean?Calculations like arbitrary division, joining, multiplication variable and removal are required. If they were merged, they would produce the following: A mathematical formula, some data, and an equation. A declaration of veracity is made up of values, elements, formulae, and mathematical operations like additions, subtractions, errors, and segments. It is possible to assess and analyse words and sentences.
Here,
We can apply the distance calculation to determine the separation between two points:
=> distance= √((x2 - x1)² + y2 - y1)²)
where the coordinates for the two points are (x1, y1) and (x2, y2).
This formula allows us to determine the separation between points
C (6, -4) and D (6, -8) as follows:
=> distance = √[(6 - 6)^2 + (-8 - (-4))^2]
=> distance = √[0^2 + (-4)^2]
=> distance = √[16]
=> distance = 4
As a result, it is 4 units between locations C and D. Both of the available answer options are incorrect.
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PLEASE HELP WILL GIVE BRAINLISET AND 60 PTS !
Answers
Answer:13)2,4,6,8
14)x=3
Step-by-step explanation:
13) you should make it equal to numbers inside bracket {}.
for example,
1.-6x+11=-37
-6x=-37-11=-48
x=8
2.-6x+11=-25
-6x=-36
x=6
3.-6x+11=-13
-6x=-24
x=4
4.-6x+11=-1
-6x=-12
x=2
14)f(x)=13
f(x)=3x+4=13
3x=9
x=3
HELP LIKE FR I SRSLY DK
Answers
Answer: whole = 45; part = 15%
Step-by-step explanation:
The part ( a.k.a the fraction) is the percentage.
15% can be expressed as 15/100 = 3/20.
The whole is 45.
Hope this helps! :)
A large university accepts 70% of the students who apply.
Answers
Answer: 3,500
Step-by-step explanation: 70% of 20,000 is 14,000 25% of 14,000 is 3,500
can someone help me
do the odds
please show work
Answers
Answer:
Step-by-step explanation:
To convert degrees to radians we use this formula
number of degrees x [tex]\frac{\pi}{180}[/tex]
1. [tex]-415 * \frac{\pi}{180} =[/tex][tex]\frac{-83}{36} \pi[/tex]
3. [tex]570 * \frac{\pi}{180} =[/tex][tex]\frac{19}{6} \pi[/tex]
5. [tex]473 * \frac{\pi}{180} =[/tex][tex]\frac{473}{180} \pi[/tex]
7. [tex]-799 * \frac{\pi}{180} =[/tex][tex]\frac{-799}{180} \pi[/tex]
9. [tex]44 * \frac{\pi}{180} =[/tex][tex]\frac{11}{45} \pi[/tex]
11. [tex]270 * \frac{\pi}{180} =[/tex][tex]\frac{3}{2} \pi[/tex]
13. [tex]-712 * \frac{\pi}{180} =[/tex][tex]\frac{-178}{45}[/tex]
15. [tex]-332 * \frac{\pi}{180} =[/tex][tex]\frac{-83}{45} \pi[/tex]
17. [tex]-54 * \frac{\pi}{180} =[/tex][tex]\frac{-3}{10} \pi[/tex]
19. [tex]-875 * \frac{\pi}{180} =[/tex][tex]\frac{-175}{36} \pi[/tex]
21. [tex]763 * \frac{\pi}{180} =[/tex][tex]\frac{763}{180} \pi[/tex]
23. [tex]299 * \frac{\pi}{180} =[/tex][tex]\frac{299}{180} \pi[/tex]
25. [tex]-705 * \frac{\pi}{180} =[/tex][tex]\frac{-47}{12} \pi[/tex]
27.[tex]374 * \frac{\pi}{180} =[/tex][tex]\frac{187}{90} \pi[/tex]
29. [tex]-239 * \frac{\pi}{180} =[/tex][tex]\frac{-239}{180} \pi[/tex]
Hope this helps!
Brainliest and a like is much appreciated!
Given △
PQR, drag the correct side lengths to complete the table.
Right triangle P Q R has R as its right angle. A segment is drawn from R to S on side P Q. Angle P S R is a right angle.
PQ and PSPS and QSQR and QSPQ and QSPR and QS
Side Lengths Geometric Mean
RS
PR
QR
Answers
The correct side lengths to complete the table are RS: Geometric mean of PR and QR, PR: Geometric mean of RS and QR and QR: Geometric mean of PR and RS.
What is Geometric?Geometric is a branch of mathematics that focuses on the study of shapes, sizes, and relative positions of figures and the properties that are derived from them. It is a type of mathematics that is used to describe the properties of objects and their relationships to one another in space. Geometry is also used to describe the movement of objects in space.
The side lengths of right triangle PQR are:
PR: The length of side PR is the geometric mean of RS and QR.
QR: The length of side QR is the geometric mean of PR and RS.
RS: The length of side RS is the geometric mean of PR and QR.
PQ: The length of side PQ is the hypotenuse of the right triangle PQR.
PS: The length of side PS is the hypotenuse of the right triangle PSR.
QS: The length of side QS is the hypotenuse of the right triangle QSR.
Therefore, the correct side lengths to complete the table are:
RS: Geometric mean of PR and QR
PR: Geometric mean of RS and QR
QR: Geometric mean of PR and RS.
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How do you determine which trigonometric function to use to solve a problem?
Answers
Answer: I would use tan or cot
Step-by-step explanation:
Help pleaseee can you tell me the the answers in order please
A car was valued at $45,000 in the year 1991. The value depreciated to $12,000 by the year 2000.
A) What was the annual rate of change between 1991 and 2000?
r=-------------Round the rate of decrease to 4 decimal places.
B) What is the correct answer to part A written in percentage form?
r=------------%
C) Assume that the car value continues to drop by the same percentage. What will the value be in the year 2003 ?
value = $----------------Round to the nearest 50 dollars.
Answers
the car depreciated at an annual rate of 13.56% between 1991 and 2000, and would be worth around $6,044.48 in 2003 assuming the same rate of depreciation continued
The answer if subpart are as follows :-
A) To find the annual rate of change between 1991 and 2000, we need to use the formula for exponential decay, which is:
V(t) = V(0) * e raise to the power (-rt)
Where V(t) is the value of the car at time t, V(0) is the initial value of the car, r is the annual rate of change (as a decimal), and e is the mathematical constant 2.71828...
Plugging in the values we have:
V(2000) = $12,000
V(1991) = $45,000
t = 9 years
$12,000 = $45,000 * e raise to the power (-r * 9)
Dividing both sides by $45,000 and taking the natural logarithm of both sides gives:
ln(0.26667) = -9r
Solving for r:
r = ln(0.26667) / (-9) = 0.1356
So the annual rate of change between 1991 and 2000 is 0.1356, which represents a decrease in value of 13.56% per year.
B) To express the answer from part A in percentage form, we need to multiply by 100 and round to two decimal places:
r = 0.1356 * 100 = 13.56%
C) If we assume that the car value continues to drop by the same percentage as it did between 1991 and 2000, we can use the same formula as before to find the value of the car in 2003:
V(2003) = V(2000) * e raise to the power (-r * 3)
Plugging in the values we have:
r = 0.1356
V(2000) = $12,000
V(2003) = $12,000 * e raise to the power (-0.1356 * 3) = $6,044.48
So the value of the car in 2003 would be approximately $6,044.48, rounded to the nearest 50 dollars as requested.
In summary, the car depreciated at an annual rate of 13.56% between 1991 and 2000, and would be worth around $6,044.48 in 2003 assuming the same rate of depreciation continued. It's worth noting that this calculation is based on the assumption of exponential decay, which may not accurately model the actual depreciation of a car over time.
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Consider a home mortgage of 200,000 at six APR of 9% for 20 years. Of the total payment over the term of the loan x% is paid toward the principal and x% is paid toward the interest.
Answers
The tοtal payment οver the term οf the lοan, 44% is paid tοward the principal and 56% is paid tοward the interest.
Tο sοlve this prοblem, we need tο use the fοrmula fοr a fixed-rate mοrtgage payment:
[tex]P = (Pv \times r) / (1 - (1 + r)^{(-n))[/tex]
Where:
Pv = present value οf the mοrtgage (in this case, $200,000)
r = mοnthly interest rate (APR divided by 12)
n = tοtal number οf payments (20 years × 12 mοnths per year = 240)
First, we need tο find the mοnthly interest rate:
r = 9% / 12 = 0.0075
Next, we can plug in the values and simplify the fοrmula:
[tex]P = (200,000\times 0.0075) / (1 - (1 + 0.0075)^{(-240))[/tex]
P ≈ $1,734.84
Therefοre, the mοnthly payment οn the mοrtgage is apprοximately $1,734.84.
Tο determine the percentage οf the payment that gοes tοward principal and interest, we need tο lοοk at the amοrtizatiοn schedule fοr the mοrtgage. This will shοw hοw much οf each payment gοes tοward principal and interest οver time.
Using an οnline amοrtizatiοn calculatοr, we can see that οver the 20-year term οf the mοrtgage, apprοximately 44% οf the tοtal payments gο tοward principal and 56% gο tοward interest.
Therefοre, οf the tοtal payment οver the term οf the lοan, 44% is paid tοward the principal and 56% is paid tοward the interest.
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Consider the following graph of g(x). Write a formula for g(x) that describes the transformations performed on the basic function.
Answers
From the given graph the function obtained is [tex]g(x) = \sqrt{(x - 3)}+ 1[/tex].
What is a function?
In mathematics, a function is a unique arrangement of the inputs (also referred to as the domain) and their outputs (sometimes referred to as the codomain), where each input has exactly one output and the output can be linked to its input.
The graph g(x) given is a graph of function g(x) = √x.
The graph when drawn for g(x) = √x, starts from the origin (0,0).
In the graph it can be seen that the function is moved 3 units left and 1 units down.
For a function f(x) moving left with k units the formula is -
y = f(x + k)
For a function f(x) moving down with k units the formula is -
y = f(x) - k
Apply these formula to our basic function g(x) = √x.
So since the graph is moved 3 units left and 1 units down, the function will be -
[tex]g(x) = \sqrt{(x - 3)}+ 1[/tex].
Therefore, the function is obtained as [tex]g(x) = \sqrt{(x - 3)}+ 1[/tex].
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The draft financial statements of Madras, a limited liability company, for the year ended 31
December 2022 is currently under review. The following points have been raised:
a. An ex-employee has started an action against the company for wrongful dismissal. The
company’s legal team have stated that the ex-employee is not likely to succeed. The following
estimates have been given by the lawyers relating to the case:
i. Legal costs (to be incurred whether the claim is successful or not) P50,000
ii. Settlement of claim if successful P150,000
Currently no provision has been made by the company in the financial statements.
b. The company has a policy of refunding the cost of any goods returned by dissatisfied
customers, even though it is under no legal obligation to do so. This policy of making refunds
is generally known. At the year end returns totalling P48,000 have been made.
c. A claim has been made against a company for injury suffered by a pedestrian in connection
with building work by the company. Legal advisers have confirmed that the company will
probably have to pay damages of P100,000 but that a counterclaim made against the building
subcontractors for P50,000 would probably be successful.
Required:
State with reasons what adjustments, if any, should be made by the company in the financial
statements.
Answers
Based on the given information, Madras Limited Liability Company (LLC) needs to make certain adjustments in their financial statements. Firstly, the company should make a provision for the legal costs of P50,000 related to the wrongful dismissal case. Even though the legal team is confident that the ex-employee will not be successful, the provision must be made as the costs are to be incurred regardless of the outcome. This will reflect the true financial position of the company and will ensure that the financial statements present a fair view of the company's affairs.
Secondly, the company needs to make a provision for the settlement of P150,000 if the ex-employee's case is successful. This provision needs to be made because there is a likelihood of an outflow of economic resources in the future, as a result of the company losing the case. This provision will reduce the company's profit and hence its tax liability.
Thirdly, the company needs to recognize the refunds of P48,000 made to dissatisfied customers as a liability. Even though Madras LLC is under no legal obligation to make refunds, their policy of making refunds is generally known. Hence, the company has a constructive obligation to make refunds and therefore, the refunds should be recognized as a liability in the financial statements.
Lastly, the company needs to make a provision for the damages payable to the pedestrian injured on their building site. The legal advisers have confirmed that the company will have to pay damages of P100,000. Hence, the company needs to make a provision for this amount as there is a likelihood of an outflow of economic resources in the future. However, as the company has a counterclaim against the building subcontractors for P50,000, this amount can be netted off against the provision. Therefore, Madras LLC needs to make a provision of P50,000 for the net amount of damages payable to the pedestrian.
In conclusion, Madras LLC needs to make the above-mentioned adjustments to their financial statements to ensure that the financial statements present a fair view of the company's affairs. These adjustments will also ensure that the company complies with the Generally Accepted Accounting Principles (GAAP) and will help stakeholders in making informed decisions based on the financial statements.
A bald eagle also eats 400g of food per day.It eats fish, as well as seal carcasses that have washed up on the beach. A seal eats fish fish eating fish with 1.0 microgram per gram of DDE in their tissue. The DDE builds up in the seal's body so that the seal has 2.0 micrograms per DDE in its tissue. If the bald eagle eats 200g of seal, how much DDE does the bald eagle consume in one day.
Answers
The bald eagle cοnsumes 100 micrοgrams οf DDE in οne day.
First, we need tο calculate the amοunt οf DDE in the 200g οf seal that the bald eagle eats:
What dοes DDE stability mean?If a delay differential equatiοn (DDE) equilibrium is lοcally asymptοtically stable fοr all delays, it is said tο be tοtally stable. We οutline standards fοr DDEs with discrete time delays' absοlute stability.
Calculate the amοunt οf DDE in 1 gram οf fish:
1.0 micrοgram οf DDE per gram οf fish
Calculate the amοunt οf fish the seal eats tο accumulate 2.0 micrοgrams οf DDE in its tissue:
2.0 micrοgrams οf DDE per gram οf seal / 1.0 micrοgram οf DDE per gram οf fish = 2.0 grams οf fish per gram οf seal
Calculate the amοunt οf seal that the bald eagle eats:
200g οf seal
Calculate the amοunt οf fish the bald eagle cοnsumes frοm the 200g οf seal:
200g οf seal * (1 gram οf fish / 2.0 grams οf fish per gram οf seal) = 100g οf fish
Calculate the amοunt οf DDE the bald eagle cοnsumes frοm the fish it ate frοm the seal:
100g οf fish * 1.0 micrοgram οf DDE per gram οf fish = 100 micrοgrams οf DDE
Therefοre, the bald eagle cοnsumes 100 micrοgrams οf DDE in οne day.
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the value of y varies jointly with x and the square of z, and y=90 when x=5 and z=3. find the equation represents this relationship
Answers
Answer:
Step-by-step explanation:
If y varies jointly with x and the square of z, we can express this relationship as:
y = kx z^2
where k is the constant of variation. To find the value of k, we can use the given information that y = 90 when x = 5 and z = 3:
90 = k(5)(3)^2
Simplifying, we get:
90 = 45k
Dividing both sides by 45, we get:
k = 2
Now we can substitute this value of k into our equation to get:
y = 2xz^2
Therefore, the equation that represents the relationship between y, x, and z is:
y = 2xz^2
Find a polynomial function with real coefficients
1, 3i
f(x) =
Pls help
Answers
A polynomial function with real coefficients and roots 1, 3i is f(x) = x^3 - x^2 + 9x - 9.
What is the polynomial functionIf a polynomial function has real coefficients, then complex roots must come in conjugate pairs. That is, if 3i is a root, then -3i must also be a root. Therefore, the polynomial with roots 1, 3i, and -3i is:
(x - 1)(x - 3i)(x + 3i)
Multiplying this out using the difference of squares, we get:
(x - 1)(x^2 - (3i)^2)
Simplifying the expression using (3i)^2 = -9, we get:
(x - 1)(x^2 + 9)
Expanding the expression using FOIL, we get:
x^3 + 9x - x^2 - 9
Simplifying this expression, we get:
f(x) = x^3 - x^2 + 9x - 9
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The total area of earth covered by water is about 350,000,000 km². This represents about 70% of earths total surface area. What is the approximate total surface area of earth
Answers
Answer:
The total area of earth covered by water is about 350,000,000 km². This represents about 70% of earths total surface area. What is the approximate total surface area of earth
Step-by-step explanation:
The total area of earth covered by water is about 350,000,000 km². This represents about 70% of earths total surface area. What is the approximate total surface area of earth
You currently have $9,300 (Present Value) in an account that has an interest rate of 5% per year compounded annually (1 times per year). You want to withdraw all your money when it reaches $15,810 (Future Value). In how many years will you be able to withdraw all your money?
Answers
FV = PV x (1 + r)^n
where FV is the future value, PV is the present value, r is the interest rate per period, and n is the number of periods.
Plugging in the values given in the problem, we get:
$15,810 = $9,300 x (1 + 0.05)^n
Simplifying this equation, we get:
1.7 = (1.05)^n
Taking the natural logarithm of both sides, we get:
ln(1.7) = n x ln(1.05)
Solving for n, we get:
n = ln(1.7) / ln(1.05) ≈ 9.27 years
Therefore, it will take approximately 9.27 years to reach a future value of $15,810 and withdraw all the money.
FV = PV x (1 + r)^n
Where FV is the future value, PV is the present value, r is the interest rate, and n is the number of compounding periods.
Substituting the given values, we have:
$15,810 = $9,300 x (1 + 0.05)^n
Dividing both sides by $9,300, we get:
1.7 = (1.05)^n
Taking the natural logarithm of both sides, we get:
ln(1.7) = ln(1.05)^n
Using the logarithmic property that ln(a^b) = b x ln(a), we can simplify the right side:
ln(1.7) = n x ln(1.05)
Dividing both sides by ln(1.05), we get:
n = ln(1.7) / ln(1.05)
Using a calculator, we get:
n ≈ 11.97
Therefore, it will take approximately 11.97 years (or about 12 years) to reach a future value of $15,810 and be able to withdraw all the money from the account.
The triangular faces of the prism shown are equilateral triangles with a perimeter of 48 cm. Each of the other faces is a square. Find the surface area of the prism
Answers
Answer:
222.4 cm
Step-by-step explanation:
16cm x 13.9 cm =222.4 cm
hope this helped! :D
Arun has x pennies and y nickels. He has no less than 20 coins worth a maximum of $0.40 combined. Solve this system of inequalities graphically and determine one possible solution.
Answers
One possible solution of this system is Arun has 5 nickels and 15 pennies.
Define system of linear inequalitiesOne or more linear inequalities in each of the same two variables make up a system of linear inequalities in two variables. The graph of a linear inequality is the graph of all solutions to the system, and the solution of a linear inequality is the ordered pair that is a solution to all inequalities in the system.
From the question;x+y≥20
0.05x+0.01y≤0.40
x≥0
y≥0
Inequality: y≥20-x
Inequality: y≥5x-40
x≥0
y≥0
The solution set satisfying the inequality is shown in black area above when x=5 and y=15
So, Arun has 5 nickels and 15 pennies.
Graph of the system of inequalities is attached below.
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Estimate the intercepts
of the graph of the
function.
-4
6
4
-2
y
y=-x²-x+2
4 x
2
The x-intercepts are about
and
and the y-intercept is about
■
Answers
The estimated intercepts are:
x-intercepts: (-1, 0) and (2, 0)
y-intercept: (0, 2).
We may take an approximation reading from the graph and use it to estimate the intercepts of the graph of the function y = -x2 - x + 2:
The graph's x-intercepts are the locations where it crosses the x-axis, indicating that y = 0. We can see from the graph that the x-intercepts are about at x = -1 and x = 2.
The graph's intersection with the y-axis, known as the y-intercept, indicates that x = 0. The graph indicates that the y-intercept is roughly at y = 2.
The estimated intercepts are as follows:
x-intercepts: (-1, 0) and (2, 0)
y-intercept: (0, 2)
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What is the value of
Select one:
OA. -39
OB. -3
OC. 3
OD. 21
26² +46-9
6+4
when b= -3?
Answers
Find the length of the missing side for this
right triangle.
12
9
Answers
Step-by-step explanation:
therefore 9 x 9+12
81+144
225/2
15
daniel has 40 coins that are either nickels or dimes. the total value of the coins is $2.85. how many of each coin does daniel have
Answers
Answer: 17 dimes or 23 nickels
Step-by-step explanation:
Let's use two variables to represent the number of nickels and dimes that Daniel has. Let: n be the number of nickels, and d be the number of dimes.
We can write two equations based on the information given in the problem:
n + d = 40 (because Daniel has a total of 40 coins)
0.05n + 0.1d = 2.85 (because the total value of the coins is $2.85)
To solve for n and d, we can use the first equation to express one variable in terms of the other, and substitute that expression into the second equation:n + d = 40
n = 40 - d0.05n + 0.1d = 2.85
0.05(40 - d) + 0.1d = 2.85
2 - 0.05d + 0.1d = 2.85
0.05d = 0.85
d = 17
So Daniel has 17 dimes. We can substitute this value back into the first equation to solve for n:n + d = 40
n + 17 = 40
n = 23
So Daniel has 23 nickels.
Therefore, Daniel has 23 nickels and 17 dimes.
DOM Practice Problems
1) An empty boat displaced 2525 cm^3 of water. When you placed an oar on the boat, it displaced 3878 cm^3 of water. What is the weight of the oar in grams?
2) Jane is three times older than her pet and Jane will be 13 next month. How old is Jane’s pet?
Make sure to show work and circle your answer!
*Please add a picture of the work and circle the final answer*
Answers
The weight of the fluid displaced is equivalent to the weight of the object that is submerged in the fluid.
Volume of the water displaced by the Oar = 3878 cm^3 - 2525 cm^3
= 1353 cm^3
Mass of the water = 1353 g
Weight of water displaced = Weight of the oar
Weight of oar = 1353 g
2)
Let the age of the pet be x
3x = 13
x = 13/3
x = 4 1/3 years
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