find the critical points, relative extrema, and saddle points of the function. (if an answer does not exist, enter dne.) f(x, y) = x2 + y2+ 2x − 6y + 5
Answers
The critical point is (-1, 3), The function has a relative minimum at (-1, 3), and there are no saddle points.
What is saddle point?
In mathematics, a saddle point refers to a point on a surface or in a function where it is neither a local minimum nor a local maximum but exhibits a unique property.
To find the critical points, relative extrema, and saddle points of the function \(f(x, y) = x^2 + y^2 + 2x - 6y + 5,\) we need to find the partial derivatives with respect to x and y and set them equal to zero.
Partial derivative with respect to x:
∂f/∂x = 2x + 2
Partial derivative with respect to y:
∂f/∂y = 2y - 6
Setting these partial derivatives equal to zero and solving for x and y, we have:
2x + 2 = 0 -> x = -1
2y - 6 = 0 -> y = 3
The critical point is (-1, 3).
To determine the nature of the critical point, we can use the second partial derivative test. We need to calculate the second partial derivatives:
\(\partial^2f/\partial x^2 = 2\\\\{\partial^2 f}/{{\partial y^2}} = 2\\\\\partial^2f/\partialx \partial y = 0\\)
Calculating the discriminant \(D = (\partial^2f/\partial x^2)(\partial^2f/\partial y^2) - (\partial^2f/\partial x\partialy)^2\), we have:
\(D = (2)(2) - (0)^2 = 4\)
Since D > 0 and \((\partial^2f/\partial x^2) > 0\), we can conclude that the critical point (-1, 3) is a relative minimum.
Therefore, the function has a relative minimum at (-1, 3), and there are no saddle points.
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Related Questions
using the va/linear foot method, the total va that must be used in a service calculation for a 50' show window is?
Answers
The total VA( volt-ampere ) that must be used in a service calculation for 50' show window is 125000VA.
What is VA linear foot method?A volt-ampere (SI symbol: VA or V A, abbreviated as VA) is the unit of perceived power in an electrical circuit. The apparent power is equal to the product of the root mean square voltage (in volts) and the root mean square current (in amperes). Volt-amperes are commonly used to analyze alternating current (AC) circuits. In direct current (DC) circuits, this product equals the real power in watts. The volt-ampere is dimensionally identical to the watt: 1 VA = 1 W in SI units).
The total VA that must be used in a service calculation for 50' show window is, Therefore, by using VA linear foot method,
200 VA per linear foot×50'=10000VA10000VA×1.25
=125000VA
Hence, the total VA that must be used in a service calculation for 50' shadow is 125000VA.
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Which of the following discrete probability distributions do not have a specified maximum value of X. Select all that apply. a. Binomial b. Hypergeometric c. Negative Binomial d. Geometric e. Poisson
Answers
The negative binomial, geometric, and Poisson distributions do not have a specified maximum value of X.
In the negative binomial distribution, X represents the number of trials needed to achieve a fixed number of successes. The number of trials can vary indefinitely, so there is no maximum value for X.
Similarly, in the geometric distribution, X represents the number of trials needed to achieve the first success. Since the number of trials can continue indefinitely until the first success occurs, there is no predetermined maximum value for X.
The Poisson distribution models the number of events occurring in a fixed interval of time or space. The number of events can be arbitrarily large, and thus there is no specific maximum value for X.
On the other hand, the binomial and hypergeometric distributions have a fixed number of trials or population size, respectively, which defines the maximum value of X. In these distributions, X represents the number of successes within the specified constraints.
Therefore, the negative binomial, geometric, and Poisson distributions do not have a specified maximum value of X, making them distinct from the binomial and hypergeometric distributions.
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statistics that allow for inferences to be made about a population from the study of a sample are known as____
Answers
Statistics that allow for inferences to be made about a population from the study of a sample are known as inferential statistics.
Inferential statistics is a branch of statistics that deals with making inferences about a population based on information obtained from a sample. It involves estimating population parameters, such as mean and standard deviation, using sample statistics, such as sample mean and sample standard deviation.
The main goal of inferential statistics is to determine how reliable and accurate the estimated population parameters are based on the sample data. This is done by calculating a confidence interval or conducting hypothesis testing.
Confidence intervals provide a range of values in which the population parameter is likely to lie, whereas hypothesis testing involves testing a null hypothesis against an alternative hypothesis.
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THIS IS DUE RN PLEASE HELP!!!
Answers
Answer:
c = 6d
Step-by-step explanation:
the cost is equal to $6/day
Giveng(x) is the inverse of f(x), andf(-4)= 9, what is the value of:8(9) – 3f (-4)?
Answers
It is given that the function g(x) is the inverse of f(x) so it follows:
\(g(x)=f^{-1}(x)\)It is given that f(-4)=9 so it follows:
\(\begin{gathered} f(-4)=9 \\ f^{-1}f(-4)=f^{-1}(9) \\ -4=g(9) \end{gathered}\)So the value of g(9)-3f(-4) is given by:
\(\begin{gathered} g(9)-3f(-4)=-4-3(9) \\ =-4-27 \\ =-31 \end{gathered}\)Hence the value is -31.
in a circle of radius 3.4 cm, what is the length of the arc opposite a central angle that measures 46 degrees?
Answers
The length of the arc opposite a central angle that measures 46 degrees is 2.72 cm.
What is circle?
The measurement of the circle's boundaries is called as the circumference or perimeter of the circle. whereas the circumference of a circle determines the space it occupies. The circumference of a circle is its length when it is opened up and drawn as a straight line. Units like cm or unit m are typically used to measure it. The circle's radius is considered while calculating the circumference of the circle using the formula. As a result, in order to calculate the circle's perimeter, we must know the radius or diameter value.
in a circle of radius 3.4 cm
central angle that measures 46 degrees
length of arc = (46/360) * 2π*3.4
=2.72cm
Hence the length of the arc opposite a central angle that measures 46 degrees is 2.72 cm
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A chemical engineer has tested 56 water samples. These samples make up 25% of the total number of samples that need testing.
Select from the drop-down menu to correctly identify the total number of water samples that need testing.
There are a total of
Choose...
water samples to be tested.
Answers
Answer:
224
Step-by-step explanation:
56 x 4 = 224 (aka 100%)
Sorry I can't explain more, but I hope this helps!
Answer:
224
Step-by-step explanation:
according to your text, which of the following is the primary source of primate endangerment today? habitat destruction human diseases social stress and dislocation use of primates for pets
Answers
Based on the text, the primary source of primate endangerment today is habitat destruction.
Habitat destruction is considered the primary source of primate endangerment based on various factors mentioned in the text. Primates, like many other species, heavily rely on their natural habitats for survival, including food, shelter, and breeding. However, human activities such as deforestation, urbanization, and land conversion for agriculture or infrastructure development have significantly reduced and fragmented primate habitats.
Habitat destruction leads to the loss of critical resources and disrupts the ecological balance necessary for primate populations to thrive. As their habitats shrink, primates face increased competition for limited resources, reduced access to food and water sources, and decreased opportunities for successful reproduction and rearing of offspring. This loss of habitat also exposes primates to increased vulnerability to predation, disease transmission, and human-wildlife conflicts.
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someone help me with this
find points a b c
Answers
Answer:
<a=32
<b=40
<c=40
Step-by-step explanation:
to find angle a you have to subtract the 50 minus 180 to find the angle close to the 50 because angles in a straight line add up to 180. the answer will be
180-50=130
after finding the angle in that triangle you must add it to the other angle present which is 18° then subtract by 180 because angles in a straight line add up to 180
130+18+a=180
a=180-148
a=32 and that's how you find a
to find b you must know that the angle at the center is twice the angle at the circumference meaning the large angle C is 90°,now if it's 90° inorder to find the big angle B you must add the 18+90 then subtract 180
18+90+B=180
B=180-108
=72
since the combination of angle a and b will give you 72 you can find angle c by subtracting a from 72
c=72-32
=40
then if you look at angle c and angle b you can tell that they are alternating meaning angle b is also 40
I hope this helps
Which two ratios represent quantities that are proportional 5/7 and 7/14, 9/10 and 10/9, 56/64 and 36/48, or 21/28 and 12/16
Answers
To determine whether two ratios represent quantities that are proportional, we need to check if their values are equal. Let's examine each pair of ratios:
5/7 and 7/14:
To check if these ratios are proportional, we simplify them to their simplest forms. The first ratio is already simplified, but the second ratio can be simplified to 1/2. Since 5/7 is not equal to 1/2, these ratios are not proportional.
9/10 and 10/9:
By simplifying both ratios, we find that they are equal to each other in their simplest forms. Therefore, 9/10 and 10/9 are proportional.
56/64 and 36/48:
After simplifying both ratios, we get 7/8 for the first ratio and 3/4 for the second ratio. Since 7/8 is not equal to 3/4, these ratios are not proportional.
21/28 and 12/16:
Upon simplifying, we obtain 3/4 for both ratios. Therefore, 21/28 and 12/16 are proportional.
In summary, out of the four given pairs of ratios, only the ratios 9/10 and 10/9, as well as 21/28 and 12/16, represent quantities that are proportional. It is important to simplify the ratios to their simplest forms before comparing them to determine proportionality.
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Brian is throwing a party. He needs 3/4 of a pound of hamburger meat for each person at the party. If 12 people are coming to the party, how many pounds of hamburger meat will Brian need to buy?
Answers
9 pounds of hamburger meat will be needed by Brian.
We are given value for one unit. The calculation is required for more than one units, hence, multiplication will be performed.
As per the given information, amount of hamburger meat required for one person is = 3/4 pound
Amount of hamburger meat required for 12 people = (3/4) × 12
Performing division to find the amount of hamburger meat required for 12 people
Amount of hamburger meat required for 12 people = 3 × 3
Performing multiplication to find the amount of hamburger meat required for 12 people
Amount of hamburger meat required for 12 people = 9 pounds
Therefore, Brain needs to buy 9 pounds of hamburger meat.
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Ellie wants to work out the height of a building which has a fence all around it
From P she sees that the angle of elevation of the top is 28 degrees
From Q 20m closer the angle of elevation is 40 degrees
Work out the height of the building
Answers
The Height of the Building is 28.87 m .
in the question ,
it is given that
distance between P and Q \(=\) 20 m
From P the angle of elevation is 28°
and from Q the angle of elevation is 40°
From the figure
In triangle BAQ
tan40° = BA/AQ
tan40° = h/x
h = x * tan40°
In triangle BAP
tan28° = BA/AP
tan28° = h/(x+20)
h = (x+20) * tan28°
Equating both the h , we get
x * tan40° = (x+20) * tan28°
x* tan40° = x*tan28° + 20* tan28°
x*(tan40° - tan28°) = 20* tan28°
x*(0.840 - 0.531) = 20*(0.531)
x*(0.309) = 10.62
x = 10.62/0.309
x = 34.368
Substitute h = 34.368 in h = x * tan40°
we get ,
h = (34.368)*(0.840)
h = 28.8699
h = 28.87
Therefore , The Height of the Building is 28.87 m .
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PLEASE HELP ME THIS IS MY FINAL !!!!
Two taxi services charge different rates. Taxi A charges $0.40 per mile
traveled plus an initial charge of $2.00. Taxi B charges $0.50 per mile
traveled. The situation is modeled by this system, where xis the number of
miles traveled and y is the charge for that distance, in cents:
y= 40x+ 200
y= 50x
How many miles must each taxi travel for the charges to be equal, and what
is the charge for that distance?
Answers
Answer:
it would take 20 miles and cost 10 dollars.
Step-by-step explanation: Like up the equations so that 50x=40x+200. When you solve for x (number of miles) you find that x=20. Use 20 in either equation (0.5x or 0.4x+2) to get 10 (total cost).
6W - 12x + 7w - 8x =
Answers
Explanation:
6W + 7W = 13W
-12x - 8x = -20x
Which of the following transformations are linear? Select all of the linear transformations. There may be more than one correct answer: Be sure you can justify your answers ~8 A T(A) = ASA-I from R2x2 to R2x2 where S = 55 B. T(A) = A from R2xs to R2x5 ~9 -2 C.T(A) = A from R to RZx2 D. T(A) = 2A from R6x4 to R6x4 ET(A) = A A from R2x2 to R 2x2 5 JET(A) = A+ Is from RSx5 to RSx5
Answers
A, C, and E are linear transformations. To justify: A: T(A) = ASA-I is linear because it satisfies the two properties of linearity:
1. Additivity: T(A+B) = T(A) + T(B) for any matrices A and B in R2x2. This can be shown by plugging in (A+B) for A in T(A) and simplifying.
2. Homogeneity: T(kA) = kT(A) for any scalar k and matrix A in R2x2. This can be shown by plugging in kA for A in T(A) and simplifying.
C: T(A) = A from R to R2x2 is linear because it satisfies the two properties of linearity:
1. Additivity: T(A+B) = T(A) + T(B) for any matrices A and B in R. This can be shown by plugging in (A+B) for A in T(A) and simplifying.
2. Homogeneity: T(kA) = kT(A) for any scalar k and matrix A in R. This can be shown by plugging in kA for A in T(A) and simplifying.
E: T(A) = A from R2x2 to R2x2 is linear because it satisfies the two properties of linearity:
1. Additivity: T(A+B) = T(A) + T(B) for any matrices A and B in R2x2. This can be shown by plugging in (A+B) for A in T(A) and simplifying.
2. Homogeneity: T(kA) = kT(A) for any scalar k and matrix A in R2x2. This can be shown by plugging in kA for A in T(A) and simplifying.
B, D, and J are not linear transformations.
To justify:
B: T(A) = A from R2xs to R2x5 is not linear because it does not satisfy the additivity property of linearity. Specifically, T(A+B) ≠ T(A) + T(B) for some matrices A and B in R2xs.
D: T(A) = 2A from R6x4 to R6x4 is not linear because it does not satisfy the homogeneity property of linearity. Specifically, T(kA) ≠ kT(A) for some scalar k and matrix A in R6x4.
J: T(A) = A+Is from RSx5 to RSx5 is not linear because it does not satisfy either the additivity or homogeneity properties of linearity. Specifically, T(A+B) ≠ T(A) + T(B) and T(kA) ≠ kT(A) for some matrices A and B in RSx5 and scalar k.
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Today, 6 friends went out for lunch. Their total bill was $27.60, including tax and gratuity. They decided to split the bill equally and each paid with a $10 bill. How much money will each person get back?
Answers
Step-by-step explanation:
Right, okay, so this is a bit of a weird one. Let's go step by step.
"Today, 6 friends went out for lunch." = The number 6 is gonna be in our equation somewhere.
"Their total bill was $27.60" = so is the number 27.6
"They decided to split the bill equally" = 27.6 "split equally" (aka divided by) 6 friends is 4.6
"each paid with a $10 bill" = This is where it gets a lil weird. So, if they divided the bill among them, none of their amounts are gonna be anywhere near ten dollars. This is one of those questions that wouldn't really happen in real life. People would probably use fives instead, but whatever. So a number we'll be using for something is 10.
"How much money will each person get back?" = So we have to find the amount they all paid (10) minus the amount each one had to pay (4.6).
To put it all into a full equation...
10 - ( 27.6 / 6 )
Divide.
10 - 4.6
Subtract.
5.4
Put back into money form.
$5.40
Answer:
Each person will get back $5.40.
Answer:
if each paid a $10 bill, in total they paid $60 (cuz 10 x 6)
60 - 27.60 = 32.4
32.4/6 = 5.4 (divide the change between 6 people)
Each person will get $5.40 back.
hope it helps :)
Calculate the area bounded by the curve
Calculate the area A of the shaded region. 2- y = 2 sin (x) x -2 2 y = 4/9 x -3 Give an exact answer.
Answers
The exact area of the shaded region is 12 + 2cos(2).
To calculate the area A of the shaded region bounded by the curve y = 2 - 2sin(x), x = -2, and x = 2, we need to integrate the function over that interval.
First, let's find the points of intersection between the curve and the line y = 4/9x - 3.
Setting the equations equal to each other:
2 - 2sin(x) = 4/9x - 3
2sin(x) = -4/9x + 1
sin(x) = -2/9x + 1/2
To find the points of intersection, we solve for x:
x = -2, 2 (from the given interval)
Now, we integrate the function y = 2 - 2sin(x) over the interval [-2, 2]:
A = ∫[from -2 to 2] (2 - 2sin(x)) dx
To evaluate this integral, we can use antiderivative rules:
A = [2x - 2(-cos(x))] [from -2 to 2]
A = [2(2) - 2(-cos(2))] - [2(-2) - 2(-cos(-2))]
A = [4 + 2cos(2)] - [-4 + 2cos(-2)]
A = 8 + 4cos(2) + 4 - 2cos(2)
A = 12 + 2cos(2)
Therefore, the exact area of the shaded region is 12 + 2cos(2).
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Smoking and use of electronic cigarettes (vaping) in relation to preterm birth and small-for-gestational-age in a 2016 U.S. national sample pbu med
Answers
Smoking and use of electronic cigarettes (vaping) in relation to preterm birth -
Around pregnancy, women who smoke might be inspired to switch to vaping (using electronic cigarettes, or e-cigs) in an effort to reduce the known risks of smoking. E-cigarettes normally include nicotine, but they either completely eliminate or drastically cut down on exposure to tobacco's combustion byproducts. 31 973 live singleton births in the United States were the subject of our study in 2016. 5029 (14%) mothers were "single smokers" during the three months prior to becoming pregnant, while 976 (3%) mothers used both tobacco and e-cigarettes ("dual-users"). 44% of pre-pregnancy single smokers stayed single smokers, whereas 1% switched to dual use in the last trimester. However, late-pregnancy sole vapers and dual-users had increased risk of SGA compared to non-users (aOR 2.4, 95% CI 1.0-5.7 for sole vapers, and aOR 2.3 95% CI 1.3-4.1 for dual-users). These findings suggest that vapers during pregnancy had similar risk of preterm as non-users but still had elevated risk for restricted fetal growth.What is e-cigarette meaning?
A device that has the shape of a cigarette, cigar, or pen and does not contain tobacco. It uses a battery and contains a solution of nicotine, flavorings, and other chemicals, some of which may be harmful.
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PLEASE HELP! PICTURE BELOW
Answers
Answer: 42
Step-by-step explanation: 7+7+7+7+7+7
Answer:
147 square feet.
Step-by-step explanation:
Basically you find the triangle’s area 7 x 7 / 2 = 24.5
two triangle = 49
total area = 196
subtract the two triangles from total area
196-49=147
Answer detailed please
Answers
Answer:
container A
Step-by-step explanation:
In Container A, we can plot the points (0,60) adn (2, 35)
The slope is :
\(m_A = \frac{y_2-y_1}{x_2-x_1} \\\\= \frac{35-60}{2-0} \\\\= \frac{-25}{2}\\ \\m_A = -12.5\\\)
For container B, the slope is:
\(m_B = \frac{y_2-y_1}{x_2-x_1} \\\\= \frac{32-54}{3-1} \\\\= \frac{-22}{2}\\ \\m_B = -11\\\)
The negative sign of the slope indicates the direction of the slope
\(|m_A| = 12.5\\\\|m_B| = 11\)
12.5 > 11
The slope of container A is steeper than container B
Therefore, the water is draining out of container A at a faster rate than container B
solve for w and simplify the answer
Answers
Answer: w=20/3
Step-by-step explanation: start by multiplying -3/2 by 2 and multiply -10 by 2 as well. you would get -3w = -20. divide both sides by -3 and you’ll get 20/3.
Answer in standard form
Answers
Answer:Any number that we can write as a decimal number, between 1.0 and 10.0, multiplied by a power of 10, is said to be in standard form. 1.23 × 108; If you observe carefully, 1.23 is a decimal number between 1.0 and 10.0 and so we have the standard form of 123,000,000 as 1.23 × 10 8.
Step-by-step explanation:
P.S i am emo
-8x-3=13-9x what is the answer for x?
Answers
Answer:
x=16
Step-by-step explanation:
-8x-3=13-9x
-8x+9x=13+3
x=16
Answer:
x = 16
Step-by-step explanation:
subtract 8x from both sides
-3 = 13 -x subtract 13 to both sides
-16 = -x multiply both sides by -1 which gives you 16 = x
Write the equation of the line in slope intercept form that passes through the point (-3, 5) and is parallel to y= - 2/3x
Answers
Answer:
\(\displaystyle y=-\frac{2}{3}x+3\)
Step-by-step explanation:
We want to find the equation of the line that is parallel to:
\(\displaystyle y=-\frac{2}{3}x\)
And passes through (-3,5).
First, we need to determine the slope of our new line.
Remember that parallel lines have the same slope.
Since the slope of our original line is -2/3, this means that the slope of our new line must also be -2/3.
Now, we can use the point-slope form given by:
\(y-y_1=m(x-x_1)\)
We will let (-3, 5) be (x₁, y₁). By substitution:
\(\displaystyle y-(5)=-\frac{2}{3}(x-(-3))\)
Simplify:
\(\displaystyle y-5=-\frac{2}{3}(x+3)\)
Distribute:
\(\displaystyle y-5=-\frac{2}{3}x-2\)
Add 5 to both sides. So, our equation is:
\(\displaystyle y=-\frac{2}{3}x+3\)
Answer:
\(\displaystyle y = -\frac{2}{3}x + 3\)
Step-by-step explanation:
5 = –⅔[–3] + b
2
\(\displaystyle 3 = b \\ \\ y = -\frac{2}{3}x + 3\)
Parallel equations have SIMILAR RATE OF CHANGES [SLOPES], so –⅔ remains as is.
I am joyous to assist you at any time.
a card is drawn at random from a standard deck. that card is not put back in the deck, and a second card is drawn at random from the remaining cards in the deck. neither of the cards drawn so far are put back in the deck, and a third card is drawn at random from the remaining cards in the deck. what is the probability that all three of the cards are tens?
Answers
The probability that all three of the cards are tens is 0.018.
The probability that the first card drawn is a ten is 4/52 since there are 4 tens in a deck of 52 cards.
The probability that the second card drawn is a ten, given that the first card was a ten and was not put back in the deck, is 3/51 since there are now only 3 tens left in a deck of 51 cards.
The probability that the third card drawn is a ten, given that the first two cards were tens and were not put back in the deck, is 2/50 since there are now only 2 tens left in a deck of 50 cards.
Therefore, the probability that all three cards are tens is:
(4/52) * (3/51) * (2/50) = 1/5525 ≈ 0.00018 or about 0.018%.
So, the probability of drawing three tens in a row without replacement is very low.
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Given f(x) = 2x2 – 9x + 2, g(x) = 1 - 6x, and
h(x) = x2 – 4, find the following function:
(h+f)(x)
Answers
Answer:
\((h+f)(x)=3x^2-9x-2\)
Step-by-step explanation:
\(f(x)=2x^2-9x+2\\g(x)=1-6x\\h(x)=x^2-4\)
Looks like g(x) is irrelevant here.
You can expand this like so:
\((h+f)(x)\\h(x)+f(x)\)
And even further:
\((x^2-4)+(2x^2-9x+2)\)
Now, it's just a matter of simplifying.
\(x^2-4+2x^2-9x+2\\\\(x^2+2x^2)+(-9x)+(-4+2)\\\\3x^2-9x-2\)
Therefore:
\((h+f)(x)=3x^2-9x-2\)
A point P os equi distant from R(-2,4) and S(6,-4) and its x co ordinate is twice its Y co ordinate find co ordinates of P
Answers
Answer: \(P(-4,-2)\)
Step-by-step explanation: Distance between two points is calculated as
\(d=\sqrt{(x_{2}-x_{1})^{2}+(y_{2}-y_{1})^{2}}\)
Equidistant means the same distance, i.e., the distance between points P and R is equal to the distance between points P and S.
Suppose P's y-coordinate is a. If its x-coordinate is double, then
(x,y) = (2a,a)
Thus
\(\sqrt{(2a+2)^{2}+(a-4)^{2}} =\sqrt{(2a-6)^{2}+(a+4)^{2}}\)
Solving
\(4a^{2}+8a+4+a^{2}-8a+16=4a^{2}-24a+36+a^{2}+8a+16\)
\(5a^{2}+20=5a^{2}-16a+52\)
\(-16a=32\)
\(a=-2\)
y-coordinate is \(-2\), then x-ccordinate is
2a = 2(-2) = \(-4\)
Coordinates of point P equidistant for R and S is \((-4,-2)\).
a wildlife photographer photographs a crocodile and then paddles against a river current for 6 km. Then, hoping to photograph a hippopotamus, she paddles 15 km across a lake. She paddles across the lake for one hour longer than she paddled up the river. find the speed of the boat as she paddles the lake if the river current is 2 km/h
Answers
Answer:
6 km/hr or 5 km/hr
Step-by-step explanation:
In the lake, she goes 15 km at x km/hr (named)
In the river, she goes 6 km at x-2 km/hr (current=2 km/hr)
So, the time in the lake - the time in the river = 1 hour (given)
15/x - 6/x-2 = 1 --> x=6;x=5
The speed of the boat as the photographer paddles the lake if the river current is 2 km/h is 6 km/hr and this can be determined by forming the quadratic equation.
Given :
A wildlife photographer photographs a crocodile and then paddles against a river current for 6 km.Then, hoping to photograph a hippopotamus, she paddles 15 km across a lake.She paddles across the lake for one hour longer than she paddled up the river.According to the given data, if the river current velocity is 2 km/hr then let the speed in the lake be x km/hr. So, the speed of the photographer in the river is (x - 2) km/hr
Therefore, the speed of the boat as she paddles the lake if the river current is 2 km/h is given by:
\(\dfrac{15}{x} - \dfrac{6}{x-2}=1\)
Now, simplify the above expression.
\(15(x-2)-6(x)=x(x-2)\)
\(15x-30-6x=x^2-2x\)
\(x^2-11x+30=0\)
Factorize the above equation.
\(x^2-6x-5x+30=0\)
x(x - 6) - 5(x - 6) = 0
(x - 6)(x - 5) = 0
x = 6 or 5
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You invest $20,000 in the stock market. The stock market then plummets
over the next few weeks. Each day, your investment loses half of its value. How
much will you have invested after 14 days? Write the geometric sequence
formula and show all of your work.
Answers
After 14 days, you will have approximately $2.4414 invested in the stock market.
The amount you will have invested after 14 days can be calculated using the geometric sequence formula. The formula for the nth term of a geometric sequence is given by:
an = a1 x \(r^{(n-1)\)
Where:
an is the nth term,
a1 is the first term,
r is the common ratio, and
n is the number of terms.
In this case, the initial investment is $20,000, and each day the investment loses half of its value, which means the common ratio (r) is 1/2. We want to find the value after 14 days, so n = 14.
Substituting the given values into the formula, we have:
a14 = 20000 x\((1/2)^{(14-1)\)
a14 = 20000 x \((1/2)^{13\)
a14 = 20000 x (1/8192)
a14 ≈ 2.4414
Therefore, after 14 days, you will have approximately $2.4414 invested in the stock market.
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The amount you will have invested after 14 days is given as follows:
$2.44.
What is a geometric sequence?A geometric sequence is a sequence of numbers where each term is obtained by multiplying the previous term by a fixed number called the common ratio q.
The explicit formula of the sequence is given as follows:
\(a_n = a_1q^{n-1}\)
In which \(a_1\) is the first term of the sequence.
The parameters for this problem are given as follows:
\(a_1 = 20000, q = 0.5\)
Hence the amount after 14 days is given as follows:
\(a_{14} = 20000(0.5)^{13}\)
\(a_{14} = 2.44\)
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I need help with this?
Answers
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Explanation:
To get the LCM (lowest common multiple) of 8 and 10, we can multiply the two values together to get 8*10 = 80, then we divide by the GCF (greatest common factor) which is 2 to get to the LCM of 80/2 = 40.
While 80 is a common multiple of 8 and 10, it is not the smallest such value. That would be 40. So that's why we divided by 2.
Another route we can take is to list out the multiples of 8 and 10 like so
multiples of 8 = {8, 16, 24, 32, 40, 48, 56, 64, 72, 80, ...}multiples of 10 = {10, 20, 30, 40, 50, 60, 70, 80, ...}as shown in bold above, the value 40 is in both lists and it is the smallest such common item.
So this tells us that the last two digits are 4 and 0 in that order.
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The GCF of 30 and 75 is 15 since we can say
30 = 15*2
75 = 15*5
Note how the 2 and 5 have no other factors in common, other than 1. This helps us see how 15 is the largest shared factor. So the first two digits are 1 and 5 in that order.
Overall, the four digit code is 1540.