Find the points on x^2+3(y-2)^2 = 27
which are closest to and farthest from the origin
Answers
[tex](-4.89, 3)[/tex] and [tex](4.89, 3)[/tex] are the farthest from the origin and [tex](0, -1)[/tex] is the closest from the origin.
Let be a curve of the form [tex]x^{2}+3\cdot (y-2)^{2} = 27[/tex]. The distance with respect to origin is found by using the following Pythagorean identity:
[tex]r = x^{2}+y^{2}[/tex] (1)
Where [tex]r[/tex] is the square distance function.
We can modify (1) as following:
[tex]r = [27-3\cdot (y-2)^{2}]+y^{2}[/tex]
[tex]r = 27-3\cdot (y^{2}-4\cdot y +4)+y^{2}[/tex]
[tex]r = 27-3\cdot y^{2}+12\cdot y -12 + y^{2}[/tex]
[tex]r = -2\cdot y^{2}+12\cdot y+27[/tex] (1b)
Now we apply the First and second derivative tests to determine the minimum and maximum distances from the origin:
First derivative test
[tex]-4\cdot y +12 = 0[/tex]
[tex]y = 3[/tex]
Second derivative test
[tex]r'' = -4[/tex]
The y-component represents a maximum.
Now we graph the function with the ressource of a graphing tool, we find the following points:
Farthest points: [tex](-4.89, 3)[/tex], [tex](4.89, 3)[/tex].
Closest points: [tex](0, -1)[/tex].
[tex](-4.89, 3)[/tex] and [tex](4.89, 3)[/tex] are the farthest from the origin and [tex](0, -1)[/tex] is the closest from the origin.
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Related Questions
Billy invests $5,000 in an account at 4.2% for 15 years, compounded monthly. Assuming no other deposits or withdrawals are made, how much will Billy have at the end of 15 years?
Answers
The amount Billy has at the end of the 15 years is $9,377.73.
What is compound interest?It is the interest we earned on the interest.
The formula for the amount earned with compound interest after n years is given as:
A = P[tex](1 + r/n)^{nt}[/tex]
P = principal
r = rate
t = time in years
n = number of times compounded in a year.
We have,
P = $5000
r = 4.2%
t = 15 years
n = 12
A = P[tex](1 + r/n)^{nt}[/tex]
A = 5000 [tex](1 + 0.0035)^{180}[/tex]
A = 5000 x [tex]1.0035^{180}[/tex]
A = $9,377.73
Thus,
Billy has $9,377.73 at the end of the 15 years.
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The dean of a business college in the Midwest claims that he can correctly identify whether a student is a finance major or a music industry management major by the way the student dresses. Suppose in actuality that he can correctly identify finance majors 84% of the time, while 16% of the time he mistakenly identifies a music industry management major as a finance major. Presented with one student and asked to identify the major of this student (who is either a finance or music industry management major), the dean considers this to be a hypothesis test with the null hypothesis being that the student is a finance major and the alternative that the student is a music industry management major. Which of the following statements illustrates a Type I error?
a. Saying that the student is a finance major when in fact the student is a music industry management major.
b. Saying that the student is a music industry management major when in fact the student is a music industry management major.
c. Saying that the student is a finance major when in fact the student is a finance major.
d. Saying that the student is a music industry management major when in fact the student is a finance major.
Answers
Using error concepts, it is found that the option that represents a Type I error is:
d. Saying that the student is a music industry management major when in fact the student is a finance major.The definitions of each type of error are as follows:
A Type I error happens when a true null hypothesis is rejected. A Type II error happens when a false null hypothesis is not-rejected.
In this problem, the Hypothesis are:
Null: Student is a finance major.Alternative: Student is a music industry management major.By the definition of a Type I error, in this problem, it would consist in saying that a finance major student is a music industry management major student, hence option d is correct.
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A computer can do 1000 operations in 4.5×10^-6 seconds. How many operations can be done by this computer in one hour?
Answers
Answer:
0.00027.
Step-by-step explanation:
All you have to do is do the scientific notation then multiply by 60.
This morning, Raina's car had 23.21 gallons of fuel. Now, 1.5 gallons are left. How much fuel did Raina use?
Answers
Let x represent number of gallons of fuel used
23.21 gallons = x gallons + 1.5 gallons
x = 21.6 gallons were used
Find the value of x.
Answers
Answer:
9
Step-by-step explanation:
yeah, 9...........right???
One kilometre is about 0.62 miles. It is 12 kilometres from Noah's house to the
ice skating rink. About how many miles is it from Noah's house to the ice
skating rink?
u'll get extra points if u answer guys!! pls help!!!!!
Answers
Answer:
7.44miles
Step-by-step explanation:
1km = 0.62miles
12km will be ; 0.62 × 12
= 7.44miles
13. Solve to find the vertex if :
3x2 – 19x - 5
Answers
Answer:
A) y = 3(x -3)^2 -46
B) (3, -46)
C) look at the y-coordinate of the vertex
Step-by-step explanation:
A) Factor the leading coefficient from the variable terms.
y = 3(x^2 -6x) -19
Inside parentheses, add the square of half the x-coefficient. Outside, subtract the same value.
y = 3(x^2 -6x +9) -19 -3(9)
y = 3(x -3)^2 -46
__
B) Compared to the vertex form, ...
y = a(x -h)^2 +k
we find a=3, (h, k) = (3, -46).
The vertex is (3, -46).
__
C) The vertex is an extreme value (as is any vertex). The sign of the leading coefficient tells you whether the parabola opens upward (+) or downward (-). This parabola opens upward, so the vertex is a minimum.
If the leading coefficient is positive, the y-coordinate of the vertex is a minimum. If the leading coefficient is negative, the y-coordinate of the vertex is a maximum.
Step-by-step explanation:
During a sale, a store offered a 15% discount on a camera that originally sold for $690. After the sale, the discounted price of the camera was marked up by 15%. What was the price of the camera after the markup? Round to the nearest cent.
Answers
Answer:674.475
Step-by-step explanation:
(690)(0.15)= 103.5
690-103.5= 586.5 (after first markdown)
(586.5)(0.15)= 87.975
586.5+87.975 (Final price after markup)
solve the log equation
Answers
Answer:
x = -5
Step-by-step explanation:
log5((5-3x)/((7+x)^2))=1
(5-3x)/(7+x)^2 = 5
5-3x = 5x^2+70x+245
5x^2+73x+240=0
x= -5, x= -48/5
-48/5 is extraneous
x = -5
a prisms base has a perimeter of 12cm and a height of 2 cm. the area of the base was 5cm. what is the surface area of the prism.
Answers
==============================================================
Explanation:
For any prism, there are two congruent bases opposite one another. In other words, the bases are identical polygons with the same area. Each base is 5 square cm. So far, that accounts for 5+5 = 10 square cm of surface area. Let A = 10 as we'll use it later.
The perimeter is 12 cm and the height is 2 cm. It turns out that the lateral surface area is found by multiplying the two items. This is because the perimeter is made up of the lengths of the sides of the base, which when multiplied by the height, will give the area of each rectangular side panel.
So the lateral surface area is 12*2 = 24 sq cm. Let B = 24.
Overall, the total surface area is A+B = 10+24 = 34 square cm
- z > 8 equivalent inequality
Answers
Answer: z < -8
Step-by-step explanation:
Since z is negative, divide both sides by -1, which leaves you with z > -8.
Multiplying or dividing an inequality by a negative number flips the sign, thus the answer is z < 8.
Correct me if I am incorrect.
James is at the JL Long Run. He has exactly $32
and will purchase a shirt for $12. What percent of
his money will James spend on the shirt?
Answers
Part/whole= x/100
Let x= percentage of
money
12/32= x/100
1200/32= 37.5%
-3 (-3 - n) - 4 = 3n + 5
Answers
[tex]-3 (-3 - n) - 4 = 3n + 5\\\\\implies 9+3n -4 = 3n+5\\\\\implies 5 +3n = 3n+5\\\\\text{The equation is true for all values of n.}[/tex]
A birthday cake was cut into equal pieces, and 10 pieces were eaten. The
fraction below shows how much cake was left over. According to the fraction,
into how many pieces was the cake cut?
1
11
A. 1
B. 10
C. 21
D. 11
Answers
assuming the fraction is 1/11, the denominator shows how many parts the WHOLE was sliced into, namely 11 parts.
130 is what percent of 70?
Answers
Answer:
91%
Step-by-step explanation:
hopes this helps
Answer:
185.71%
Step-by-step explanation:
130 / 70 = 1.857142857
(1.857142857)(100) = 185.71%
Find the measure of angle m
Answers
Let’s call the missing angle x
60 + 84 + x = 180
144 + x = 180
X= 36
Hope this helps!
Brainliest is much appreciated!
Schedule of Cash Payments
Shakti Power Inc. was organized on February 28. Projected selling and administrative expenses for each of the first three months of operations are as follows:
March
$68,000
April
77,000
May
88,000
Depreciation, insurance, and property taxes represent $5,000 of the estimated monthly expenses. The annual insurance premium was paid on February 28, and property taxes for the year will be paid in Online file. Open the spreadsheet, perform the required analysis, and input your answers in the question below.m
Answers
dAnswer:
fffff
Step-by-step explanation:ff m
PLEASE HELP ME THIS IS THE 5TH TIME I HAVE HAD TO POST THIS AND GIVING BRAINLIST TO FIRST ANSWER
B.
C.
D.
Answers
Answer:
C.
Step-by-step explanation:
Which best describes reduced fractions that will always terminate?
A.
reduced fractions with denominators that are factors of only 5
B.
reduced fractions with denominators that are factors of 2 or 5
C.
reduced fractions with denominators that are factors of only 5 or 7
D.
reduced fractions with denominators that are factors of only 2 or 3
Answers
Answer:a
Step-by-step explanation:
Reduced fractions with denominators that are factors of 2 or 5. Therefore, the correct answer is option B.
Terminating decimals are integers with a definite or finite number of digits following the decimal point. Like fractions, decimal numbers are used to represent a portion of a whole. This course will concentrate on the type of decimal numbers known as terminating decimal numbers. The word 'terminate' means to put a stop to something. In decimal terms, it is a number that comes to an end.
Here are a few tips to assist you identify a terminating decimal number.
A non-rational number is never an ending decimal number.If the denominator of a simplified rational number can be expressed in the manner [tex]2^p5^q[/tex] or [tex]2^p[/tex] or [tex]5^q[/tex], where p, q N, then the number has a terminating decimal expansion.After the decimal point, a terminating decimal number always has a finite number of digits.Therefore, the correct answer is option B.
Learn more about the terminating fraction here:
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the price of an article is Marked 25% above the cost price .if it is solid the profit of Rs.500 after allowing 15% discount .what will be it's selling price
Answers
Answer:
Rs 8500
Step-by-step explanation:
For a cost price of c, the marked price is ...
marked = c +25%·c = 1.25c
After the 15% discount, the sale price will be ...
s = marked -15%·marked = 0.85·marked = (0.85)(1.25c) = 1.0625c
The profit will be the difference between the sale price s and the cost c:
p = s -c
500 = (1.0625c) -c = 0.0625c
Then the cost is ...
500/0.0625 = c = 8000
and the sale price is ...
s = c +p = 8000 +500 = 8500 . . . rupees
The selling price will be Rs 8500.
Help help help math math math
Answers
Answer:
yes this right cuz ye or nah?
Step-by-step explanation:
yes cuz 0 1 2 3 4 5 6 7 8 9 are the numbers
Answer: [?] is 6
Step-by-step explanation:
x=5
so, 2x=10
10-4 is 6
how many 5 letter code words can be formed from the letters of the word MATRICES
Answers
113
Hope this helped you- have a good day bro cya)
What is the greatest common factor shared by 40 and 20?
Answer here
SUBMIT
Answers
Answer:
20
Step-by-step explanation:
factors of 20 = 1 2 4 5 10 20
factors of 40 = 1 2 4 5 8 20 10
therefore 20 is the greatest common
1. Divide
(7x2 - 13x+4) - (x-1
)
Answers
Answer:7 x 2 − 14 x + 5
Step-by-step explanation:
1 In general, given a{x}^{2}+bx+cax
2
+bx+c, the factored form is:
a(x-\frac{-b+\sqrt{{b}^{2}-4ac}}{2a})(x-\frac{-b-\sqrt{{b}^{2}-4ac}}{2a})
a(x−
2a
−b+
b
2
−4ac
)(x−
2a
−b−
b
2
−4ac
)
2 In this case, a=7a=7, b=-14b=−14 and c=5c=5.
7(x-\frac{14+\sqrt{{(-14)}^{2}-4\times 7\times 5}}{2\times 7})(x-\frac{14-\sqrt{{(-14)}^{2}-4\times 7\times 5}}{2\times 7})
7(x−
2×7
14+
(−14)
2
−4×7×5
)(x−
2×7
14−
(−14)
2
−4×7×5
)
3 Simplify.
7(x-\frac{14+2\sqrt{14}}{14})(x-\frac{14-2\sqrt{14}}{14})
7(x−
14
14+2
14
)(x−
14
14−2
14
)
4 Factor out the common term 22.
7(x-\frac{2(7+\sqrt{14})}{14})(x-\frac{14-2\sqrt{14}}{14})
7(x−
14
2(7+
14
)
)(x−
14
14−2
14
)
5 Simplify \frac{2(7+\sqrt{14})}{14}
14
2(7+
14
)
to \frac{7+\sqrt{14}}{7}
7
7+
14
.
7(x-\frac{7+\sqrt{14}}{7})(x-\frac{14-2\sqrt{14}}{14})
7(x−
7
7+
14
)(x−
14
14−2
14
)
6 Simplify \frac{7+\sqrt{14}}{7}
7
7+
14
to 1+\frac{\sqrt{14}}{7}1+
7
14
.
7(x-(1+\frac{\sqrt{14}}{7}))(x-\frac{14-2\sqrt{14}}{14})
7(x−(1+
7
14
))(x−
14
14−2
14
)
7 Remove parentheses.
7(x-1-\frac{\sqrt{14}}{7})(x-\frac{14-2\sqrt{14}}{14})
7(x−1−
7
14
)(x−
14
14−2
14
)
8 Factor out the common term 22.
7(x-1-\frac{\sqrt{14}}{7})(x-\frac{2(7-\sqrt{14})}{14})
7(x−1−
7
14
)(x−
14
2(7−
14
)
)
9 Simplify \frac{2(7-\sqrt{14})}{14}
14
2(7−
14
)
to \frac{7-\sqrt{14}}{7}
7
7−
14
.
7(x-1-\frac{\sqrt{14}}{7})(x-\frac{7-\sqrt{14}}{7})
7(x−1−
7
14
)(x−
7
7−
14
)
10 Simplify \frac{7-\sqrt{14}}{7}
7 7− 14 to 1-\frac{\sqrt{14}}{7}1− 7 14
7(x-1-\frac{\sqrt{14}}{7})(x-(1-\frac{\sqrt{14}}{7}))
7(x−1− 7 /14 )(x−(1− 7 14 )) 11 Remove parentheses.
7(x-1-\frac{\sqrt{14}}{7})(x-1+\frac{\sqrt{14}}{7})
7(x−1− 7/ 14 .7(x−1+ 7 14 )
Helppppp pleaseee????
Answers
Answer:
Lower quartile 3, median 5, Upper quartile 7
Step-by-step explanation:
First divide the data in half 1 3 4 and 6 7 7
The median is the middle between 4 and 6, so it is 5.
The lower quartile is the median in the lower half, 3
The upper quartile is the median in the upper half, 7
If I have a 1/4 chance of winning a bet, but lose it 40 times in a row, what percentage chance is that?
Answers
The factor that most heavily influences your credit score is
A. length of credit history
B. types of credit
C. amount owed
D. payment history
Answers
Answer:
D.payment history
Step-by-step explanation:
Help
Geometry 1
Find z
Answers
Answer:
8
Step-by-step explanation:
The triangles are the same, except one is dilated.
So the hypotenuse of one is 5, and the other is 10. The triangle is dilated to double the other's size. so 4*2 = 8
I have no idea what i just wrote, but the answer is correct.
if EF = 8x + 16, FG = 60, and eg = 156, find the value of x
Answers
Answer:
10
Step-by-step explanation:
8x+16+60=156
8x+76=156
8x=80
x=10
Can someone pls answer them all?