Find the minimum distance from the parabola x-y^2=0
to the point (0,3).
Answers
Answer:
√5
Step-by-step explanation:
The distance from the given point to the curve can be found using the distance formula. The resulting expression can be minimized to find the minimum distance.
d = √((x2 -x1)² +(y2 -y1)²)
__
Point on the ParabolaA point on the parabola can be described by ...
x -y² = 0
x = y² . . . . . add y²
Then a point on this curve is ...
(y², y)
Distance to Given PointThe distance to it from (0, 3) is ...
d = √((0 -y²)² +(3 -y)²) = √(y⁴ +y² -6y +9)
Find the MinimumThe distance will be minimized when the derivative of the radical expression is zero:
d(y⁴ +y² -6y +9)/dy = 0 = 4y³ +2y -6
0 = 2y³ +y -3 . . . . . . . . remove a factor of 2
This will have a rational root in the set {±1, ±3}.
Trial and error shows that y=1 is the only real solution to this equation.
__
Then the minimum distance is ...
d = √(1⁴ +1² -6·1 +9) = √5
_____
Additional comment
The attached graph shows that a circle with radius √5 centered at (0, 3) will intersect the parabola at exactly one point. That confirms our solution.
Related Questions
A signal can be sent from one location to another by running different colored flags up a flagpole, one above the other. There are 15 different colored flags to choose from but only 8 flags will be flown. Find the number of different signals consisting of 8, if the first flag must be blue.
If the first flag is blue then the number of different signals consisting of 8 flags is ??
Answers
Using the permutation formula, it is found that there are 17,297,280 different signals consisting of 8 flags.
In this problem, the order in which the flags are visited is important, hence the permutation formula is used to solve this question.
What is the permutation formula?The number of possible permutations of x elements from a set of n elements is given by:
[tex]P_{(n,x)} = \frac{n!}{(n-x)!}[/tex]
The first flag is blue, then the remaining 7 are taken from a set of 14, hence:
[tex]P_{(14,7)} = \frac{14!}{7!} = 17,297,280[/tex]
There are 17,297,280 different signals consisting of 8 flags.
More can be learned about the permutation formula at https://brainly.com/question/25925367
Russell needs to fertilize the grass in his
back yard, shown below. In order to know
how much fertilizer to buy, he must know
the square footage of his yard.
If the entire yard is covered with grass,
how many square feet of grass does he
have?
< 60 feet->
36 feet
60 feet
36 feet
30 feet
Answers
Answer:
60 feet?
Step-by-step explanation:
The area covered with grass, in square feeet, is the area of the shape of the yard.
What is the Area of a Yard?The area of a yard can be calculated by determining the shape of the yard, and using the appropriate area formula of the shape to find the area of the yard.
Image of the yard is missing. However, assuming the yard is a rectangular shape with a dimension of 10 ft by 6 ft, therefore:
The square feet of grass Russell has = area of rectangle = (10)(6) = 60 ft²
In summary, the area covered with grass, in square feeet, is the area of the shape of the yard.
Learn more about area of yard on:
https://brainly.com/question/854971
Charlie is riding his bicycle. He rides 44.8 kilometers in 7 hours. What is his speed in kilometers per hour?
Answers
This is because it’s distance / time
Evaluate the expression when a = 6 and x= -5.
-a + 8x
Answers
Answer:
-46
Step-by-step explanation:
when a= 6 and ×=-5
-a + 8×= -6+8×-5
= -6+(-40)= -6-40= -46
jack had m problems to complete during his vacation. (a) how many problems did jack solve per day? (b) suppose jack was solving 15 problems per day. (c) How many problems were assigned for homework
Answers
Answer:
a) m problems, d days to complete.
m/d
b) m/15d
c)-if 15 was connected; 15d
if 15 WAS NOT connected, m problems
NEED HELP ASAP
In the diagram, m ZAFB = 78°
Which angle is complementary to ZAFB and what is its measure?
Answers
Answer:
Angle BFC is complimentary to AFB. Its measure is 12.
Step-by-step explanation:
Complementary angles add up to 90 degrees. When these two angles combine, it adds up to 90. 90-78 = 12. This angle's measure is 12.
True or false?
The greater a fractional part of a circle an angle takes up, the smaller it’s measurement will be.
Answers
This is the Answer :
true
You roll a 6-sided die two times.
What is the probability of rolling a 5 and then rolling a 3?
Write your answer as a fraction or whole number.
Answers
Answer:
1/36
Step-by-step explanation:
The chance of you rolling a 5 is 1/6
While the chance of you rolling a 3 is a 1/6
If you want both a 5 then a 3 then you multiply the fractions
1/6 * 1/6 = 1/36
the approximate z-score that corresponds to a right tail area of 0.29 is?
Answers
Answer:
0.55
Step-by-step explanation:
In this question we need to find the Z score says that the area under the standard normal curve to the right is 0.29. So here in this question I have drawn here the normal distribution curve. So at this point we need to calculate the z value And with the probability of 29%. So to find the value of Z says that probability of zero great Small, that is equal to 0.29. So I can write this left hand side as one minus probability of less than small. It's called a 0.29 probability of zero, less than or equal to zero will do 0.29 one minus .29 which is equal to 0.71. So here we know the value of probability And we need to find the value of zero and there are various methods to calculate that one is the using the normal distribution tables and then there is the um MS Excel should. So from the table you can find the area closest to 0.71. So here the flow chart for finding me value. Using normal distribution table is given. So the first thing is from this table of the standard normal distribution, look at the probability value. So as you can see from this this is the snapshot of the table we need to find the probability value. So We have got the value of 0.71. So this is the nearest value to that you need to, next second is move left until the first column is reached. So move left until the first column is rich. This is the first column. Move upward until the top row is rich. Note that value. So here as you can see it is 0.5 and here it is 0.05. The intersection of the Roman columns gives the area of the two day loves. So which is 0.5 Plus 0.05 is equal to zero 55. This is the value of Z. Or as you can use the um xxl shoot to calculate the value of Z. Here, I have given the flow chart for that. Also you can use this to calculate the value of Z. So probability of mhm Less than or equal to 0.55 Is equal to 0.71. This is the answer. 0.55 is the answer for the solution.
Eugene works a total of 45 hours per week at two jobs. If his total pay is $ 386.25 (before taxes), and Eugene worked 15 hours at Mudzoff Car Wash and 30 hours at Stuck-in-the-Mud offroad trails, and his hourly rate at Stuck-in-the-Mud is $ 0.25 less than his hourly rate at Mudzoff, find Eugene's pay per hour at each job.
Answers
Help answer question
Answers
Answer:
Yes and yes
Step-by-step explanation:
Solve the system of equations by elimination. Show your work. i’ll give brainliest
Answers
Answer:
x = 5
y = 4
Step-by-step explanation:
multiply the second equation by -1 and add the first equation to eliminate "x"
[tex]4x+6y=44\\-4x-2y=-28[/tex]
_____________
[tex]4y=16[/tex]
[tex]y=16/4 =4[/tex]
Replace "y" in the first equation:
[tex]4x+6(4)=44[/tex]
[tex]4x+24=44[/tex]
[tex]4x=44-24[/tex]
[tex]x=20/4=5[/tex]
Hope this helps
Answer:
x = 5, y = 4.
Step-by-step explanation:
4x + 6y = 44 (A)
4x + 2y = 28 (B)
Subtract equations: (A) - (B).
0 + 4y = 16
y = 16/4
y = 4.
Now plug y = 4 into equation A:
4x + 6(4) = 44
4x = 44 - 24
4x = 20
x = 5.
Now check if these roots are correct by plugging them into equation B:
4x + 2y = 28
4(5) + 2(4) = 28 - check OK.
0.3x =2.1 how would i solve this
Answers
[tex]0.3x = 2.1\\\\\implies 10\times 0.3x = 10 \times 2.1~~~~;[\text{Multiply both sides by 10}]\\\\\implies 3x = 21\\\\\implies x = \dfrac{21}3 = 7[/tex]
Abigail volunteers as a gift wrapper at a children's bookstore during the holiday season. She can gift wrap a book in 3.5 minutes. Let t be the total number of books she wraps, and let m be the total minutes she spends wrapping. The equation m=3.5t represents this situation. Graph the equation.
Answers
t is the number of books she wraps
So 3.5t is the total number of minutes she spends wrapping or m
For example on the graph
If she wraps 6 books then she spends a total of 21 minutes wrapping books because 3.5(6) is 21.
Find the slope of the line passing through (3,-4) and (3,8)
Answers
To find the slope ⇒ we must know the formula
Formula = [tex]\frac{y2-y1}{x2-x1}[/tex]
(x1, y1) ⇒ (3, -4)(x2, y2) ⇒ (3,8)Now let's solve and plug the known variables
Slope = [tex]\frac{8-(-4)}{3-3} =\frac{12}{0}[/tex]
Nothing can be divided by zero
⇒ in this case, the slope is undefined
*interesting fact: the line is vertical
Hope that helps!
Express with fractional exponents instead of radicals.
6√x² y³
Answers
Answer:
using of fractional exponents give us the value 6(x^2y^3)^1/2 or 6xy^3/2.
find the mean, variance, and standard deviation of sampling distribution of the sample population p=.2 and n=107
Answers
Answer:
2923 is your p is equal to 2 and n
Determine the total length of the major and minor axes for the ellipse 25x^2+y^2=25
Will give brainliest
Answers
Answer:
Step by step Solution :-
25X^2 + Y^2 = 25
A) Finding X value :-
1. Subtract Y^2 from both sides:
25X^2 = 25 - Y^2
2. Divide both sides by 25 :
( 25X^2 ) ÷ 25 = ( 25 - Y^2 ) ÷ 25
3. Dividing by 25 undo the multiplication by 25 :
X^2 = ( 25 - Y^2 ) ÷ 2
4. Divide ( 25 - Y^2 ) by 25 :
X^2 = ( - Y^2 ÷ 25 ) + 1
5. Take Square Root for both sides of equation ( before & after (=) ) :
X = √ ( 25 - Y^2 ) ÷ 5
X = - √ ( 25 - Y^2 ) ÷ 5
------------
Now that we knew what X value is, we'll figure out Y value too!
B) Finding Y value ( Finding Square Root ):-
Y^2 = 5√ ( 1 - X^2 )
1. Finding Square Root :
25X^2 + Y^2 = 25
2. Subtract 25X^2 value from both sides :
Y^2 = 25 - 25X^2
3. Take square root for both sides of equation :
Y = 5√ ( 1 - X^2 )
Y = - 5√ ( 1 - X^2 )
I also need this one thank you
Answers
When the y-value of the f like is zero the y-value of the g line is -2
Leila wanted to order her IFTAR meal from La Gondola, Al Khobar. The menu stated that their pasta is a blend of wheat and corn. La Gondola does not disclose the percentage of each ingredient in the blend but we know that the wheat in the blend contains 5% protein, and the corn in the blend contains 10% protein. Overall, each 57 gram serving of pasta contains 4 grams of protein.
Leila told her sister that there was more wheat than corn in the pasta. Use multiple representations to justify if this is a true statement. (You may use DESMOS for graphing. You must also put in the algebraic solution and a table.)
Answers
Step-by-step explanation:
Let the amount of wheat is x and amount of corn is y.
The total amount of pasta is
x + y = 57Amount of protein in same pasta is
5% of x + 10% of y = 4or
0.05x + 0.1y = 4The graphical solution is attached
x = 34, y = 23It is easy to solve the system by substitution
y = 57 - x0.05x + 0.1(57 - x) = 40.05x + 5.7 - 0.1x = 40.1x - 0.05x = 5.7 - 40.05x = 1.7x = 1.7/0.05x = 34Then the value of y is
y = 57 - 34 = 23As we see x > y, so Leila is right
The above problem is solved using Multiple Representations. Multiple representations are used to achieve a deeper comprehension of concepts related to the same operation.
How do we evaluate the veracity of Leila's assertion?We can arrive at whether the statement is true or false by solving for the value of Y using the graphical method. Where Y is the amount of wheat and X is the amount of corn.
Our function is given as follows:
X + Y= 57. ..........1
Recall that the total amount of pasta is 57 grams
Recall as well that the total amount of protein in the pasta is given as:
0.05x + 0.1y= 4grams.......2
By inputting equations 1 and 2 into the Desmos Graph, we have x to be equal to = 34, and y = 23. (please see the attached image).
Recall that Leila's assertion was that there is more corn in the Pasta. Since x is the amount of corn, then Leila's assertion is True that: x>y.
The algebraic solution is arrived at using substitution.
Rewriting equation (1), we have
y = 57 - x .......................(3)
Let us substitute y into equation (2) above. That gives us:
0.05x + 0.1(57 - x) = 4.........................(4)
Expanding the brackets, we obtain
0.05x + 5.7 - 0.1x = 4
Collecting like terms, we can rewrite the quation as:
0.1x - 0.05x = 5.7 - 4
0.05x = 1.7
Rewriting the equation such that it is subject to x, we have
x = 1.7/0.05
x = 34
If from the above, x = 34, inputting that into equation (3) above, we have
y = 57 - 34; Therefore,
y = 23
Learn more about Multiple Representation at:
https://brainly.com/question/24708207
Which of the following may fall outside a triangle?
A. incenter and circumcenter
B. orthocenter and circumcenter
C. circumcenter and centroid
0 D. centroid and incenter
Answers
Answer: B
Step-by-step explanation:
A car rental agency rent compact, midsize, and luxury cars. Its goal is to purchase 48 cars for a total of $932,000 and to earn a daily rental of $ 1,265 from all the cars. The compact cars cost $13,000 each earn $ 20 per day in rental, the midsize cars cost $ 25,000 each earn $ 27 per day, and the luxury cars cost $ 29,000 each and earn $ 45 per day. Your task will be to find the number of each type of car the agency should purchase to meet its goal.
Answers
Answer:
25 compact15 midsize8 luxuryStep-by-step explanation:
The set of relationships can be formulated as three equations in three unknowns. These can be written as an augmented matrix and solved using a calculator.
Let x, y, z represent the numbers of compact, midsize, and luxury cars, respectively. Then the relations are ...
x + y + z = 48 . . . . . . total number of cars purchased
13x +25y +39z = 932 . . . . . total cost in thousands
20x +27y +45z = 1265 . . . . daily rental revenue
The augmented matrix of coefficients looks like ...
[tex]\left[\begin{array}{ccc|c}1&1&1&48\\13&25&39&932\\20&27&45&1265\end{array}\right][/tex]
And its solution is ...
(x, y, z) = (25, 15, 8)
The agency should purchase 25 compacts, 15 midsize, and 8 luxury cars.
A large car dealership claims that 47% of its customers are looking to buy a sport utility vehicle (SUV). A random sample of 61 customers is surveyed. What is the probability that less than 40% of the sample are looking to buy an SUV?
Answers
Using the normal distribution and the central limit theorem, it is found that the probability is of 0.1368 = 13.68%.
Normal Probability DistributionIn a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
It measures how many standard deviations the measure is from the mean. After finding the z-score, we look at the z-score table and find the p-value associated with this z-score, which is the percentile of X.By the Central Limit Theorem, for a proportion p in a sample of size n, the sampling distribution of sample proportion is approximately normal with mean [tex]\mu = p[/tex] and standard deviation [tex]s = \sqrt{\frac{p(1 - p)}{n}}[/tex], as long as [tex]np \geq 10[/tex] and [tex]n(1 - p) \geq 10[/tex].In this problem:
47% of its customers are looking to buy a sport utility vehicle (SUV), hence p = 0.47.A sample of 61 customers is taken, hence n = 61.The mean and the standard error are given by:
[tex]\mu = p = 0.47[/tex]
[tex]s = \sqrt{\frac{p(1 - p)}{n}} = \sqrt{\frac{0.47(0.53)}{61}} = 0.0639[/tex]
The probability that less than 40% of the sample are looking to buy an SUV is the p-value of Z when X = 0.4, hence:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{0.4 - 0.47}{0.0639}[/tex]
Z = -1.095
Z = -1.095 has a p-value of 0.1368.
0.1368 = 13.68% probability that less than 40% of the sample are looking to buy an SUV.
To learn more about the normal distribution and the central limit theorem, you can check https://brainly.com/question/24663213
please help! math
(3/7) (-2/5 x 9/11)
Answers
Answer:
-54/385
Step-by-step explanation:
please help me.. no links pls
Answers
Answer:27
Step-by-step explanation:
Its pretty simple. Perimeter is the addition of all the sides. Add 4+9+8+6 to get 27.
Astronomers measure large distances in light-years. One light-year is the distance that light can travel in one year, or approximately 5,880,000,000,000 miles. Suppose a star is 13.6 light-years from Earth. In scientific notation, how many miles away is it?
a)5.88 × 1012 miles
b)7.9968 × 1013 miles
c)5.88 × 1013 miles
d)1.36 × 1012 miles
Answers
Answer:
b) 7.9968 × 1013 miles
Step-by-step explanation:
So one light-year equals 588 × 10^10
13.6 light-years equals 13.6 × 588 × 10^10 = 79968 × 10^9 = 7.9968 × 1013 miles
i need help with this i will mark BRAINLIEST and give alot of points
Answers
Answer:
Below
Step-by-step explanation:
Diameter = 2r (r is radius) so the diameter is 40 inches
Circumference= 2pi r= 40pi or 125.663
Area= pi r^2= pi(20)^2= 400 pi pr 1256.637
Answer:
Diameter: 40 inches
Circumference: 40π, or ~125.66 inches
Area: 400π, or ~1256.64 inches
Step-by-step explanation:
Diameter is twice the radius, so 20×2 = 40 inches.
Circumference formula is C = 2πr, so plugging everything in, C = 2π×20,
and simplify, C = 40π, or C ≈ 125.66 inches.
Area formula is A = πr², so plugging everything in, A = π20², and then simplify, A = 40π, or A ≈ 1256.64 inches.
The function f (x) is given by the set of ordered pairs 1,0 (-10,2), (0,6) (3,17) (-2,-1) which equation is true
f(-10)=1
f(2)=-10
f(0)=6
f(1)=-10
please show work!!
Answers
Because the number in () is the x value which is 0 and the answer, 6 ,is the y-value.
The format is f(x) = y
Only one that matches the given points is (0,6)
Answer:
f(0)=6
Step-by-step explanation:
It should be the third one because it is the only one that has the x-value in the parentheses and equals the y-value. (I think please someone back me up)
In a triangle ABC, a = 13. b = 11 and c = 15. Solve the triangle.
Answers
Answer:
169 + 121 = 225
Step-by-step explanation:
It is not a right triangle
A squared + b square should equal c squared.
169 + 121 = 290
Kang Tae Moo thinks of a number. He adds 13 to the number. He multiples the result by 3. This gives the same result as if he multiplied the number by 9 and then subtracted 3. What number is Kang Tae Moo thinking of?
Answers
Answer:
7
Step-by-step explanation:
We can setup this equation as x representing his number. (x+13) * 3 = 9x -3.
Now, we just need to solve for x.
3(x+13)=9x-3
x+13=3x-1
14=2x
x=7