Find the point on the curve y = √ 2 x + 4 which is closest to the point ( 3 , 0 ) .

Answers

Answer 1

Here you'll need differential calculus.

The distance between (3,0) and (x, sqrt(2)*x + 4) is given by the distance formula:

distance: sqrt [ (3+x)^2 + (sqrt(2)*x + 4)^2 ]

Differentiate this, and then set the resulting derivative = to 0. Solve for x. Test your results to ensure that the distance d is actually the SMALLEST, given the root(s) x that you've found.

Write the coordinates of this point on the curve as ( x, f(x) ).

Related Questions

What happens to people who don’t know toothpaste from putty?

Answers

Their window falls out.

Final answer:

Toothpaste is designed specifically for oral hygiene and contains abrasives and fluoride, unlike putty. Recognizing and using toothpaste instead of incorrect substances like putty is crucial for maintaining dental health.

Explanation:

When a person does not know how to distinguish between toothpaste and putty, they may lack basic knowledge about oral hygiene and the purpose of toothpaste. Toothpaste is formulated to clean and maintain the health of teeth; it usually contains abrasives that scrub the teeth and fluoride that helps prevent cavities.

It is essential to use toothpaste rather than any other substance, such as putty, which does not provide the same benefits and can be harmful if ingested. Learning to recognize and use toothpaste correctly is part of basic health awareness and contributes to overall wellbeing.

Please help I really need an answer fast!!!
A, toy company manufactures arcade games. They are marketing a new pinball machine to children. It is similar in size to the adult version of the same game.
Adult pinball machine GAME with base ME measuring 35 inches and sides measuring 56 inches. Child pinball machine G prime A prime M prime E prime with base M prime E prime measuring 14 inches

If the perimeter of the adult pinball machine is 167 inches, what is the length, in inches of Segment line G prime A prime? Type the numeric answer only in the box below.

Answers

The answer is 8.

first of all you need to find the missing length on the adult version.
so the work would be:
-add up all the known sides of adult so
(56+56+35)=147

-then take the total perimeter and subtract so
167-147=20

-then you need to compare the two known sides of both the adult and kids version. so that would be the bottom line EM.
They are 35 and 14 so divide
35/14=2.5

Now you know the dilation so you can figure out the missing side GA on the childs by taking the missing side from the adult dividing by the dilation 2.5 to get the answer so
20/2.5= 8

the answer is 8.

I got this correct on the quiz.

g(x)=4x^2-3x+7
find g(3)

Answers

As g(x) is 4x²-3x+7 and we need to find g(3) it means in the given polynomial we have to replace the variable X with 3
So here You go,
4(3²) -3(3)+7 i.e. __________34
HOPE THIS HELPS

G(x) = 4x^2 - 3x + 7
find g(3)

Answer:

Plug it in:

g(3) = 4(3)^2 - 3(3) + 7

g = 4(9) - 9 + 7

simplify:

g = 36 - 9 + 7

g = 34 <<<< the answer to this.

Hope this helped!

~Shane

[(7−5)÷12]×2
help quick

Answers

your answer would be 12

The first step for solving this expression is to subtract the numbers in the first set of parenthesis.
(2 ÷ 12) × 2
Now write the division as a fraction.
[tex] \frac{2}{12} [/tex] × 2
Reduce the fraction with 2.
[tex] \frac{1}{6} [/tex] × 2
Finally,, reduce the fraction with 2 one last time.
[tex] \frac{1}{3} [/tex]
This means that the correct answer to your question is [tex] \frac{1}{3} [/tex].
Let me know if you have any further questions.
:)

Given the arithmetic sequence an = 3 + 2(n − 1), what is the domain for n?

A. All integers where n ≥ 0
B. All real numbers
C. All integers where n ≤ 1
D. All integers where n ≥ 1

Answers

[tex]a_n=3+2(n-1)\\\\n\in\mathbb{N^+}\\\\Answer:\ D.\text{All integers where}\ n\geq1[/tex]

All numbers greater or equal to 1

You roll two 6-sided dice. what is the probability that both dice have even numbers?

Answers

Each dice has 3 even numbers.
2 4 6 and 2 4 6. Duplicates are allowed.

There are 36 combinations

The number of successes is 3 * 3 = 9

The probability is 9/36 = 1/4.

One painter can paint a house in 12 hours another can paint the house in 8 hours, how long will it take for both of them to paint 1 house

Answers

4.8 hours.

You can get this by setting up the equation:
x/8 + x/12 = 1
Where x is equal to the amount of hours spent working. In this equation x/4 would be the first painter. In 8 hours he would paint on room. x/12 would be the second painter. When you add them together using common denominators, you can find x.

Which graph shows a polynomial function of an even degree?

Answers

The definition of a even function is:
A function is even if, for each x in the domain of f, f (- x) = f (x).
The even functions have reflective symmetry through the y-axis.
We have then that the graph that meets this definition is:
graph 1 (from left to right)
Answer:
graph 1 (from left to right)

Of course the answer would be the first option. If you observe, it is the only graph having the same endpoints pointing downward which means positive and even. If it's an odd degree, the endpoints of the graph will be different- either up-down or down-up. So the first option is the ckrrect answer. Just take note that the graph will be a hint that can tell you if it has an even or odd degree.

I can't figure out how to solve this

Answers

Because both lines AT and AN are tangents, they are equal to each other.

Because angle ATN is 70 degrees, then angle ANT is also 70 degrees

The 3 inside angles of a triangle = 180 degrees,
so angle A would = 180 - 70 - 70
Angle A = 180 -70-70 = 40 degrees

Natasha wants to use the fermi process to estimate the number of pennies that would fill a toy chest. as part of the process, she needs to estimate the volume of the toy chest. she figures the toy chest is about 50 in. long, 20 in. wide, and 20 in. tall. which estimate best approximates the volume of the toy chest? 2×103 in³ 2×104 in³ 2×105 in³ 2×106 in³

Answers

The answer is B 2 X 10^4 in^3

Answer:

Dimension of toy chest

Length =50 inches

Width = 20 inches

Height = 20 inches

Volume of toy chest = Length × Breadth ×Height

= 50 ×20 × 20

= 1000 × 20

= 20,000 inches cube.

[tex]=2\times 10^4 inches ^3[/tex] appears best approximation.

Option B

The ratio of gold charms to silver charms is 1:3. Which statement does not describe the relationship?

Answers

If the ratio of gold to silver is 1:3, then for every gold charm, there are 3 silver charms. That is the opposite of the first choice, so the first choice does not describe the relationship, and is the correct answer.

Final answer:

The ratio of gold charms to silver charms is 1:3, with 1 representing the number of gold charms and 3 representing the number of silver charms. The statement that does not describe the relationship is the one that does not accurately represent this ratio.

Explanation:

The ratio of gold charms to silver charms is 1:3. In this ratio, the first number (1) represents the number of gold charms, and the second number (3) represents the number of silver charms. Therefore, the statement that does not describe the relationship is the one that does not accurately represent this ratio.

If two angles are both vertical and supplementary, can we determine the angles? If so, what are they?

Answers

we know that
if A and B are vertical angles
so
angle A is equal angle B
A=B

and
if A and B are supplementary angles
so
angle A +angle B is equal to 180 degrees
A+B=180°

therefore
A=B
A+A=180-----> 2A=180-----> A=90°

the answer is
the angles are 90 degrees

Answer:

Step-by-step explanation:

In afamily with 3 children, what is the probability that they have 2 boys and 1 girl

Answers

2/3 multiply by 1/3 which is 2/9.
everytime u look the word *and* just multiply the probability but if u see the word *or* then add the probability.

Linda has completed 24 deliveries so far this week. she needs to make 40 deliveries for the week. what percentage of her deliveries has linda completed?

Answers

Final answer:

Linda has completed 60% of her deliveries for the week.

Explanation:

Linda has completed 24 deliveries out of a total of 40 deliveries for the week. To find the percentage of deliveries Linda has completed, we can divide the number of completed deliveries by the total number of deliveries and multiply by 100.

Percent of deliveries completed = (Number of completed deliveries / Total number of deliveries) * 100

Percent of deliveries completed = (24/40) * 100 = 60%

How do you work with bidmas?

Answers

BIDMAS

1) Brackets
2) Indices
3) Division and Multiplication. Start on the left and work them out in the order that you find them
4) Addition and Subtraction. When only addition and subtraction are left in the sum work them out in the order you find them. starting from the left of the sum and working towards the right.

Steve buys 14 ounces of kiwis and 2 pounds of peaches.How many more ounces do the peaches weigh then the kiwis?

Answers

1 pound = 16 ounces

2 pounds x 16 ounces = 32 ounces for the peaches.

32 ounces - 14 ounces = 18

The peaches weigh 18 more ounces.

What are the approximate solutions of 4x^2 + 2x = 17, rounded to the nearest hundredth?

A: x ≈ −2.33 and x ≈ 1.83
B: x ≈ −1.83 and x ≈ 2.33
C: x ≈ −9.31 and x ≈ 7.31
D: No real solutions

Answers

4x^2 + 2x - 17 = 0

Answer is B

x = -1.826 x = 2.326

Rounded to the nearest thousandth x = -1.83 and x = 2.33

the answer to this question is the selection b

What is the GCF of the terms in 4a^4+6a^2?

Answers

The GCF means Greatest common factor.
In this case it would be the biggest number that goes into 4 and 6 which is 2.

The first half of you answer is 2

The second half means the most amount of a’s that can go into the biggest number of a’s (doesn’t multiply)
Example:
a^4 means there are 4 a’s multiplying
a^2 means there are 2 a’s multiplying
a*a*a*a
a*a
Going back to the most amount a’s going into the biggest number of a’s means that in this equation the most amount of a’s that go into the biggest number of a’s is a^2.

Your answer is 2a^2

Final answer:

The GCF (Greatest Common Factor) of the terms in the algebraic expression 4a^4+6a^2 is found by observing the numerical coefficients (4 and 6) and the variables (a^4 and a^2). The GCF of 4 and 6 is 2, and the GCF of a^4 and a^2 is a^2, so the GCF of the terms in the expression is 2a^2.

Explanation:

The GCF (Greatest Common Factor) of two or more terms is the greatest number that divides each of the terms without any remainder. The GCF of the terms in the algebraic expression 4a^4+6a^2 can be found by observing the numerical coefficients and the variables.

1. The numerical coefficients of the terms are 4 and 6. The GCF of 4 and 6 is 2.

2. The variables in the terms are a^4 and a^2. The GCF of a^4 and a^2 is a^2, because a^2 is the factor that appears in both terms to the smallest power.

By combining the GCF of the numerical coefficients with the GCF of the variables, we find that the GCF of the terms in the algebraic expression 4a^4+6a^2 is 2a^2.

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Bob is opening a store that will sell various kinds of fish and plants for aquariums. To start, he is organizing the fish and plants in the aquariums at the front of the store. He has 24 fish, 18 plants, and 5 fish tanks for the front of the store. He wants to divide the fish among the fish tanks as evenly as possible. He wants to put the plants only in the outer four fish tanks.

Answers

4 tanks will have four meanwhile 1 tank will have 5. also there will be 3 plants in the tanks meanwhile only 1 tank will have 4. this is what i got by reading your problem, i couldnt find anything about it on the internet but i hope this helps.

Answer:

4 tanks will have four meanwhile 1 tank will have 5. also there will be 3 plants in the tanks meanwhile only 1 tank will have 4.

Step-by-step explanation:

im bad at everything so its likly wrong

From 1992 through 2007, the purchasing power of a dollar decreased by about 3.5% per a year. Using 1992, as the base for comparison, what was the purchasing power of a dollar in 2007? Formula: y=C(1−r)t

$0.48
$0.57
$0.44
$0,59

Answers

Answer: fourth option $0.59

Explanation:

1) Given formula: y=C(1−r)^t

I will change t for x just due to editor limitations: y = C(1-r)ˣ

2) In that:

C =$1,
r = 3.5% = 3.5/100 = 0.035
x = t = 2007 - 1992 = 15

3) Compute

y = $1 (1 - 0.035)¹⁵ = $1 (0.965)¹⁵ = $0.586 ≈ $0.59

Answer: $0.59

Which statement is true about the circumference of a circle?
The circumference is the measurement around the circle.
The circumference is the measurement of the radius.
The circumference is the measurement of the diameter.
The circumference is double the radius.

Answers

A.) the circumference is the measurement around the circle

[tex]\boxed{\large{\bold{\textbf{\textsf{{\color{blue}{Answer}}}}}}:)}[/tex]

circumference of a circle:-The circumference is the measurement around the circle.

What is the constant of proportionality in the equation 6y=3x6y=3x6, y, equals, 3, x?

Answers

For this case we have the following equation:
6y = 3x
From here, we must clear the value of y.
We have then:
y = (3/6) x
Rewriting we have:
y = (1/2) x
The proportionality constant is:
k = 1/2
Answer:
the constant of proportionality in the equation 6y = 3x is:
1/2

Which phrase describes the algebraic expression x/15?
the quotient of a number and 15

the product of a number and 15

the sum of a number and 15

15 divided by a number

Answers

The quotient of a number and 15

This circle and x + 2y = 12 create a system of equations. Find all solutions, if any, of the resulting system. There are no solutions (0, 6) and (12, 0) (0, 5) and (12, 0) (0, 5) and (5, 0)

Answers

the answer is (0,5) and (12,0)

Answer:

C. (0.5)&(12.0)

Step-by-step explanation:

If a rectangle measures 8 feet on the short side and 9.8 feet on the long side what is the area of the rectangle in square feet

Answers

To solve this, we are going to use the formula for the area of a rectangle: [tex]A=wl[/tex]
where
[tex]A[/tex] is the area of the rectangle
[tex]w[/tex] is the width of the rectangle
[tex]l[/tex] is the length of the rectangle

Since the short side of a rectangle is the width of the rectangle, [tex]w=8ft[/tex]. Similarly, the long side a rectangle is the length of the rectangle, so [tex]l=9.8ft[/tex]. Now we can replace those values in our formula to find [tex]A[/tex]:
[tex]A=wl[/tex]
[tex]A=(8ft)(9.8ft)[/tex]
[tex]A=78.4ft^2[/tex]

We can conclude that the area of our rectangle is 78.4 square feet.

maria's school is selling tickets to a choral performance. on the first day of ticket sales the school sold 4 adult tickets and 1 child ticket for a total of $47. the school took in $58 on the second day by selling 5 adult tickets and 1 child ticket. what is the price each of one adult ticket and one child ticket?

Answers

For this case, the first thing we must do is define variables.
We have then:
x = price of adult tickets
y = price of child tickets
We write the system of equations:
4x + y = 47
5x + y = 58
Solving the system of equations we have:
x = 11
y = 3
Answer:
11 $ price of adult tickets
3 $ price of child tickets

Which of the following is an example of a function?

{(-1, 0), (-1, 3), (3, 9), (5, 10}

{(1, 3), (2, 5), (3, 8), (4, 10)}

{(4, 6), (5, 9), (4, 7)}

{(0, 2), (0, 3), (1, 5), (4, 5)}

Answers

A. Not a function since we have the points (-1,0) and (-1,3). The x value repeats while the y values are different. Plugging in x = -1 leads to multiple outputs, which shows we don't have a function. To get a better visual, you can plot the points. You'll see that the points form a vertical line. Therefore, this graph fails the vertical line test.

B. This is a function. All of the x values are different. The points, when graphed, pass the vertical line test. In other words, its impossible to draw a vertical line through any two points on the graph. Any x input here leads to exactly one y output.

C. This is not a function. Like choice A, we have repeated x values. In this case we have (4,6) and (4,7). The x value x = 4 repeats itself leading to multiple outputs y = 6 and y = 7

D. This is also not a function. The x value x = 0 repeats itself. The graph fails the vertical line test.

--------------------------------

Answer: Choice B

One hundred employees of a company are asked how they get to work and whether they work full time or part time. The table below shows the results. If one of the 100 employees is randomly selected, find the probability of getting someone who carpools or someone who works full time.

Full time Part time
Public Transportation 7 10
Bicycle 4 3
Drive alone 30 31
Carpool 6 9

Answers

The probability is 56/100, or 14/25 = 0.56.

These events are not mutually exclusive, meaning they can happen at the same time. This means we use

P(A or B) = P(A) + P(B) - P(A and B)

P(carpool or full time) = P(carpool) + P(full time) - P(carpool & full time)

There are 6+9=15 people out of 100 that carpool.
There are 7+4+30+6=47 people out of 100 that work full time.
There are 6 people out of 100 that carpool and work full time.

This gives us
15/100 + 47/100 - 6/100 = 56/100

Final answer:

The probability of getting someone who carpools or someone who works full time is 0.36.

Explanation:

To find the probability of getting someone who carpools or someone who works full time, we need to add the probabilities of the two events.

The probability of getting someone who carpools is 6/100 and the probability of getting someone who works full time is 30/100.

So the probability of either event happening is (6/100) + (30/100) = 36/100 = 0.36.

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The ratio of the height of a wall to the length of the wall is 2:3. the area of the wall is 384 sq. ft. what are the height and length of the wall?

Answers

The dimensions of the wall are found by defining variables based on the given ratio and area, resulting in a height of 16 ft and a length of 24 ft.

The question involves finding the dimensions of a wall given the ratio of its height to length and its total area. To solve this, let's denote the height of the wall as 2x and the length of the wall as 3x, based on the ratio 2:3. The area of the wall is the product of its height and length, which means (2x) ×(3x) = 384 sq. ft.

Now, by simplifying the equation, we get [tex]6x^2[/tex] = 384. Dividing both sides by 6 gives us [tex]x^2[/tex] = 64. Taking the square root of both sides, we find x = 8. Therefore, the height of the wall is 2x = 16 ft and the length of the wall is 3x = 24 ft.

Kyle was playing a new video game.He scored 128 points on his first game.He scored 305 points on his second game,and 490 on his third game.how many points did Kyle score?

Answers

First game= 128
Second game= 305
Third game= 490

Add the points per game together.

= 128 + 305 + 490
= 923 points

ANSWER: He scored 923 points during the three games.

Hope this helps! :)

Kyle scored a total of 923 points after playing all the three games.

What is addition ?

Addition is defined as combining two or more number together.

Given is Kyle who is playing a new video game. He scored 128 points on his first game, 305 points on his second and 490 points on his third game

The total points scored by Kyle will be the sum of the individual points in each game. Therefore, adding each set of points, we get -

P[T] = 128 + 305 + 490 = 923 points.

Therefore, Kyle scored a total of 923 points after playing all the three games.

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