Which of the following is closest to the distance that the tip of the hand travels as it moves from
the 12 to the 3?

Answer:

First one true, second false, third true

Step-by-step explanation:

Question:

Find the point (,) on the curve [tex]y = \sqrt x[/tex] that is closest to the point (3,0).

[To do this, first find the distance function between (,) and (3,0) and minimize it.]

Answer:

[tex](x,y) = (\frac{5}{2},\frac{\sqrt{10}}{2}})[/tex]

Step-by-step explanation:

[tex]y = \sqrt x[/tex] can be represented as: [tex](x,y)[/tex]

Substitute [tex]\sqrt x[/tex] for [tex]y[/tex]

[tex](x,y) = (x,\sqrt x)[/tex]

So, next:

Calculate the distance between [tex](x,\sqrt x)[/tex] and [tex](3,0)[/tex]

Distance is calculated as:

[tex]d = \sqrt{(x_1-x_2)^2 + (y_1 - y_2)^2}[/tex]

So:

[tex]d = \sqrt{(x-3)^2 + (\sqrt x - 0)^2}[/tex]

[tex]d = \sqrt{(x-3)^2 + (\sqrt x)^2}[/tex]

Evaluate all exponents

[tex]d = \sqrt{x^2 - 6x +9 + x}[/tex]

Rewrite as:

[tex]d = \sqrt{x^2 + x- 6x +9 }[/tex]

[tex]d = \sqrt{x^2 - 5x +9 }[/tex]

Differentiate using chain rule:

Let

[tex]u = x^2 - 5x +9[/tex]

[tex]\frac{du}{dx} = 2x - 5[/tex]

So:

[tex]d = \sqrt u[/tex]

[tex]d = u^\frac{1}{2}[/tex]

[tex]\frac{dd}{du} = \frac{1}{2}u^{-\frac{1}{2}}[/tex]

Chain Rule:

[tex]d' = \frac{du}{dx} * \frac{dd}{du}[/tex]

[tex]d' = (2x-5) * \frac{1}{2}u^{-\frac{1}{2}}[/tex]

[tex]d' = (2x - 5) * \frac{1}{2u^{\frac{1}{2}}}[/tex]

[tex]d' = \frac{2x - 5}{2\sqrt u}[/tex]

Substitute: [tex]u = x^2 - 5x +9[/tex]

[tex]d' = \frac{2x - 5}{2\sqrt{x^2 - 5x + 9}}[/tex]

Next, is to minimize (by equating d' to 0)

[tex]\frac{2x - 5}{2\sqrt{x^2 - 5x + 9}} = 0[/tex]

Cross Multiply

[tex]2x - 5 = 0[/tex]

Solve for x

[tex]2x =5[/tex]

[tex]x = \frac{5}{2}[/tex]

Substitute [tex]x = \frac{5}{2}[/tex] in [tex]y = \sqrt x[/tex]

[tex]y = \sqrt{\frac{5}{2}}[/tex]

Split

[tex]y = \frac{\sqrt 5}{\sqrt 2}[/tex]

Rationalize

[tex]y = \frac{\sqrt 5}{\sqrt 2} * \frac{\sqrt 2}{\sqrt 2}[/tex]

[tex]y = \frac{\sqrt {10}}{\sqrt 4}[/tex]

[tex]y = \frac{\sqrt {10}}{2}[/tex]

Hence:

[tex](x,y) = (\frac{5}{2},\frac{\sqrt{10}}{2}})[/tex]

Answer:

9.549296

Step-by-step explanation:

30/pi = 9.549296 for diameter

Answer:

$17.29

Step-by-step explanation:

8% = 0.08

216.09(0.08) = 17.29

Answer:

What you did is correct!

Answer:

$25,377.11 or

$25,759.92

Step-by-step explanation:

hope that helps

Answer: y = 4

Step-by-step explanation:

Answer:

75 square feet

Step-by-step explanation:

Break this apart and turn it into a rectangle

You can the use 15 times 5 to find your answer

Answer:

378x³⁰²

Step-by-step explanation:

378x378x378x378x378x378x378x378x378

=378*x^378*x^378*x^378*x^378*x^378*x^378*x^378*x^378

=378*x3024

=378x³⁰²

Hope this helps

Answer:

9.95

Step-by-step explanation:

Answer:

9 19/20 = 9.95

Step-by-step explanation:

Answer:

24×36×5=4,320

4,320÷6=720

Answer:

I don't understand your question.

Answer:

12×5+45-36=60+9=69 is your answer

Answer:

12×5=60+45=105-36=69

Answer:

look at the answer below

Step-by-step explanation:

this is xy + 25 = 0 if you wanted it. hope it helps

Answer:

(Rational Functions Practice)

3. Graph the function. (1 point)

xy+25=0

Step-by-step explanation:

Graph B. is the correct answer

Answer:

1) b - correct statement: The interquartile range of the number of volunteers is 16

2) c - correct statement: About 50% of the students have between a 75 and a 90

Step-by-step explanation:

1B --> 66 - 50

2C --> About 50% of the students have between a 75 and a 90

Answer:

1200INCHES²

Step-by-step explanation:

the formula for the area of rectangle and rhombus is same so l*b will work....120*10=1200

Answer:

Step-by-step explanation:

Through is upholstering a rectangular ottoman that measures 21 cm x 18 cm x 15 cm. What will be the total square centimeters of fabric that Sue must use to cover all faces of the Ottoman

Answer:

the graph is the one with h(x)=2x-6

Step-by-step explanation:

it will hit the y-axis at (0,-6) and it will hit the x-axis at (3,0)

The graph of h(x)=p(x)-6 is shown below.

All the points (and only those points) which lie on the graph of the function satisfy its equation.

Thus, if a point lies on the graph of a function, then it must also satisfy the function.

We are given that;

p(x)=2x

Now,

To find the graph of h(x) = p(x) - 6, we need to use the concept of transformations of functions. A transformation is a change in the position, shape, or size of a function’s graph.

To graph h(x), we can start by graphing p(x) = 2x and then shifting it down by 6 units. The graph of p(x) is a straight line that passes through the origin and has a slope of 2. To shift it down by 6 units, we can subtract 6 from the y-coordinate of every point on the line. For example, the point (1, 2) on p(x) becomes (1, -4) on h(x).

The graph of h(x) is also a straight line that has the same slope as p(x), but has a y-intercept of -6. The equation of h(x) is y = 2x - 6.

Therefore, the graph of the function will be shown below.

Learn more about points lying on graph of a function here:

brainly.com/question/1979522

#SPJ2

Answer:

She can use any square object around her. Since squares are made up of right angles, any side she chooses can be used to compare the angle of the door. If the square corner fits perfectly, the angle is 90. If the square fits with space, obtuse. If the square doesn’t fit, acute

Step-by-step explanation:

Answer: 2

2x-7=11  X=9  set up the up the negative portion of solutions Set up the negative portion of the 2x - 7= - 11   x= -2  and then x = 9,-2

Step-by-step explanation:

Answer:

Step-by-step explanation:

-2x+7≥-11

-2x≥-18

2x≤18

x≤9

Answer:

1 1/2 feet

Step-by-step explanation:

Martin is making a model of a Native American canoe. He has 5 1/2 feet of wood he uses 2 3/4 feet for the whole and 1 1/4 feet for a paddle how much does he have left

This is calculated as:

5 1/2 feet - ( 2 3/4 feet + 1 1/4 feet)

Lowest Common Denominator 4

5 1/2 feet - (2 + 1 ( 3 + 1/4)

5 1/2 feet - 3 + 1

5 1/2 feet - 4 feet

= 1 1/2 feet of wood left

Answer:

Trudy will have 4 pieces of the fabric.

Step-by-step explanation:

Since, 1 foot of the fabric = 12 inches

If Trudy cuts the fabric into pieces of 3 inch.

Number of pieces she will have = [tex]\frac{\text{Total length of the fabric}}{\text{Length of one piece}}[/tex]

                                                     = [tex]\frac{12}{3}[/tex]

                                                     = 4 pieces

Therefore, she will have 4 pieces of the fabric.

Answer:

11 = (15 -6r) + 2r

11= 15-6r+2r

11=15-4r

4=4r

r=1

Answer:

B.) y - 6 = -8/5(x + 2)

Step-by-step explanation:

Remember in order to find the slope intercept form on 2 points, you need these equations: [tex]\frac{x_2 -x_1}{y_2 -y_1}[/tex] and [tex]y-y_1=m(x-x_1)[/tex]

To find the slope, you will need to use the first equation. In this case the equation will look like this: [tex]\frac{(-2)-6}{3-(-2)}=-\frac{8}{5}[/tex]

Then use the second equation, plug in the numbers, and you will get B as your answer

Answer:

D.  y = -2/3 x + 4/3

Step-by-step explanation:

When you have a perpendicular line, everything except the y-intercept becomes opposite. So 3/2x + 6 will become -2/3x.

To find the slope, you have to plug the coordinates into the equation so far which is y = -2/3x + b

y = -2/3x + b

2 = -2/3(-1) + b

2 = 2/3 + b

4/3 = b

So the equation is y = -2/3 x + 4/3.

Answer:

D

Step-by-step explanation:

Look at where the graph intercepts on the x-axis

If u can't see it's 2 and 10

Answer:

the answer is D

Step-by-step explanation:The answer is 2 and 10 because its directly on the line.

Hope I helped