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sammy [17]
3 years ago
5

What is the number writren in standard form six million, seven hundred ,twenty

Mathematics
2 answers:
Ksju [112]3 years ago
7 0
6 000 720

= 6.00072 * 10⁶
enot [183]3 years ago
4 0
6,720,000. I hope that helps!
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Find the point on the parabola y^2 = 4x that is closest to the point (2, 8).
guapka [62]

Answer:

(4, 4)

Step-by-step explanation:

There are a couple of ways to go at this:

  1. Write an expression for the distance from a point on the parabola to the given point, then differentiate that and set the derivative to zero.
  2. Find the equation of a normal line to the parabola that goes through the given point.

1. The distance formula tells us for some point (x, y) on the parabola, the distance d satisfies ...

... d² = (x -2)² +(y -8)² . . . . . . . the y in this equation is a function of x

Differentiating with respect to x and setting dd/dx=0, we have ...

... 2d(dd/dx) = 0 = 2(x -2) +2(y -8)(dy/dx)

We can factor 2 from this to get

... 0 = x -2 +(y -8)(dy/dx)

Differentiating the parabola's equation, we find ...

... 2y(dy/dx) = 4

... dy/dx = 2/y

Substituting for x (=y²/4) and dy/dx into our derivative equation above, we get

... 0 = y²/4 -2 +(y -8)(2/y) = y²/4 -16/y

... 64 = y³ . . . . . . multiply by 4y, add 64

... 4 = y . . . . . . . . cube root

... y²/4 = 16/4 = x = 4

_____

2. The derivative above tells us the slope at point (x, y) on the parabola is ...

... dy/dx = 2/y

Then the slope of the normal line at that point is ...

... -1/(dy/dx) = -y/2

The normal line through the point (2, 8) will have equation (in point-slope form) ...

... y - 8 = (-y/2)(x -2)

Substituting for x using the equation of the parabola, we get

... y - 8 = (-y/2)(y²/4 -2)

Multiplying by 8 gives ...

... 8y -64 = -y³ +8y

... y³ = 64 . . . . subtract 8y, multiply by -1

... y = 4 . . . . . . cube root

... x = y²/4 = 4

The point on the parabola that is closest to the point (2, 8) is (4, 4).

4 0
2 years ago
A recipe calls for 1 ½ cups of flour, 2/3 cup of white sugar, and 1/3 cup of brown sugar. The recipe makes 6 servings. A) How ma
Goryan [66]
<span>A) How many cups of flour are there per serving? 

</span>1 ½ cups of flour --------<span>6 servings
?     cups of flour ------- 1 serving

      </span>1 ½ 
------------ 
        6 

= 3/2 x 1/6
= 1/4

answer: 1/4 cups of flour per serving

<span>B) how many total cups of sugar(white and brown) are there per serving?
</span>total white and brown: <span>2/3 + 1/3 = 3/3 = 1 cups (combine)

1 cup of sugar (white and brown) </span>--------6 servings
? cups of sugar (white and brown) ------ 1 serving

  1
-----  = 1/6
  6
answer: 1/6 cups of sugar (white and brown) per serving

<span> (c) Suppose you modify the recipe so that it makes 9 servings. How much more flour do you need for the modified recipe than you need for the original recipe?
</span>
3/2  cups of flour --------6 servings
? cups of flour -----------9 servings


  9 * 3/2             
-----------  
      6

= (13 1/2) / 6
= 2 1/4

2 1/4 ( 9 servings) - 1 1/2(6 servings) = 3/4 cups

answer: you need 3/4 more cups of flour

6 0
3 years ago
Read 2 more answers
A cafe offers senior citizens a 15% discount off its regular price of $8.95 for the dinner buffet.
jonny [76]

a) 75 percent of the regular price is the price for senior citizens.

b) $6.712 is the price for senior citizens.

<u>Step-by-step explanation</u>:

  • The regular price is the 100% = $8.95
  • The offer price for senior citizen = 15% discount from 100%

∴ Percent of the regular price for senior citizens = 100% - 15% = 75%

The price for the senior citizens = 75% of $8.95

⇒ (75/100)\times8.95

⇒ 0.75\times8.95

⇒ 6.712 dollars.

∴ The price for senior citizens = $6.712

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3 years ago
Giving away 100 points :)<br> Hope you have a nice day
Verizon [17]

Answer:

THANKS BRO

Step-by-step explanation:

5 0
2 years ago
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A number line going from negative 4 to positive 4. What is the distance between 0 and –2? Use the number line to answer the ques
Nana76 [90]

Answer:

I wish <em>i could help </em>

Step-by-step explanation:

4 0
3 years ago
Read 2 more answers
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