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hjlf
3 years ago
12

QUESTION ON THE PICTURE

Mathematics
1 answer:
Helen [10]3 years ago
3 0
Answer: 1 1/2
Explanation: the first number of the division problem stays the same but you flip the second fraction witch is 1/2 then that will be 2/1 then change the division symbol into a multiplication symbol and 3/4 times 2/1 and that equals6/4 and 6/4 is divisible by two so you divide 6/4 x 2. That equals 3/2 and you had to make that a mixed number so you divide two and 33 on the inside of the house and two on the outside. Two goes into threewants and when is your whole number and your remainder is one and one is your numerator and two is your denominator. You might understand it better if you see my work which a photo of it is down below.

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Answer:

x = -25

Step-by-step explanation:

25 = -7(x + 5) + 5x

25 = -7x - 25 + 5x

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1/2(x+10)= 1/4 (x-8) x= <br> (must be a fraction)
Alex_Xolod [135]

Answer:

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Step-by-step explanation:

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5 0
3 years ago
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
3 years ago
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