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eduard
3 years ago
8

I AM GIVING 50 POINTS AND BRAINLIEST

Mathematics
2 answers:
skad [1K]3 years ago
4 0

Answer:

c. t=±x√2a

Step-by-step explanation:

Ilia_Sergeevich [38]3 years ago
3 0

Answer:

your answer is definitely c :)

Step-by-step explanation:

c. t=±x√2a

HAVE A GOOD DAY !!!

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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
3 years ago
Find the volume of the frog queen building in Graz, Austria. The building is 18 meters long, 17 meters tall, and 18 meters wide
densk [106]

Answer: 5,508 m3

Step-by-step explanation:  V= 18 x 17 x 18 = 5,508 m3

8 0
3 years ago
Read 2 more answers
Is y = 0.860x + 3.302 a linear function?
gulaghasi [49]

Answer:

yes

Step-by-step explanation:

Yes.  The given function has the form y = mx + b, which is that of a linear function.  Here the slope, m, is 0.860, and the y-intercept is 3.302.

8 0
3 years ago
Tess plants flowers every year, and she noticed that her flowers tend to bloom earlier when the spring weather is warmer. She co
OlgaM077 [116]

Answer:

=17

Step-by-step explanation:

We need the slope and the y-intercept to find the equation of the linear model.

This line goes through (0,28) and (1,26), so the slope is

\frac{26 - 28}{1} = -2

1

26−28

​  =−2

The equation that best describes this model is

\widehat{y} = -2x + 28

y

​  =−2x+28

Plug in x = 5.5 in the above equation to get

​\widehat{y}

y

​   ​=−2x+28

=(−2)(5.5)+28

=−11+28

=17

Based on this equation, the date in April her flowers will bloom if the average temperature in March is

5 0
2 years ago
Read 2 more answers
What is the theoretical probability of rolling a 1 or a 2 on the 6-sided die? answer as a fraction
Neko [114]

Answer:

1/3

Step-by-step explanation:

as 1/6 for a one and 1/6 for a 2 and 1/6 + 1/6 is 2/6 or 1/3

4 0
3 years ago
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