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bonufazy [111]
3 years ago
8

It takes james 2.5 minutes to type 150 words at that rate how mant words can james type in 6 minutes

Mathematics
2 answers:
erma4kov [3.2K]3 years ago
8 0

\large\huge\green{\sf{Answer:-}}

  • option b is correct

\large\huge\green{\sf{solution:-}}

  • in 2.5 minutes word that are typed=150

  • in 1 minutes word that should be type= 150/2.5=60

  • in 6minutes word that should be type= 60x6=360
sergey [27]3 years ago
5 0

The number of words james can type in 6 minutes at the same rate is 360 words

Given:

Number of minutes to type 150 words = 2.5 minutes

let

number of words James can type in 6 minutes = x

Equate the ratio of the number of words to number of minutes

150 : 2.5 = x : 6

150/2.5 = x/6

cross product

150 × 6 = 2.5 × x

900 = 2.5x

x = 900/2.5

x = 360 words

Therefore, the number of words james can type in 6 minutes is 360 words

Learn more about ratio:

brainly.com/question/16981404

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Step-by-step explanation:

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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 ...

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... 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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Natali5045456 [20]

Answer:

Option C, both functions have an y-intersect equal to 2.

Step-by-step explanation:

When we have a function f(x), the y-intercept is the value f(0). This is the point where the graph of the function intersects the y-axis.

Then, for f(x) = -x^2 + 5*x + 2

The y-intercept is:

f(0) = -0^2 + 5*0 + 2 = 2

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We can see that the graph intersects the graph at y = 2

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sergiy2304 [10]

Answer:

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