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3 years ago

Find the vertex of the function h(x) = -x^2 + 14

Mathematics

1 answer:

Mazyrski [523]3 years ago

5 0

The vertex form:

$f(x)=a(x-h)^2+k\\\\(h,\ k)-vertex$

$h(x)=-x^2+14=-(x-0)^2+14\to h=0,\ k=14$

<h3>Answer: (0, 14).</h3>

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3 years ago

Find the length of the curve y = integral from 1 to x of sqrt(t^3-1)

Arlecino [84]

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3 years ago

The graph of function f is shown above. if g(x)=x^2/f(x) what is the value of g'(1)?

Alla [95]

Answer:

Step-by-step explanation:

Find the equation of the segment going from (0,-5) to (3,7)

y intercept = -5

Slope = (-5 - 7) / (0 - 3) = -12/-3 = 4

equation: y = 4x - 5

g(x) = x^2 / f(x)

f(x)= (4x - 5)

g(x) = x^2 / (4x - 5)

g'(x) = x^2 * (4x - 5)^-1

g'(x) = 2x*(4x - 5)^-1 + (-1) *4* x^2 (4x - 5)^-2

I will leave that monster the way it is and just find g'(1)

g'(1) = 2(1) * (4(1) - 5)^-1 + (-1) (1)^2 *4* (4(1) - 5)^-2

g'(1) = 2(1) * (-1)^-1 + (-1) (1)^2 *4 * (-1)^2

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g'(1) = - 2 + (-1) (1)^2 (4)

g'(1) = - 2 - 4

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2 years ago

Help!.!.!.!.!.!.!.!.!.!.!.!.!.!!.!.!.!.!.!.!.!.!.!.

bezimeni [28]

Answer:

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Step-by-step explanation:

Let us plan out our steps, and solve for each:

<em>1. Given the information, let us create a proportionality as such:</em>

48 = 1 ⇒ x - centimeters of the snowflake in real life

18 x

<em>2. Now let us cross multiply, and solve through simple algebra for x:</em>

48 * x = 18,

x =<em> 0.375 centimeters of the snowflake in real ife</em>

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3 years ago