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Pachacha [2.7K]
3 years ago
11

In the equation y = kx, k represents the constant of proportionality. If the constant is 5, write an equation to represent this

proportional relationship.
Mathematics
1 answer:
nata0808 [166]3 years ago
7 0

Answer & Step-by-step explanation:

If you simplify the given equation of y=kx to solve for k, you would divide both sides by x:

y=kx\\\\\frac{y}{x} =\frac{kx}{x}\\\\\frac{y}{x}=k

We are told that the constant, <em>k</em>, is 5. So, this can be written as:

5=\frac{y}{x}

:Done

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MA_775_DIABLO [31]

Answer:

12 and 13 I believe

Step-by-step explanation:

12x12=144

13x13=169

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3 years ago
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Step-by-step explanation:

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2 years ago
Find the x-coordinates of any relative extrema and inflection point(s) for the function f(x)= 6x^1/3 + 3x^4/3. You must justify
irina [24]

Answer:

x-coordinates of relative extrema = \frac{-1}{2}

x-coordinates of the inflexion points are 0, 1

Step-by-step explanation:

f(x)=6x^{\frac{1}{3}}+3x^{\frac{4}{3}}

Differentiate with respect to x

f'(x)=6\left ( \frac{1}{3} \right )x^{\frac{-2}{3}}+3\left ( \frac{4}{3} \right )x^{\frac{1}{3}}=\frac{2}{x^{\frac{2}{3}}}+4x^{\frac{1}{3}}

f'(x)=0\Rightarrow \frac{2}{x^{\frac{2}{3}}}+4x^{\frac{1}{3}}=0\Rightarrow x=\frac{-1}{2}

Differentiate f'(x) with respect to x

f''(x)=2\left ( \frac{-2}{3} \right )x^{\frac{-5}{3}}+\frac{4}{3}x^{\frac{-2}{3}}=\frac{-4x^{\frac{2}{3}}+4x^{\frac{5}{3}}}{3x^{\frac{2}{3}}x^{\frac{5}{3}}}\\f''(x)=0\Rightarrow \frac{-4x^{\frac{2}{3}}+4x^{\frac{5}{3}}}{3x^{\frac{2}{3}}x^{\frac{5}{3}}}=0\Rightarrow x=1

At x = \frac{-1}{2},

f''\left ( \frac{-1}{2} \right )=\frac{4\left ( -1+4\left ( \frac{-1}{2} \right ) \right )}{3\left ( \frac{-1}{2} \right )^{\frac{5}{3}}}>0

We know that if f''(a)>0 then x = a is a point of minima.

So, x=\frac{-1}{2} is a point of minima.

For inflexion points:

Inflexion points are the points at which f''(x) = 0 or f''(x) is not defined.

So, x-coordinates of the inflexion points are 0, 1

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3 years ago
Y=log x If y=10, then what is x?
netineya [11]

Answer:

First question, x= 10^10.

Second question is 10!. or 362880

Step-by-step explanation:

First Question:

Simple logx has a base of 10, i.e log10 x,

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when taking the base "10" from the right side to the left, the number on the left side becomes the power of the base, in this case 10 from the right will be base and 10 from the left will power and log will vanish.

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love history [14]

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1 = b

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2 years ago
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