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3 years ago

Please give correct answer!

Mathematics

1 answer:

Roman55 [17]3 years ago

3 0

If the object is a true parallelogram, then p=36.4/5.2=7 yd.
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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

7 0

3 years ago

Two gongs strike at intervals of 24 and 40minutes respectively. At twist time will they strike together again if they start simu

solmaris [256]

Answer:

They will sound together at 2pm

Step-by-step explanation:

Now, the first thing we need to calculate is , in how many minutes will the two gongs strike together.

To be able to do this, we need to calculate the least common multiple of the two numbers 24 and 40

The lowest common multiple between both is 120

This means that the two gongs will sound together at exactly 120 minutes

Now since 1 hour is 60 minutes, this means that 120 minutes will be = 120/60 = 2 hours

Since they both sounded together at 12 noon and the next time they will be sounding is next two hours, their sounding time will thus be 12 noon + 2 hours = 2 pm

8 0

3 years ago

In a recent town election, 1,860 people voted for either candidate A or candidate B for the position of supervisor.

Lera25 [3.4K]

837.

EXPLANATION:

if candidate A recieved 55% of the votes,

Then candidate B recieved 45% of the votes, because it must equal 100%

45% of 1860 is 837.

Hope this helpz!

4 0

2 years ago

On a coordinate plane, a straight line and a parallelogram are shown. The straight line has a negative slope and has a formula o

suter [353]

Answer:

B. (3, –1)

Step-by-step explanation:

Reflection in the line y=-x is described by the transformation ...

(x, y) ⇒ (-y, -x)

Then the point of interest becomes ...

F(1, -3) ⇒ F'(3, -1) . . . . matches choice B

7 0

2 years ago

PLS HELP

Fiesta28 [93]

Answer:

1. 1/3 x 2/2 = 1/3

2. 1/4 x 5/5 = 1/4

3. 1/6 x 4/4 = 1/6

4. 9/8 x 3/4 = (9x3)/(8x4) = 27/32

4. 4/5 x 2/2 = 4/5

Step-by-step explanation:

n/n = 1

7 0

2 years ago