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2 years ago

Evaluate the expression: 10P3

Mathematics

1 answer:

anyanavicka [17]2 years ago

4 0

Answer:

720

Step-by-step explanation:

nPk = n!/(n-k)!

10P3 = 10!/(10-3)! = 10!/7!

= 10·9·8 = 720

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F(x) = 3x + x3

____ [38]

Answer:

Please check the explanation.

Step-by-step explanation:

Given

f(x) = 3x + x³

Taking differentiate

$\frac{d}{dx}\left(3x+x^3\right)$

$\mathrm{Apply\:the\:Sum/Difference\:Rule}:\quad \left(f\pm g\right)'=f\:'\pm g'$

$=\frac{d}{dx}\left(3x\right)+\frac{d}{dx}\left(x^3\right)$

solving

$\frac{d}{dx}\left(3x\right)$

$\mathrm{Take\:the\:constant\:out}:\quad \left(a\cdot f\right)'=a\cdot f\:'$

$=3\frac{d}{dx}\left(x\right)$

$\mathrm{Apply\:the\:common\:derivative}:\quad \frac{d}{dx}\left(x\right)=1$

$=3\cdot \:1$

$=3$

now solving

$\frac{d}{dx}\left(x^3\right)$

$\mathrm{Apply\:the\:Power\:Rule}:\quad \frac{d}{dx}\left(x^a\right)=a\cdot x^{a-1}$

$=3x^{3-1}$

$=3x^2$

Thus, the expression becomes

$\frac{d}{dx}\left(3x+x^3\right)=\frac{d}{dx}\left(3x\right)+\frac{d}{dx}\left(x^3\right)$

$=3+3x^2$

Thus,

f'(x) = 3 + 3x²

Given that f'(x) = 15

substituting the value f'(x) = 15 in f'(x) = 3 + 3x²

f'(x) = 3 + 3x²

15 = 3 + 3x²

switch sides

3 + 3x² = 15

3x² = 15-3

3x² = 12

Divide both sides by 3

x² = 4

$\mathrm{For\:}x^2=f\left(a\right)\mathrm{\:the\:solutions\:are\:}x=\sqrt{f\left(a\right)},\:\:-\sqrt{f\left(a\right)}$

$x=\sqrt{4},\:x=-\sqrt{4}$

$x=2,\:x=-2$

Thus, the value of x will be:

$x=2,\:x=-2$

5 0

2 years ago

45, 10, 48, 19,36, 25, 63, 14, 39<br> What is the median of the number of fish?

tiny-mole [99]

Answer:

Step-by-step explanation:

3 0

2 years ago

Read 2 more answers

What is the equation of the line that passes through the point

snow_lady [41]

Answer:

$3x-2y=2$

Step-by-step explanation:

The equation of line having slope $\frac{3}{2}$ and passing through $(-4,-7)$ .

$The\ equation\ of\ line\ is\ given\ by\ y=mx+c\ where\ m\ is\ the\ slope\ of\ line.\\\\Here\ m=\frac{3}{2}\\\\Equation\ y=\frac{3}{2}x+c\\\\Line\ passes\ through\ (-4,-7),\ it\ will\ satisfy\ the\ equation\ of\ line.\\\\-7=\frac{3}{2}\times (-4)+c\\\\-7=-6+c\\\\c=-7+6\\\\c=-1\\\\y=\frac{3}{2}x-1\\\\2y=3x-2\\\\3x-2y=2$