Which statement is correct?

What 2 numbers multiply to -18 and add up to -4

ivann1987 [24]

Answer:

-9 x 1 x 1 x 1 x 2 = (-18)

-9 + 1 + 1 + 1 + 2 = (-4)

5 0

3 years ago

What is the derivative of y with respect to x if y = 2/X4

zepelin [54]

You're correct, the answer is C.

Given any function of the form $y=x^n$ , then the derivative of y with respect to x ( $\frac{dy}{dx}$ ) is written as:
$\frac{dy}{dx}=nx^n^-^1$

In which $n$ is any constant, this is called the power rule for differentiation.

For this example we have $y= \frac{2}{x^4}$ , first lets get rid of the quotient and write the expression in the form $y=x^n$ :
$y= \frac{2}{x^4} =2x^-^4$

Now we can directly apply the rule stated at the beginning (in which $n=-4$ ):
$\frac{dy}{dx}=(2)(-4)x^{-4-1}=-8 x^{-5}= -\frac{8}{x^5}$

Note that whenever we differentiate a function, we simply "ignore" the constants (we take them out of the derivative).

6 0

3 years ago

find the area of the trapezium whose parallel sides are 25 cm and 13 cm The Other sides of a Trapezium are 15 cm and 15 CM

Snezhnost [94]

$\huge\underline{\red{A}\blue{n}\pink{s}\purple{w}\orange{e}\green{r} -}$

Given - A trapezium ABCD with non parallel sides of measure 15 cm each ! along , the parallel sides are of measure 13 cm and 25 cm

To find - Area of trapezium

Refer the figure attached ~

In the given figure ,

AB = 25 cm

BC = AD = 15 cm

CD = 13 cm

Construction -

$draw \: CE \: \parallel \: AD \: \\ and \: CD \: \perp \: AE$

Now , we can clearly see that AECD is a parallelogram !

$\therefore$ AE = CD = 13 cm

Now ,

$AB = AE + BE \\\implies \: BE =AB - AE \\ \implies \: BE = 25 - 13 \\ \implies \: BE = 12 \: cm$

Now , In ∆ BCE ,

$semi \: perimeter \: (s) = \frac{15 + 15 + 12}{2} \\ \\ \implies \: s = \frac{42}{2} = 21 \: cm$

Now , by Heron's formula

$area \: of \: \triangle \: BCE = \sqrt{s(s - a)(s - b)(s - c)} \\ \implies \sqrt{21(21 - 15)(21 - 15)(21 - 12)} \\ \implies \: 21 \times 6 \times 6 \times 9 \\ \implies \: 12 \sqrt{21} \: cm {}^{2}$

Also ,

$area \: of \: \triangle \: = \frac{1}{2} \times base \times height \\ \\\implies 18 \sqrt{21} = \: \frac{1}{\cancel2} \times \cancel12 \times height \\ \\ \implies \: 18 \sqrt{21} = 6 \times height \\ \\ \implies \: height = \frac{\cancel{18} \sqrt{21} }{ \cancel 6} \\ \\ \implies \: height = 3 \sqrt{21} \: cm {}^{2}$

Since we've obtained the height now , we can easily find out the area of trapezium !

$Area \: of \: trapezium = \frac{1}{2} \times(sum \: of \:parallel \: sides) \times height \\ \\ \implies \: \frac{1}{2} \times (25 + 13) \times 3 \sqrt{21} \\ \\ \implies \: \frac{1}{\cancel2} \times \cancel{38 }\times 3 \sqrt{21} \\ \\ \implies \: 19 \times 3 \sqrt{21} \: cm {}^{2} \\ \\ \implies \: 57 \sqrt{21} \: cm {}^{2}$