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3 years ago

PLEASE HELP! GIVING BRAINLIEST

Mathematics

1 answer:

Tanya [424]3 years ago

8 0

Answer:

x=7.31

Step-by-step explanation:

There are two x's, so they represent the equation 2x=14.62. If we solve for x, we have to divide each side by 2:

2x/2=14.62/2.

If we divide, we get x=7.31

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Reciprocate 2 5/9 plz and thx

ZanzabumX [31]

Answer: 9/23

Step-by-step explanation:

1- Convert the mixed fraction to an improper fraction. 9 x 2 + 5 = 23 and keep the original denominator. 23/9

2- Now “flip” the fraction to its reciprocal. 23/9 becomes 9/23

3- Check to see if it can be reduced. It cannot so there’s your answer. 9/23

6 0

3 years ago

If f is a differentiable function, find an expression for the derivative of each of the following functions

almond37 [142]

12a. Answer: d) x⁶ f'(x) + 6x⁵ f(x)

Step-by-step explanation:

Use the multiplication formula for derivatives:

y = a · b → y' = a'b + ab'

y = x⁶ · f(x)

a = x⁶ b = f(x)

a' = 6x⁵ b' = f'(x)

y' = a'b + ab'

y' = 6x⁵ f(x) + x⁶ f'(x)

***************************************************************

12b. Answer: $\bold{b)\ y=\dfrac{xf'(x)-9f(x)}{x^{10}}'}$

Step-by-step explanation:

Use the division formula for derivatives:

$y=\dfrac{a}{b}$ → $y' = \dfrac{a'b - ab'}{b^2}$

$y=\dfrac{f(x)}{x^9}\\\\a=f(x)\qquad b=x^9\\\\a'=f(x)\qquad b'=9x^8\\\\y'=\dfrac{a'b-ab'}{b^2}\\\\y'=\dfrac{x^9f'(x)-9x^8f(x)}{(x^9)^2}\\\\.\ =\dfrac{x^9f'(x)-9x^8f(x)}{x^{18}}\\\\\text{factor out }x^{8}: y'=\dfrac{xf'(x)-9f(x)}{x^{10}}$

Note: You can also move the denominator to the top (it will have a negative exponent) and use the multiplication formula for derivatives.

5 0

3 years ago

The volume of water and a rectangle swimming pool can be modeled by the function v(x)=x^3+13x-210. If the depth of the pool is g

S_A_V [24]

Answer:

Required,

$L=\frac{3+\sqrt{37}}{2}-\frac{144}{x-3}$

$W=\frac{3-\sqrt{37}}{2}-\frac{144}{x-3}$

Step-by-step explanation:

Given volume and depth respectively,

$V(x)=x^3+13x-210$ and $x-3$

To find length and width of the rectanglular swiming pool we know,

Volume=length $\times$ height $\times$ depth.

Let depth=D=x-3, length=L, width=W, then

$V=DLW$

$x^3+13x-210= LW(x-3)$

$LW=\frac{x^3+13x-210}{x-3}$

After divide we will get $x^2-3x-22$ with remainder -144.

Thus,

$x^3+13x-210=(x^2-3x-22)(x-3)-144=(x-3)LW$

Now to find root of,

$x^2-3x-144=\frac{3\pm\sqrt{9+88}}{2}=\frac{3\pm \sqrt{37}}{2}$

Thus,

$L=\frac{3+\sqrt{37}}{2}-\frac{144}{x-3}$

$W=\frac{3-\sqrt{37}}{2}-\frac{144}{x-3}$

5 0

3 years ago

PLEASE HELP I've tried putting all my working out into the box but it said wrong to..

Inessa05 [86]

Answer:

£59.25

Step-by-step explanation:

It appears you can measure the height of the trapezoid [trapezium :-) ??]. If you can't, you can use the Pythagorean Theorem (image attached). Draw a line from the upper right-hand corner down to the baseline--the 20m side. You'll form a right triangle with one leg h , hypotenuse 17m and the other leg 8m (the difference between 20m and 12m).

(leg)^2 + (leg)^2 = (hypotenuse)^2

h^2 + 8^2 = 17^2

h^2 + 64 = 289

h^2 = 225

h = 15m

The area of the trapezium is $A=\frac{1}{2}h\left(b_1+b_2\right)$ where the b's are the lengths of the two bases (upper and lower sides).