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3 years ago

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Mathematics

2 answers:

Bond [772]3 years ago

7 0

Answer:

3rd option

Step-by-step explanation:

Given z is inversely proportional to (y - 2)² then the equation relating them is

z = $\frac{k}{(y-2)^2}$ ← k is the constant of proportion

To find k use the condition when y = 5, z = 9 , then

9 = $\frac{k}{(5-2)^2}$ = $\frac{k}{3^2}$ = $\frac{k}{9}$ ( multiply both sides by 9 )

81 = k

z = $\frac{81}{(y-2)^2}$ ← equation of proportion

SIZIF [17.4K]3 years ago

4 0

Try 3rd one that’s the best one on there

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Find the rational zeros of the polynomial function, f(x)= 4x^3-8x^2-19x-7

Dima020 [189]

Answer:

The rational zero of the polynomial are $\pm \frac{7}{4}, \pm \frac{1}{4},\pm \frac{7}{2},\pm \frac{1}{2},\pm 7,\pm 1$ .

Step-by-step explanation:

Given polynomial as :

f(x) = 4 x³ - 8 x² - 19 x - 7

Now the ration zero can be find as

$\dfrac{\textrm factor of P}{\textrm factor Q}$ ,

where P is the constant term

And Q is the coefficient of the highest polynomial

So, From given polynomial , P = -7 , Q = 4

Now , $\dfrac{\textrm factor of \pm P}{\textrm factor of \pm Q}$

I.e $\dfrac{\textrm factor of \pm P}{\textrm factor of \pm Q}$ = $\frac{\pm 7 , \pm 1}{\pm 4 ,\pm 2,\pm 1 }$

Or, The rational zero are $\pm \frac{7}{4}, \pm \frac{1}{4},\pm \frac{7}{2},\pm \frac{1}{2},\pm 7,\pm 1$

Hence The rational zero of the polynomial are $\pm \frac{7}{4}, \pm \frac{1}{4},\pm \frac{7}{2},\pm \frac{1}{2},\pm 7,\pm 1$ . Answer

7 0

4 years ago

17. El precio de los terrenos en Lima es proporcional al área e inversamente proporcional a su distancia con respecto al centro

grin007 [14]

Answer:

375000

Step-by-step explanation:

We have that in this case the following proportion would be fulfilled:

Price * Distance / area

Now, we have that for a distance of 45 km and an area of 900 m ^ 2 the price is 250,000, now for a distance of 40 km but with an area of 1,200 m ^ 2, how would the price be, we replace:

250000 * 45/900 = P * 40/1200

12500 * 1200/40 = P

P = 375000

Which means that for these conditions the price is 375000.

3 0

3 years ago

Solve 5.7y - 3.9y I is not smart lolz

denpristay [2]

5.7 of anything minus 3.9 of the same thing leaves 1.8 of them.

8 0

4 years ago

What is the inverse of the function? f(x)=3x−1

Hatshy [7]

Answer:

The inverse is 1/3 (x+1)

Step-by-step explanation:

y = 3x-1

Exchange x and y

x = 3y-1

Solve for y

Add 1 to each side

x+1 = 3y-1+1

x+1 = 3y

Divide each side by 3

(x+1)/3 = 3y/3

1/3(x+1) =y

The inverse is 1/3 (x+1)

5 0

3 years ago

Find the derivative of the following. please show the steps when you answer :1) f(x) = 8xe^x2) y= 5xe^x^43) f(x)= x^8+5/x4) f(t)

borishaifa [10]

Answer:

Since,

$\frac{d}{dx}x^n = nx^{n-1}$

$\frac{d}{dx}(f(x).g(x)) = f(x).\frac{d}{dx}(g(x)) + g(x).\frac{d}{dx}(f(x))$

$\frac{d}{dx}(\frac{f(x)}{g(x)})=\frac{g(x).f'(x) - f(x) g'(x)}{(g(x))^2}$

1) $y = 8x e^x$

Differentiating with respect to x,

$\frac{dy}{dx}=8( x \times e^x + e^x) = 8(xe^x + e^x) = 8e^x(x+1)$

2) $y = 5x e^{x^4}$

Differentiating w. r. t x,

$\frac{dy}{dx}=5(x\times 4x^3 e^{x^4}+e^{x^4})=5e^{x^4}(4x^4+1)$

3) $y = x^8 + \frac{5}{x^4}$

Differentiating w. r. t. x,

$\frac{dy}{dx}=8x^7 - \frac{5}{x^5}\times 4 = 8x^7 - \frac{20}{x^5}=\frac{8x^{12}-20}{x^5}$

4) $f(t) = te^{11}-6t^5$

Differentiating w. r. t. t,

$f'(t) = e^{11} - 30t^4$

5) $g(p) = p\ln(2p+3)$

Differentiating w. r. t. p,

$g'(p) = p\frac{1}{2p+3}(2) + \ln(2p+3) = \frac{2p}{2p+3}+\ln(2p+3)$

6) $z = (te^{6t}+e^{5t})^7$

Differentiating w. r. t. t,

$\frac{dz}{dt}=7(te^{6t}+e^{5t})^6 ( 6te^{6t}+e^{6t} + 5e^{5t})$

7) $w =\frac{2y + y^2}{7+y}$

Differentiating w. r. t. y,

$\frac{dw}{dy} = \frac{(7+y)(2+2y)-(2y+y^2)}{(7+y)^2} = \frac{14 + 2y + 14y +2y^2 - 2y - y^2}{(7+y)^2}=\frac{14+14y+y^2}{(7+y)^2}$

7 0

4 years ago