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3 years ago

Evaluate g(x)=3x when x=-2,0and 5

Mathematics

1 answer:

Law Incorporation [45]3 years ago

6 0

Answer:

When x = -2, g(x) = -6

When x = 0, g(x) = 0

When x = 5, g(x) = 15

Step-by-step explanation:

We have a function and are asked to evaluate and solve when we have three different values for x.

To solve, all we need to do is substitute the numbers with the corresponding value.

3(-2)

-6

3(0)

3(5)

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Use the quadratic formula to solve 9x2 + 6x – 17 = 0. A. B. x = –1, –5 C. D.

Taya2010 [7]

Answer:

$x_{1} = -\frac{1}{3} +\sqrt{2} ; x_{2} = -\frac{1}{3}-\sqrt{2}$

Step-by-step explanation:

9x² + 6x – 17 = 0

Apply the quadratic formula

$x = \frac{-b\pm\sqrt{b^2-4ac}}{2a}$

a = 9; b = 6; y = -17

$x = \frac{-6\pm\sqrt{6^2 - 4\times 9 \times(-17)}}{2\times 9}$

$x = \frac{-6\pm\sqrt{36+36\times17}}{18}$

$x = \frac{-6\pm\sqrt{36(1+17)}}{18}$

$x = \frac{-6\pm 6 \sqrt{18}}{18}$

$x = \frac{-1\pm \sqrt{9\times2}}{3}$

$x = \frac{-1\pm 3\sqrt{2}}{3}$

$x_{1} = -\frac{1}{3} +\sqrt{2} ; x_{2} = -\frac{1}{3}-\sqrt{2}$

The graph below shows the roots at x₁ =1.081 and x₂ = -1.748.

6 0

3 years ago

Please help with this calculus problem!

ELEN [110]

$\dfrac{\mathrm dQ}{\mathrm dt}=\dfrac{a(1-5bt^2)}{(1+bt^2)^4}$
$Q(t)=\displaystyle\int\frac{a(1-5bt^2)}{(1+bt^2)^4}\,\mathrm dt$

Let $t=\dfrac1{\sqrt b}\tan u$ , so that $\mathrm dt=\dfrac1{\sqrt b}\sec^2u\,\mathrm du$ . Then the integral becomes

$\displaystyle\frac a{\sqrt b}\int\frac{1-5b\left(\frac1{\sqrt b}\tan u\right)^2}{\left(1+b\left(\frac1{\sqrtb}\tan u\right)^2\right)^4}\sec^2u\,\mathrm du$
$=\displaystyle\frac a{\sqrt b}\int\frac{1-5\tan^2u}{(1+\tan^2u)^4}\sec^2u\,\mathrm du$
$=\displaystyle\frac a{\sqrt b}\int\frac{1-5\tan^2u}{\sec^6u}\,\mathrm du$
$=\displaystyle\frac a{\sqrt b}\int(\cos^6u-5\sin^2u\cos^4u)\,\mathrm du$
$=\displaystyle\frac a{\sqrt b}\int(6\cos^2u-5)\cos^4u\,\mathrm du$

One way to proceed from here is to use the power reduction formula for cosine:

$\cos^{2n}x=\left(\dfrac{1+\cos2x}2\right)^n$

You'll end up with

$=\displaystyle\frac a{16\sqrt b}\int(5\cos2u+8\cos4u+3\cos6u)\,\mathrm du$
$=\displaystyle\frac a{16\sqrt b}\left(\frac52\sin2u+2\sin4u+\frac12\sin6u\right)+C$
$=\dfrac a{32\sqrt b}(5\sin2u+4\sin4u+\sin6u)+C$
$Q(t)=\dfrac{at}{(1+bt^2)^3}+C$

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3 years ago

The perimeter of a rectangle is 68cm the length is 4cm less than three time its width write a system of equation to find the dim

ss7ja [257]

Check photo for details

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3 years ago

Calculate: ㅤ <img src="https://tex.z-dn.net/?f=%5Clim_%7Bx%20%5Crightarrow%20%2B%5Cinfty%7Dx%28%5Csqrt%7Bx%5E%7B2%7D-1%7D-x%29"

RSB [31]

Answer:

$\displaystyle \large \boxed{ \lim_{x \rightarrow +\infty} {x\left(\sqrt{x^2-1}-x\right)}=-\dfrac{1}{2}}$

Step-by-step explanation:

Hello, please consider the following.

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For x close to 0, we can write

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