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1 year ago

If y= 2x-3 were chnged to y=2x+5 how would the graph of the new function compare with the original

Mathematics

2 answers:

ivanzaharov [21]1 year ago

8 0

The new function moved up by 8 units from the original.

The only difference in the functions is the y-intercept. The slope remained the same ( $2$ ), but the y-intercept went up by 8, meaning the function moved up 8 units.

See the attached image for a graph of both functions. The new function is the solid blue line.

zloy xaker [14]1 year ago

6 0

Answer: +8
I think that is what you asked

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Step-by-step explanation:

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3 years ago

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2 years ago

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Barack walks 2 kilometers south and then x kilometers east. He ends 5 kilometers away from his starting position. Find x

amid [387]

Answer:

4.6 km

Step-by-step explanation:

-This is a Pythagorean Theorem problem where the distances walked are effectively the base and height of the imaginary right triangle thereof.

#Apply Pythagorean theorem to solve:

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3 years ago

Rewrite the following integral in spherical coordinates.

lora16 [44]

In cylindrical coordinates, we have $r^2=x^2+y^2$ , so that

$z = \pm \sqrt{2-r^2} = \pm \sqrt{2-x^2-y^2}$

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$1 \le r \le \sqrt2$ means our region is between two cylinders with radius 1 and $\sqrt2$ . In spherical coordinates, the inner cylinder has equation

$x^2+y^2 = 1 \implies \rho^2\cos^2(\theta) \sin^2(\phi) + \rho^2\sin^2(\theta) \sin^2(\phi) = \rho^2 \sin^2(\phi) = 1 \\\\ \implies \rho^2 = \csc^2(\phi) \\\\ \implies \rho = \csc(\phi)$

This cylinder meets the sphere when

$x^2 + y^2 + z^2 = 1 + z^2 = 2 \implies z^2 = 1 \\\\ \implies \rho^2 \cos^2(\phi) = 1 \\\\ \implies \rho^2 = \sec^2(\phi) \\\\ \implies \rho = \sec(\phi)$

which occurs at

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where $n\in\Bbb Z$ . Then $\frac\pi4\le\phi\le\frac{3\pi}4$ .

The volume element transforms to

$dx\,dy\,dz = r\,dr\,d\theta\,dz = \rho^2 \sin(\phi) \, d\rho \, d\theta \, d\phi$

Putting everything together, we have

$\displaystyle \int_0^{2\pi} \int_1^{\sqrt2} \int_{-\sqrt{2-r^2}}^{\sqrt{2-r^2}} r \, dz \, dr \, d\theta = \boxed{\int_0^{2\pi} \int_{\pi/4}^{3\pi/4} \int_{\csc(\phi)}^{\sqrt2} \rho^2 \sin(\phi) \, d\rho \, d\phi \, d\theta} = \frac{4\pi}3$

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2 years ago

Newberg is 5 miles due north of the airport, and Rockport is 12 miles due east of the airport. How far apart are Newberg and Roc

amid [387]

Step-by-step explanation:

No of miles Newberg is north of airport = 5

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