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3 years ago

Heather is going to graph y = -3x2 + 3. How is the parent graph transformed?

Mathematics

2 answers:

Olenka [21]3 years ago

6 0

i belive the answer is A..

Yuki888 [10]3 years ago

3 0

Any x² graph is a parabola. The negative in front is going to flip the parabola upside down to look like a camel hump. The 3 is going to make the graph narrower. The three at the end makes the y intercept 3. So the top of the graph will be shifted up to (0,3).
The answer would be A I believe

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Find tan A and tan B.

Alex

Step-by-step explanation:

$\tan(a) = \frac{26}{10} = 2.6 \\ \tan(b) = \frac{10}{26}$

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2 years ago

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3 years ago

1. (a) Solve the differential equation (x + 1)Dy/dx= xy, = given that y = 2 when x = 0. (b) Find the area between the two curves

erastova [34]

(a) The differential equation is separable, so we separate the variables and integrate:

$(x+1)\dfrac{dy}{dx} = xy \implies \dfrac{dy}y = \dfrac x{x+1} \, dx = \left(1-\dfrac1{x+1}\right) \, dx$

$\displaystyle \frac{dy}y = \int \left(1-\frac1{x+1}\right) \, dx$

$\ln|y| = x - \ln|x+1| + C$

When x = 0, we have y = 2, so we solve for the constant C :

$\ln|2| = 0 - \ln|0 + 1| + C \implies C = \ln(2)$

Then the particular solution to the DE is

$\ln|y| = x - \ln|x+1| + \ln(2)$

We can go on to solve explicitly for y in terms of x :

$e^{\ln|y|} = e^{x - \ln|x+1| + \ln(2)} \implies \boxed{y = \dfrac{2e^x}{x+1}}$

(b) The curves y = x² and y = 2x - x² intersect for

$x^2 = 2x - x^2 \implies 2x^2 - 2x = 2x (x - 1) = 0 \implies x = 0 \text{ or } x = 1$

and the bounded region is the set

$\left\{(x,y) ~:~ 0 \le x \le 1 \text{ and } x^2 \le y \le 2x - x^2\right\}$

The area of this region is

$\displaystyle \int_0^1 ((2x-x^2)-x^2) \, dx = 2 \int_0^1 (x-x^2) \, dx = 2 \left(\frac{x^2}2 - \frac{x^3}3\right)\bigg|_0^1 = 2\left(\frac12 - \frac13\right) = \boxed{\frac13}$

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2 years ago

Solve each inequlity 5- 2( 3x-4) -2x < -6x + 4

almond37 [142]

Answer:

x > 9/2

Step-by-step explanation:

don't get scared :) we can isolate the variable easily!

distribute

5 -2( 3x-4) -2x < -6x + 4

5 -6x + 8 - 2x < -6x + 4

-8x + 13 < -6x + 4

+6x -13 +6x -13

-2x < -9

x > 9/2

change the direction of the sign because we divided by a negative

There you go!

I hope this helps (:

8 0

3 years ago

Assume a round of golf requires four hours of leisure time, and attending a concert requires two hours. If the price of a round

nekit [7.7K]

Answer:

Step-by-step explanation:

Relatively less golf and attend relatively more concerts whenever his leisure time becomes more scarce.

- This is called the marginal utility, that with every successive unit that utility decreases. With each passing hour while playing golf Joe is less inclined to play for an extra hour. When leisure time is less than 2 hrs he is equally likely to opt out of golf for concert.

4 0

3 years ago