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3 years ago

10

Which of the following require that you have parallel sides

1 answer:

Mariana [72]3 years ago

4 0

Alternate Interior Angles

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Sofia is learning to knit. After her first three stitches, she had to undo the last two. Then she made three more stitches and a

Marizza181 [45]

She’ll have to make 4 more stitches in order to get 6 good ones. Each time she creates 3 she undoes 2 which after 4 more times would leave her with 6 good stitches.

4 0

3 years ago

I don't know this problem!

liraira [26]

The answer is 70 I think

6 0

3 years ago

Read 2 more answers

Let F (x; y) = xy2i + x2y j. Evaluate ∫F.ds (from c to [infinity]) where C is the upper half of the circle of radius 1 centered

77julia77 [94]

Answer:

The integral $\int F \bullets ds$ is 0.

Step-by-step explanation:

A parameterization of curve C can be:

X (t) = cost 0 <= t <= pi

Y (t) = sint 0 <= t <= pi

r (t) = costi + sintj

r '(t) = -sinti + costj

$Fds = [-costsin^3t + sintcos^3t] dt$

The integral $\int F \bullets ds$ is given by:

$\int _0^{\pi }\left[-costsin^3t + sintcos^3t dt\right]dt$

$= \int _0^{\pi }-sin ^3tcostdt + \int _0^{\pi }sintcos^3tdt = 0$

4 0

3 years ago

Solve for x if log 9 base x + log 3 base x^2 = 2.5

Y_Kistochka [10]

Not sure if the equation is

$\log_9x+\log_3(x^2)=\dfrac52$

or

$\log_x9+\log_{x^2}3=\dfrac52$

If it's the first one:

$9^{\log_9x+\log_3(x^2)}=9^{\log_9x}\cdot9^{\log_3(x^2)}$

$9^{\log_9x+\log_3(x^2)}=9^{\log_9x}\cdot(3^2)^{\log_3(x^2)}$

$9^{\log_9x+\log_3(x^2)}=9^{\log_9x}\cdot3^{2\log_3(x^2)}$

$9^{\log_9x+\log_3(x^2)}=9^{\log_9x}\cdot3^{\log_3(x^2)^2}$

$9^{\log_9x+\log_3(x^2)}=9^{\log_9x}\cdot3^{\log_3(x^4)}$

$9^{\log_9x+\log_3(x^2)}=x\cdot x^4$

$9^{\log_9x+\log_3(x^2)}=x^5$

On the other side of the equation, we'd get

$9^{5/2}=(3^2)^{5/2}=3^{2\cdot(5/2)}=3^5$

Then

$x^5=3^5\implies\boxed{x=3}$

If it's the second one instead, you can use the same strategy as above:

$x^{\log_x9+\log_{x^2}3}=x^{\log_x9}\cdot x^{\log_{x^2}3}$

$x^{\log_x9+\log_{x^2}3}=x^{\log_x9}\cdot\left((x^2)^{1/2}\right)^{\log_{x^2}3}$

(Note that this step assume $x>0$ )

$x^{\log_x9+\log_{x^2}3}=x^{\log_x9}\cdot(x^2)^{(1/2)\log_{x^2}3}$

$x^{\log_x9+\log_{x^2}3}=x^{\log_x9}\cdot(x^2)^{\log_{x^2}\sqrt3}$

$x^{\log_x9+\log_{x^2}3}=9\sqrt3$

Then we get

$9\sqrt3=x^{5/2}\implies x=(9\sqrt3)^{2/5}\implies\boxed{x=3}$

6 0

3 years ago

il63 [147K]

There is a 35% chance the first one will not work, and a 49% the second one will not work. (Theoretically there is an 81% chance neither of them will work.)

8 0

4 years ago