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3 years ago

Rewrite 18 /5 as a mixed number. 5 1/3 5 5/3 3 3/5 3 5/3

Mathematics

2 answers:

maria [59]3 years ago

7 0

Answer:

your awnser is 3 3/5

Step-by-step explanation:

all u do is 18 divided by 5 wich gives u 3 with a leftover of 3 so that gives u 3 3/5

erastova [34]3 years ago

6 0

Answer:

3 3/5

Step-by-step explanation:

You count by 5 until it wont fit in to 18 what you have left over ( 3 ) is your numerater. However many times 5 went into 18 Is your whole number.

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Please answer 7 and 8, thank you guys for helping! <3

elena-14-01-66 [18.8K]

7: since they went down further you go further from zero: -28-40=-68 or D.
8: they lost 6 and then 8 so 6+8=14 but they lost them so -14 or A :)

6 0

3 years ago

Read 2 more answers

More Calculus! (I'm so sorry)

Olenka [21]

Recall that converting from Cartesian to polar coordinates involves the identities

$\begin{cases}y(r,\phi)=r\sin\phi\\x(r,\phi)=r\cos\phi\end{cases}$

As a function in polar coordinates, $r$ depends on $\phi$ , so you can write $r=r(\phi)$ .

Differentiating the identities with respect to $\phi$ gives

$\begin{cases}\dfrac{\mathrm dy}{\mathrm d\phi}=\dfrac{\mathrm dr}{\mathrm d\phi}\sin\phi+r\cos\phi\\\\\dfrac{\mathrm dx}{\mathrm d\phi}=\dfrac{\mathrm dr}{\mathrm d\phi}\cos\phi-r\sin\phi\end{cases}$

The slope of the tangent line to $r(\phi)$ is given by

$\dfrac{\mathrm dy}{\mathrm dx}=\dfrac{\frac{\mathrm dy}{\mathrm d\phi}}{\frac{\mathrm dx}{\mathrm d\phi}}=\dfrac{\frac{\mathrm dr}{\mathrm d\phi}\sin\phi+r\cos\phi}{\frac{\mathrm dr}{\mathrm d\phi}\cos\phi-r\sin\phi}$

Given $r(\phi)=3\cos\phi$ , you have $\dfrac{\mathrm dr}{\mathrm d\phi}=-3\sin\phi$ . So the tangent line to $r(\phi)$ has a slope of

$\dfrac{\mathrm dy}{\mathrm dx}=\dfrac{-3\sin^2\phi+3\cos^2\phi}{-3\sin\phi\cos\phi-3\cos\phi\sin\phi}=\dfrac{3\cos2\phi}{-3\sin2\phi}=-\cot2\phi$

When $\phi=120^\circ=\dfrac{2\pi}3\text{ rad}$ , the tangent line has slope

$\dfrac{\mathrm dy}{\mathrm dx}=-\cot\dfrac{4\pi}3=-\dfrac1{\sqrt3}$

This line is tangent to the point $(r,\phi)=\left(-\dfrac32,\dfrac{2\pi}3\right)$ which in Cartesian coordinates is equivalent to $(x,y)=\left(\dfrac34,-\dfrac{3\sqrt3}4\right)$ , so the equation of the tangent line is

$y+\dfrac{3\sqrt3}4=-\dfrac1{\sqrt3}\left(x-\dfrac34\right)$

In polar coordinates, this line has equation

$r\sin\phi+\dfrac{3\sqrt3}4=-\dfrac1{\sqrt3}\left(r\cos\phi-\dfrac34\right)$
$\implies r=-\dfrac{3\sqrt3}{2\sqrt3\cos\phi+6\sin\phi}$

The tangent line passes through the y-axis when $x=0$ , so the y-intercept is $\left(0,-\dfrac{\sqrt3}2\right)$ .

The vector from this point to the point of tangency on $r(\phi)$ is given by the difference of the vector from the origin to the y-intercept (which I'll denote $\mathbf a$ ) and the vector from the origin to the point of tangency (denoted by $\mathbf b$ ). In the attached graphic, this corresponds to the green arrow.

$\mathbf b-\mathbf a=\left(\dfrac34,-\dfrac{3\sqrt3}4\right)-\left(0,-\dfrac{\sqrt3}2\right)=\left(\dfrac34,-\dfrac{\sqrt3}4\right)$

The angle between this vector and the vector pointing to the point of tangency is what you're looking for. This is given by

$\mathbf b\cdot(\mathbf b-\mathbf a)=\|\mathbf b\|\|\mathbf b-\mathbf a\|\cos\theta$
$\dfrac98=\dfrac{3\sqrt3}4\cos\theta$
$\implies\theta=\dfrac\pi6\text{ rad}=30^\circ$

The second problem is just a matter of computing the second derivative of $\phi$ with respect to $t$ and plugging in $t=2$ .

$\phi(t)=2t^3-6t$
$\phi'(t)=6t^2-6$
$\phi''(t)=12t$
$\implies\phi''(2)=24$

6 0

3 years ago

QUESTION 1

podryga [215]

Answer: The team won 47 games.

Step-by-step explanation: The total games played was 84, and that means all games added together, but victories and losses. If the games they lost is called X, and the team won 10 more games than it lost, then it means the games they won is X + 10.

To find the value of wins and losses, we can now express both properly as;

X + (X +10) = 84

2X + 10 = 84

Subtract 10 from both sides of the equation

2X = 74

Divide both sides of the equation by 2

X = 37.

If the number of games won is X + 10, then games won is derived as

Wins = X + 10

Wins = 37 + 10

Wins = 47

The team won 47 games