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guapka [62]
3 years ago
6

Heather purchased a motorcycle for $4800 with 40% down. She will make 24

Mathematics
1 answer:
topjm [15]3 years ago
4 0

Answer:

$5952

Step-by-step explanation:

The principal of $4800 will become after 24 months at an interest of 12% APR,

4800(1 + \frac{2 \times 12}{100}) = 5952 dollars.

Now, the monthly payment is $135.57 for 24 months.

So, the payment by installment is $(135.57 × 24) = $3253.68.

Therefore, the down payment was $(5952 - 3253.68) = $2698.32.

Therefore, the total paid for the motorcycle including the down payment was $5952. (Answer)

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Use the Chain Rule to find the indicated partial derivatives. u = x2 + yz, x = pr cos(θ), y = pr sin(θ), z = p + r; (partial u)/
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u(x,y,z)=x^2+yz

\begin{cases}x(p,r,\theta)=pr\cos\theta\\y(p,r,\theta)=pr\sin\theta\\z(p,r,\theta)=p+r\end{cases}

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\begin{cases}x(2,2,0)=4\\y(2,2,0)=0\\z(2,2,0)=4\end{cases}

Denote by f_x:=\dfrac{\partial f}{\partial x} the partial derivative of a function f with respect to the variable x. We have

\begin{cases}u_x=2x\\u_y=z\\u_z=y\end{cases}

The Jacobian is

\begin{bmatrix}x_p&x_r&x_\theta\\y_p&y_r&y_\theta\\z_p&z_r&z_\theta\end{bmatrix}=\begin{bmatrix}r\cos\theta&p\cos\theta&-pr\sin\theta\\r\sin\theta&p\sin\theta&pr\cos\theta\\1&1&0\end{bmatrix}

By the chain rule,

u_p=u_xx_p+u_yy_p+u_zz_p=2xr\cos\theta+zr\sin\theta+y

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u_r=u_xx_r+u_yy_r+u_zz_r=2xp\cos\theta+zp\sin\theta+y

u_r(2,2,0)=2\cdot4\cdot2\cos0+4\cdot2\sin0+0\implies\boxed{u_r(2,2,0)=16}

u_\theta=u_xx_\theta+u_yy_\theta+u_zz_\theta=-2xpr\sin\theta+zpr\cos\theta

u_\theta(2,2,0)=-2\cdot4\cdot2\cdot2\sin0+4\cdot2\cdot2\cos0\implies\boxed{u_\theta(2,2,0)=16}

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