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2 years ago

7

A single bus fare costs $2.35. A monthly pass costs $45.75. Celine estimates that she will ride the bus 25 times this month. Kam

al estimates that he will ride the bus 18 times. should they both buy monthly passes? Explain.

1 answer:

Sav [38]2 years ago

8 0

Answer:

No they shouldn't.

Step-by-step explanation:

Monthly pass: Celine: $1,143 Kamal: $823

Single Pass: Celine: $58 Kamal: $42

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F(x, y) = x2 + y2 + 4x − 4y, x2 + y2 ≤ 81 find the extreme values of f on the region described by the inequality.

Whitepunk [10]

Take partial derivatives and set them equal to 0:

$\nabla F(x,y)=\langle2x+4,2y-4\rangle=\mathbf 0$

We find one critical point within the boundary of the disk at $(x,y)=(-2,2)$ . The Hessian matrix for this function is

$\mathbf H(x,y)=\begin{bmatrix}f_{xx}&f_{xy}\\f_{yx}&f_{yy}\end{bmatrix}=\begin{bmatrix}2&0\\0&2\end{bmatrix}$

which is positive definite, and incidentally independent of $x$ and $y$ , so $F(x,y)$ attains a minimum $F(-2,2)=-8$ .

Meanwhile, we can parameterize the boundary by $\mathbf r(t)=\langle9\cos t,9\sin t\rangle$ with $0\le t\le2\pi$ , which gives

$F(x,y)=F(x(t),y(t))=f(t)=81\cos^2t+81\sin^2t+36\cos t-36\sin t=81+36(\cos t-\sin t)$

with critical points at

$f'(t)=0\implies 36(-\sin t-\cos t)=0\implies\sin t+\cos t=0\implies t=\dfrac{3\pi}4,\dfrac{7\pi}4$

At these points, we get

$f\left(\dfrac{3\pi}4\right)=81-36\sqrt2\approx30.0883$
$f\left(\dfrac{7\pi}4\right)=81+36\sqrt2\approx131.9117$

so we attain a maximum only when $t=\dfrac{7\pi}4$ , which translates to $(x,y)=\left(\dfrac9{\sqrt2},-\dfrac9{\sqrt2}\right)$ .

3 0

2 years ago

Jan began with 5/6 pound of modeling clay she used 1/5 of the clay to make decorative magnets. She divided the remaining clay in

lawyer [7]

Starting weight: 5/6 lb. Of this, Jan used 1/5, which would be (1/5)(5/6) lb,
or 1/6 lb, leaving 4/6 lb, or 2/3 lb. unused.

2/3 lb
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1/12 lb/portion.

5 0

2 years ago

Andrei wants to fill a glass tank with marbles, and then fill the remaining space with water. WWW represents the volume of water

andre [41]

Answer:

32 Liters

Step-by-step explanation:

In the glass tank:

W = represents the volume of water Andrei uses (in liters)

n =Number of marbles

Given that: $W=32-0.05n$

The volume of the glass tank is the volume of the water in the tank plus the total volume of n marbles added.

Therefore:

$W+0.05n=32$

Volume of the tank =32 Liters

6 0

2 years ago

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Compute the least-squares regression line for predicting y from a given the following summary statistics. Round final answers to

qwelly [4]

Answer: Regression line equation: $\hat{y}=-1.008x+39.1704$

Step-by-step explanation:

Equation of least-squares regression line for predicting y :

$\hat{y}=b_1x+b_o$

, where $\text{Slope} (b_1)=r\dfrac{s_y}{s_x}$ , $\text{intercept}(b_0)=\bar{y}-b_1\bar{x}$

Given: $\bar{x}=8.8,\ s_x=1.5,\ s_y=1.8,\ \bar{y}=30.3,\ r=-0.84$

Then,

$b_1=(-0.84)\dfrac{ 1.8}{ 1.5}\\\\\Rightarrow\ b_1=-1.008$

Now,

$b_0=30.3-(-1.008)(8.8)=30.3+8.8704\\\\\Rightarrow\ b_0=39.1704$

Then, Regression line equation: $\hat{y}=-1.008x+39.1704$

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2 years ago

The figure below shows a line graph and two shaded triangles that are similar:Which statement about the slope of the line is tru

zzz [600]

Here is something to keep in mind.
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so personally would have to go with -4
because the x-axis is by 4 each time. and this slope is going downward.

your answer will be D

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2 years ago

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