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2 years ago

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A cargo ship left port A and is headed across the ocean to shipping port B. After one month, the ship stopped at a refueling sta

tion along a path described by a vector with components LeftAngleBracket 14, 23 RightAngleBracket. After another month, on the same path, the ship reached port B, twice the distance from port A as the fueling station.
What are the characteristics of the vector representing the path of the ship?

components:LeftAngleBracket 7, 11.5 RightAngleBracket, magnitude: 13.46
components:LeftAngleBracket 7, 11.5 RightAngleBracket, magnitude: 53.85
components:LeftAngleBracket 28, 46 RightAngleBracket, magnitude: 13.46
components:LeftAngleBracket 28, 46 RightAngleBracket, magnitude: 53.85

2 answers:

Sergeu [11.5K]2 years ago

8 0

Answer:

D

Step-by-step explanation:

Edge 2020

Yuri [45]2 years ago

8 0

Answer:

d

Step-by-step explanation:

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When a number is decreased by 8.5%, the result is 33. What is the original number to the nearest tenth?

Reil [10]

Answer:

Step-by-step explanation:

Let the original number be x

(100-8.5)% of x = 33

91.5% of x = 33

$\frac{91.5}{100}x=33\\\\x=33*\frac{100}{91.5}\\\\x=36.07$

x= 36.1

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2 years ago

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 $(x,y)=\left(\dfrac9{\sqrt2},-\dfrac9{\sqrt2}\right)$ .

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2 years ago

When p2 – 4p is subtracted from p2 + p – 6, the result is . To get p – 9, subtract from this result.

DochEvi [55]

Answer:

When p2 – 4p is subtracted from p2 + p – 6, the result is:

p2+p-6-(p2-4p)=p2+p-6-p2+4p=5p-6

To get p – 9, subtract from this result x:

5p-6-x=p-9

Solving for x:

5p-6-x+x-p+9=p-9+x-p+9

4p+3=x

x=4p+3

Answer:

1) When p2 – 4p is subtracted from p2 + p – 6, the result is 5p-6

2) To get p – 9, subtract from this result 4p+3

Step-by-step explanation:

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2 years ago

The speed of light is about 1.86×10^5 miles per second. The star Sirius is about 5.062×10^13 miles from Earth. About how many se

marysya [2.9K]

Answer:

2.72 × 10^8 seconds

Step-by-step explanation:

1. Organize the given information to help you create the equation:

- Light travels 1.86 × 10^5 miles per 1 second

- Light travels 5.062 × 10^13 miles per <em>n</em> seconds

- Need to solve for <em>n</em>

2. Set up the equation (Make sure that both numerators and both denominators match units, so the seconds are either both on top or both on bottom, NOT switched):

$\frac{1.86 * 10^5}{1}$ = $\frac{5.062 * 10^1^3}{n}$

3. Cross multiply (Multiply the first fraction's numerator by the second's denominator, and vice versa. It doesn't matter what number is on which side of the = sign)

<em>n </em>× (1.86 × 10^5) = 5.062 × 10^13

4. Solve for <em>n</em> by isolating the variable and dividing.

$\frac{n (1.86 * 10^5)}{1.86 * 10^5}$ = $\frac{5.062 * 10^1^3}{1.86 * 10^5}$

<em>n</em> = $\frac{5.062 * 10^1^3}{1.86 * 10^5}$

<em>n </em>= 2.72 × 10^8 (Make sure to include the unit, seconds)

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2 years ago

Patrick has just finished building a pen for his new dog. The pen is 3 feet wider than it is long. He also built a doghouse to p

zalisa [80]

General Idea:

(i) Assign variable for the unknown that we need to find

(ii) Sketch a diagram to help us visualize the problem

(iii) Write the mathematical equation representing the description given.

(iv) Solve the equation by substitution method. Solving means finding the values of the variables which will make both the equation TRUE

Applying the concept:

Given: x represents the length of the pen and y represents the area of the doghouse

<u>Statement 1: </u>"The pen is 3 feet wider than it is long"

$Length \; of\; the \; pen = x\\ Width \; of\; the\; pen=x+3$

------

<u>Statement 2: "He also built a doghouse to put in the pen which has a perimeter that is equal to the area of its base"</u>

$Area \; of\; the\; Dog \; house=y\\ Perimeter \; of\; Dog\; house=y$

------

<u>Statement 3: "After putting the doghouse in the pen, he calculates that the dog will have 178 square feet of space to run around inside the pen."</u>

$Area \; of \; the\; Pen - Area \;of \;the\;Dog \;House=\;Space\;inside\;Pen\\ \\ x \cdot (x+3)-y=178\\ Distributing \;x\;in\;the\;left\;side\;of\;the\;equation\\ \\ x^2+3x-y=178\Rightarrow\; 1^{st}\; Equation\\$

------

<u>Statement 4: "The perimeter of the pen is 3 times greater than the perimeter of the doghouse."</u>

$Perimeter\; of\; the\; Pen=3\; \cdot \; Perimeter\; of\; the\; Dog\; House\\ \\ 2(x \; + \; x+3)=3 \cdot y\\ Combine\; like\; terms\; inside\; the\; parenthesis\\ \\ 2(2x+3)=3y\\ Distribute\; 2\; in\; the\; left\; side\; of\; the\; equation\\ \\ 4x+6=3y\\ Subtract \; 6\; and \; 3y\; on\; both\; sides\; of\; the\; equation\\ \\ 4x+6-3y-6=3y-3y-6\\ Combine\; like\; terms\\ \\ 4x-3y=-6 \Rightarrow \; \; 2^{nd}\; Equation\\$

Conclusion:

The systems of equations that can be used to determine the length and width of the pen and the area of the doghouse is given in Option B.

$178=x^2+3x-y\\ \\ -6=4x-3y$

8 0

2 years ago

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