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pickupchik [31]
2 years ago
14

Translate the phrase into an algebraic explanation. the quotient of x and 5​

Mathematics
1 answer:
horsena [70]2 years ago
4 0

Answer: \frac{x}{5} or x ÷ 5

Step-by-step explanation:

The quotient of x and 5 can be represented as \frac{x}{5} or x ÷ 5

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Suppose F⃗ (x,y)=(x+3)i⃗ +(6y+3)j⃗ . Use the fundamental theorem of line integrals to calculate the following.
Scorpion4ik [409]

In order to use the fundamental theorem of line integrals, you need to find a scalar potential function - that is, a scalar function <em>f(x, y)</em> for which

grad <em>f(x, y)</em> = <em>F</em><em>(x, y)</em>

This amounts to solving for <em>f</em> such that

∂<em>f</em>/d<em>x</em> = <em>x</em> + 3

∂<em>f</em>/∂<em>y</em> = 6<em>y</em> + 3

Integrating both sides of the first equation with respect to <em>x</em> gives

<em>f</em> = 1/2 <em>x</em> ^2 + 3<em>x</em> + <em>g(y)</em>

Differentiating with respect to <em>y</em> gives

∂<em>f</em>/∂<em>y</em> = d<em>g</em>/d<em>y</em> = 6<em>y</em> + 3

Solving for <em>g</em> gives

<em>g</em> = ∫ (6<em>y</em> + 3) d<em>y</em> = 3<em>y</em> ^2 + 3<em>y</em> + <em>C</em>

and hence

<em>f(x, y)</em> = 1/2 <em>x</em> ^2 + 3<em>x</em> + 3<em>y</em> ^2 + 3<em>y</em> + <em>C</em>

<em />

(a) By the fundamental theorem, the integral of <em>F</em> along any path starting at the point <em>P</em> (1, 0) and ending at <em>Q</em> (3, 3) is

∫ <em>F</em><em>(x, y)</em> • d<em>r</em> = <em>f</em> (3, 3) - <em>f</em> (1, 0) = 99/2 - 7/2 = 46

(b) Now we're talking about a closed path, so the integral is simply 0. We can verify this by checking the integral over the origin-containing paths:

• From the origin to <em>P</em> :

∫ <em>F</em><em>(x, y)</em> • d<em>r</em> = <em>f</em> (1, 0) - <em>f</em> (0, 0) = 7/2 - 0 = 7/2

• From <em>Q</em> back to the origin:

∫ <em>F</em><em>(x, y)</em> • d<em>r</em> = <em>f</em> (0, 0) - <em>f</em> (3, 3) = 0 - 99/2 = -99/2

Then the total integral is 7/2 + 46 - 99/2 = 0, as expected.

6 0
3 years ago
Ini apa we jawabannya pelasee​
kupik [55]

Answer:

<h3></h3><h2><u>kualitas terjemahannya mungkin tidak bagus. Jadi lihat 2 baris terakhir jika Anda tidak mengerti.</u></h2>

Jadi jumlah derajat tidak masalah. Mereka masih akan menempuh jarak yang sama.

Karena Anda mengatakan bahwa ekspres Marina berjalan pada 40 km / jam dan kami melakukan 2 jam. 40 * 2 = 80 km. Untuk Dumai Anda melakukan hal yang sama, 48 * 2 = 96.

Marina berjalan sejauh 80 km

Dumai berjarak 96 km

8 0
3 years ago
Quiz Instructions Question 18 1 pts Mrs. McMunn gets paid $50 per hour plus an initial bonus of $100. She needs to make at least
grandymaker [24]
100 is right pick to 2 and poop
8 0
2 years ago
A wet bicycle tire leaves a trace of water on the floor. The tire has a radius of 30 \text{ cm}30 cm30, start text, space, c, m,
Annette [7]

Answer:

186 cm

Step-by-step explanation:

Since the bicycle wheel is making a rotation and not a revolution, the bicycle wheel is at one point.

The length of the trace of water left on the floor is simply the circumference of the bicycle wheel

Circumference = 2πR

where R = radius of the bicycle wheel

and π = pie

Circumference = 2 × (22/7) × 30 = 188.57143 cm

7 0
3 years ago
Read 2 more answers
Use the equation e/5 = 30 to solve the following problem,
kumpel [21]

Answer:

Step-by-step explanation:

300

4

6 0
3 years ago
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