The difference of 3 times a number and 7 is written how ?

Mathematics

1 answer:

viktelen [127]3 years ago

5 0

3x-7 or Three x minus seven

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Betsy participates in a scavenger hunt that requires her to retrieve items from 4 locations. The locations are on a map with the

Andreas93 [3]

Answer:

240 yd

Step-by-step explanation:

Let A, B, C, and D represent location 1, location 2, location 3, and location 4 respectively.

Consider the figure in the attached file.

We need to find the total distance traveled by Betsy.

The distance covered by Betsy is

length of segment AB length of segment BC length of segment CD length of segment DA.

To find the distance AB, we need to find the distance from A to B on y-axis.

So, length of segment AB units

To find the distance BC, we need to find the distance from B to C on x-axis.

So, length of segment BC units

To find the distance CD, we need to find the distance from C to D on y-axis.

So, length of segment CD units

To find the distance DA, we need to find the distance from D to A on x-axis.

So, length of segment DA units

Hence, the total distance covered is units

It is given that 1 unit equals 10 yd, so distance traveled by Besty is yd

3 0

3 years ago

Calculus 3 chapter 16

o-na [289]

Evaluate $\vec F$ at $\vec r$ :

$\vec F(x,y,z) = x\,\vec\imath + y\,\vec\jmath + xy\,\vec k \\\\ \implies \vec F(\vec r(t)) = \vec F(\cos(t), \sin(t), t) = \cos(t)\,\vec\imath + \sin(t)\,\vec\jmath + \sin(t)\cos(t)\,\vec k$

Compute the line element $d\vec r$ :

$d\vec r = \dfrac{d\vec r}{dt} dt = \left(-\sin(t)\,\vec\imath+\cos(t)\,\vec\jmath+\vec k\bigg) \, dt$

Simplifying the integrand, we have

$\vec F\cdot d\vec r = \bigg(-\cos(t)\sin(t) + \sin(t)\cos(t) + \sin(t)\cos(t)\bigg) \, dt \\ ~~~~~~~~= \sin(t)\cos(t) \, dt \\\\ ~~~~~~~~= \dfrac12 \sin(2t) \, dt$

Then the line integral evaluates to

$\displaystyle \int_C \vec F\cdot d\vec r = \int_0^\pi \frac12\sin(2t)\,dt \\\\ ~~~~~~~~ = -\frac14\cos(2t) \bigg|_{t=0}^{t=\pi} \\\\ ~~~~~~~~ = -\frac14(\cos(2\pi)-\cos(0)) = \boxed{0}$