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3 years ago

A=(v+w)(k-x), for x I would appreciate it if you included the steps for solving it too!!!!

Mathematics

1 answer:

Anna71 [15]3 years ago

5 0

Step-by-step explanation:

$a=(v+w)(k-x)$

$(k - x) = \frac{a}{(v + w)}$

$x = k - \frac{a}{v + w}$

$x = \frac{kv + kw - a}{v + w}$

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7. Find all geometric sequences such that the sum of the first two terms is 24 and the sum of the first

sesenic [268]

Answer:

Step-by-step explanation:

Let the first term is n, then the second term must be an where a is a common ratio, and the third term is a^2 n

so, n + an = 24

n + an + a^2 n = 26

solve for a, then solve for n

6 0

3 years ago

Y less than x minus 3

MariettaO [177]

I assume you want the expression to this so it would be x-y-3

6 0

4 years ago

Graph y > -1/3x+5 <img src="https://tex.z-dn.net/?f=y%20%3E%20%20-%20%20%5Cfrac%7B1%7D%7B%203%20%7D%20x%20%2B%205" id="Tex

ad-work [718]

Explanation:

The function is $y>-\frac{1}{3} x+5$

To graph the function, let us find the x and y intercepts.

To find x-intercept, let us substitute y=0 in the function $y>-\frac{1}{3} x+5$

$\begin{aligned}0 &=-\frac{1}{3} x+5 \\-5 &=-\frac{1}{3} x \\x &=15\end{aligned}$

Thus, the x-intercept is $(15,0)$

To find the y-intercept, let us substitute x=0, we get,

$\begin{aligned}&y=-\frac{1}{3}(0)+5\\&y=5\end{aligned}$

Thus, the y-intercept is $(0,5)$

The graph has no asymptotes.

To plot the points in the graph, we need to substitute the values for x in the function $y>-\frac{1}{3} x+5$ , to find the y-values.

The points are $(-2,5.667),(-1,5.333),(1,4.667),(2,4.333),(3,4)$ . The image of the graph and table is attached below:

6 0

3 years ago

37. Verify Green's theorem in the plane for f (3x2- 8y2) dx + (4y - 6xy) dy, where C is the boundary of the

Nastasia [14]

I'll only look at (37) here, since

• (38) was addressed in 24438105

• (39) was addressed in 24434477

• (40) and (41) were both addressed in 24434541

In both parts, we're considering the line integral

$\displaystyle \int_C (3x^2-8y^2)\,\mathrm dx + (4y-6xy)\,\mathrm dy$

and I assume C has a positive orientation in both cases

(a) It looks like the region has the curves y = x and y = x ² as its boundary***, so that the interior of C is the set D given by

$D = \left\{(x,y) \mid 0\le x\le1 \text{ and }x^2\le y\le x\right\}$

• Compute the line integral directly by splitting up C into two component curves,

C₁ : x = t and y = t ² with 0 ≤ t ≤ 1

C₂ : x = 1 - t and y = 1 - t with 0 ≤ t ≤ 1

Then

$\displaystyle \int_C = \int_{C_1} + \int_{C_2} \\\\ = \int_0^1 \left((3t^2-8t^4)+(4t^2-6t^3)(2t))\right)\,\mathrm dt \\+ \int_0^1 \left((-5(1-t)^2)(-1)+(4(1-t)-6(1-t)^2)(-1)\right)\,\mathrm dt \\\\ = \int_0^1 (7-18t+14t^2+8t^3-20t^4)\,\mathrm dt = \boxed{\frac23}$

*** Obviously this interpretation is incorrect if the solution is supposed to be 3/2, so make the appropriate adjustment when you work this out for yourself.

• Compute the same integral using Green's theorem:

$\displaystyle \int_C (3x^2-8y^2)\,\mathrm dx + (4y-6xy)\,\mathrm dy = \iint_D \frac{\partial(4y-6xy)}{\partial x} - \frac{\partial(3x^2-8y^2)}{\partial y}\,\mathrm dx\,\mathrm dy \\\\ = \int_0^1\int_{x^2}^x 10y\,\mathrm dy\,\mathrm dx = \boxed{\frac23}$

(b) C is the boundary of the region

$D = \left\{(x,y) \mid 0\le x\le 1\text{ and }0\le y\le1-x\right\}$

• Compute the line integral directly, splitting up C into 3 components,

C₁ : x = t and y = 0 with 0 ≤ t ≤ 1

C₂ : x = 1 - t and y = t with 0 ≤ t ≤ 1

C₃ : x = 0 and y = 1 - t with 0 ≤ t ≤ 1

Then

$\displaystyle \int_C = \int_{C_1} + \int_{C_2} + \int_{C_3} \\\\ = \int_0^1 3t^2\,\mathrm dt + \int_0^1 (11t^2+4t-3)\,\mathrm dt + \int_0^1(4t-4)\,\mathrm dt \\\\ = \int_0^1 (14t^2+8t-7)\,\mathrm dt = \boxed{\frac53}$

• Using Green's theorem:

$\displaystyle \int_C (3x^2-8y^2)\,\mathrm dx + (4y-6xy)\,\mathrm dx = \int_0^1\int_0^{1-x}10y\,\mathrm dy\,\mathrm dx = \boxed{\frac53}$

4 0

3 years ago

The dot plot below shows how many customers purchased different numbers of shirts at a sale last weekend.

scoray [572]

Answer:

the answer is 1.16 shirts

Step-by-step explanation:

the mean absolute deviation is found by finding the average of the difference between each data point and the mean of the data.

1st...find the mean of the data by adding all the numbers according to the data plotted and dividing the by the numbers listed; which in this case is 10

1 +2+ 2+ 3+ 3+ 3+ 4+ 4+ 5+ 6 = 3.3

mean is 3.3

then find the difference between the mean and each data point

Data Point = 1 2 2 3 3 3 4 4 5 6

Difference from mean = 2.3 1.3 1.3 0.3 0.3 0.3 0.7 0.7 1.7 2.7

Find the average of these differences by adding the (differences from Mean) by 10

2.3 + 1.3 + 1.3 + 0.3 + 0.3 + 0.3 + 0.7 + 0.7 + 1.7 + 2.7

the mean absolute deviations is 1.16 shirts

4 0

3 years ago

Read 2 more answers