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Montano1993 [528]
3 years ago
10

Find the value of 0.34 × 9

Mathematics
2 answers:
pogonyaev3 years ago
8 0

Answer:

The answer is 3.06.

Veronika [31]3 years ago
8 0

Answer:

3.06

Step-by-step explanation:

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Use the given transformation x=4u, y=3v to evaluate the integral. ∬r4x2 da, where r is the region bounded by the ellipse x216 y2
exis [7]

The Jacobian for this transformation is

J = \begin{bmatrix} x_u & x_v \\ y_u & y_v \end{bmatrix} = \begin{bmatrix} 4 & 0 \\ 0 & 3 \end{bmatrix}

with determinant |J| = 12, hence the area element becomes

dA = dx\,dy = 12 \, du\,dv

Then the integral becomes

\displaystyle \iint_{R'} 4x^2 \, dA = 768 \iint_R u^2 \, du \, dv

where R' is the unit circle,

\dfrac{x^2}{16} + \dfrac{y^2}9 = \dfrac{(4u^2)}{16} + \dfrac{(3v)^2}9 = u^2 + v^2 = 1

so that

\displaystyle 768 \iint_R u^2 \, du \, dv = 768 \int_{-1}^1 \int_{-\sqrt{1-v^2}}^{\sqrt{1-v^2}} u^2 \, du \, dv

Now you could evaluate the integral as-is, but it's really much easier to do if we convert to polar coordinates.

\begin{cases} u = r\cos(\theta) \\ v = r\sin(\theta) \\ u^2+v^2 = r^2\\ du\,dv = r\,dr\,d\theta\end{cases}

Then

\displaystyle 768 \int_{-1}^1 \int_{-\sqrt{1-v^2}}^{\sqrt{1-v^2}} u^2\,du\,dv = 768 \int_0^{2\pi} \int_0^1 (r\cos(\theta))^2 r\,dr\,d\theta \\\\ ~~~~~~~~~~~~ = 768 \left(\int_0^{2\pi} \cos^2(\theta)\,d\theta\right) \left(\int_0^1 r^3\,dr\right) = \boxed{192\pi}

3 0
2 years ago
Write an algebraic
MatroZZZ [7]

Answer:

x = 115 - p

Step-by-step explanation:

generally in algebra you will use the letter "x" to represent a value you do not know, so it wants an algebraic expression for "p subtracted from 115", this can be rewritten as 115 - p. So the unknown value  "x" is equal to 115 - p.

6 0
3 years ago
Write an equation of a parabola that passes through the point (2,4) with vertex (-1,-1) in vertex form.
quester [9]
An applicable equation of a vertical parabola in vertex form is:

y-k = a(x-h)^2

Let x=2, y=4, h=-1 and k=-1, where (h,k) is the vertex.  Then,

4-(-1) = a(2-[-1])^2, which becomes 5 = a(9).  Therefore, a = 5/9, and the 
equation of the parabola is

y+1 = (5/9)(x+1)
8 0
3 years ago
Which of the following is equivalent to the polynomial below ? X^2-8x+19
andrey2020 [161]

Answer:

C, I believe.

7 0
3 years ago
Read 2 more answers
Fifteen more than half a number is 9
rusak2 [61]

For this case, the first thing we must do is define a variable.

We have then:

x: unknown number

We now write the equation that models the problem:

(\frac{1}{2}) x + 15 = 9

From here, we clear the value of x.

We multiply both sides of the equation by 2:

(\frac{2}{2}) x + 2 (15) = 2 (9)\\x + 30 = 18

We subtract 30 on both sides of the equation:

x + 30 - 30 = 18 - 30\\x = -12

Answer:

The value of the unknown number is given by:

x = -12

6 0
3 years ago
Read 2 more answers
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