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3 years ago

I need help with the whole problem. Please help.

Mathematics

1 answer:

xeze [42]3 years ago

6 0

It's a little weird because area of a triangle is always 1/2 bh it doesn't ask for units
A)1/2 bh (put numbers in unit of feet)
B)asks to find area using A (like you know area in unit of square feet )( every
square feet is 144 square inch)
C)1/2*3*2.2=1.1*3=3.3 square inch

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Sketch the domain D bounded by y = x^2, y = (1/2)x^2, and y=6x. Use a change of variables with the map x = uv, y = u^2 (for u ?

cluponka [151]

Under the given transformation, the Jacobian and its determinant are

$\begin{cases}x=uv\\y=u^2\end{cases}\implies J=\begin{bmatrix}v&u\\2u&0\end{bmatrix}\implies|\det J|=2u^2$

so that

$\displaystyle\iint_D\frac{\mathrm dx\,\mathrm dy}y=\iint_{D'}\frac{2u^2}{u^2}\,\mathrm du\,\mathrm dv=2\iint_{D'}\mathrm du\,\mathrm dv$

where $D'$ is the region $D$ transformed into the $u$ - $v$ plane. The remaining integral is the twice the area of $D'$ .

Now, the integral over $D$ is

$\displaystyle\iint_D\frac{\mathrm dx\,\mathrm dy}y=\left\{\int_0^6\int_{x^2/2}^{x^2}+\int_6^{12}\int_{x^2/2}^{6x}\right\}\frac{\mathrm dx\,\mathrm dy}y$

but through the given transformation, the boundary of $D'$ is the set of equations,

$\begin{array}{l}y=x^2\implies u^2=u^2v^2\implies v^2=1\implies v=\pm1\\y=\frac{x^2}2\implies u^2=\frac{u^2v^2}2\implies v^2=2\implies v=\pm\sqrt2\\y=6x\implies u^2=6uv\implies u=6v\end{array}$

We require that $u>0$ , and the last equation tells us that we would also need $v>0$ . This means $1\le v\le\sqrt2$ and $0$ , so that the integral over $D'$ is

$\displaystyle2\iint_{D'}\mathrm du\,\mathrm dv=2\int_1^{\sqrt2}\int_0^{6v}\mathrm du\,\mathrm dv=\boxed6$

4 0

3 years ago

If a test consists of ten multiple choice questions with each permitting a possible answers. How many ways are there in which a

dangina [55]

The question isn't correctly given, a possible format is in the comment below, however, the explanation will cover then concept which can be applied to different but similar

Answer:

10048576 ways

Step-by-step explanation:

We are given a question, from which we can choose aby of 4 options, this gives ua 4 possible choices for 1.

This will also apply if we have more than 1 question with the same number of options.

This can be called the product rule, as each possibility is the same of each question given :

Therefore, given 10 questions:

. We have

4 * 4 * 4 * 4 * 4 * 4 * 4 * 4 * 4 * 4 = 4^10 = 10048576 ways

5 0

3 years ago

What equation can you not use to find the answer to question 1 a and b

o-na [289]

I think the third one on both part a and b can't be used to find the answer

3 0

3 years ago

Nine more than four times a number is the same as one less than twice the number find the number

klio [65]

4x + 9 = 2x - 1
4x - 2x = -1 - 9
2x = -10
x = -10/2
x = -5 <===

8 0

3 years ago

Line segment AB has endpoints A(1, 2) and B(5, 3). Find the coordinates of the point that divides the line segment directed from

Tanzania [10]

Answer:

The coordinates of the point that divides the line segment directed from A to B in the ratio of 1:3 is P ( 2 , 2.25 ).

Step-by-step explanation:

Given:

Let Point P ( x , y ) divides Segment Am in the ratio 1 : 3 = m : n (say)

point A( x₁ , y₁) ≡ ( 1 , 2)

point B( x₂ , y₂) ≡ (5 , 3)

To Find:

point P( x , y) ≡ ?

Solution:

IF a Point P divides Segment AB internally in the ratio m : n, then the Coordinates of Point P is given by Section Formula as

$x=\frac{(mx_{2} +nx_{1}) }{(m+n)}\\ \\and\\\\y=\frac{(my_{2} +ny_{1}) }{(m+n)}\\\\$

Substituting the values we get

$x=\frac{(1\times 5 +3\times 1) }{(1+3)}\\ \\and\\\\y=\frac{(1\times 3 +3\times 2) }{(1+3)}\\\\\therefore x = \frac{8}{4}=2 \\\\and\\\therefore y = \frac{9}{4}=2.25 \\\\\\\therefore P(x,y) = (2 , 2.25)$

The coordinates of the point that divides the line segment directed from A to B in the ratio of 1:3 is P ( 2 , 2.25 ).

7 0

3 years ago

Read 2 more answers