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3 years ago

The volume formula for a triangular prism is?

Mathematics

1 answer:

timofeeve [1]3 years ago

5 0

Its half × base × height × length

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Sin(x2 y2 da r , where r is the region in the first quadrant between the circles with center the origin and radii 1 and 5

Rudik [331]

I assume there's a plus sign missing above...

Convert to polar coordinates, using

$\begin{cases}x(r,\theta)=r\cos\theta\\y(r,\theta)=r\sin\theta\end{cases}$

Then the Jacobian is

$\dfrac{\partial(x,y)}{\partial(r,\theta)}=\begin{vmatrix}x_r&y_r\\x_\theta&y_\theta\end{vmatrix}=\begin{vmatrix}\cos\theta&\sin\theta\\r\sin\theta&-r\cos\theta\end{vmatrix}=-r$

Then

$\mathrm dA=\mathrm dx\,\mathrm dy=|-r|\,\mathrm dr\,\mathrm d\theta=r\,\mathrm dr\,\mathrm d\theta$

so the integral can be written as

$\displaystyle\iint_R\sin(x^2+y^2)\,\mathrm dA=\int_0^{\pi/2}\int_1^5r\sin(r^2)\,\mathrm dr\,\mathrm d\theta$

Let $s=r^2$ , so that $\dfrac{\mathrm ds}2=r\,\mathrm dr$ .

$\displaystyle\frac12\int_0^{\pi/2}\int_1^{25}\sin s\,\mathrm ds\,\mathrm d\theta=-\frac12(\cos25-\cos1)\int_0^{\pi/2}\mathrm d\theta=\frac\pi4(\cos1-\cos25)$

3 0

3 years ago

Is one for greater than listen or equal to 0.4

rjkz [21]

Order 3/8, 3/7, and 3/9 from least to greatest without writing equivalent fractions with a common denominator explain your Strategy

3/9 3/8 3/7

The greater the denominator, the smaller the pieces are. Thus, numbers with equivalent numerators but smaller denominators will be larger than those with larger denominators.

Is 0.7 greater than less than equal to 7/9

Less than. 7/9 is 0.77777....

8 0

3 years ago

Find the properties of each Quadratic Function

vagabundo [1.1K]

Answer:

Step-by-step explanation:

1) UP

2) (2, -4)

3) x = 2

4) minimum

5) y = -4

6) Real numbers

7) -∞ ≤ x ≤ ∞, y≥ -4

8) y = -3

9) x = -2, x = 6

10) ∞

4 0

3 years ago

A woman a walked 12km at 3km/hr and cycled 18km at 9km/hr. what is her average speed for the whole journey.

Deffense [45]

Answer:

5 km/h

Step-by-step explanation:

7 0

3 years ago

Th sum of three numbers is 64. The second number is 3 more than the first. The third number is

ladessa [460]

<span>Three numbers can be defined as x, y, and z.
x + y + z = 64
y = x+3
z = 2x - 11
.
substitute for y and z
x + (x+3) + (2x-11) = 64
4x -8 = 64
4x = 72

x = 18
.
y = x+3 = 21
z = 2x -11 = 2(18) -11 = 36-11 = 25
.
x + y + z = 18 + 21 + 25 = 64
Correct.
.
Answer: The three numbers are 18, 21, and 25.</span>

8 0

3 years ago