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3 years ago

Plz help with this I don’t know what to do

Mathematics

2 answers:

WITCHER [35]3 years ago

8 0

Answers:

Row One: 9, 15
Row Two: 8, 16, 20

Input the numbers only in each box. So that means you won't type in a comma.

The least common denominator is <u>12</u>

=======================================================

Explanation:

Your teacher wants you to list the multiples of each denominator.

The multiples of 3 are: 3, 6, 9, 12, 15
The multiples of 4 are: 4, 8, 12, 16, 20

The values in bold are what will go in the boxes in those first two rows.

The least common denominator is 12 because it is the smallest thing found in common in the two lists above. In other words, 12 is the LCM (least common multiple) of 3 and 4. Note how 3*4 = 12. This works because 3 and 4 do not have any common factors between them other than 1.

The LCD (least common denominator) is the LCM of the denominators. The LCD is useful for when you want to add or subtract fractions. The denominators must be the same for you be able to add or subtract them.

kozerog [31]3 years ago

3 0

Answer:

Just guessing here but would the bottom be 4,8,12,16,20 maybe since it is going by 4 then you do the same for the top since it is going by 3

Step-by-step explanation:

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3 years ago

Select the quadratic that has roots x = 8 and x = -5.

Mars2501 [29]

$\text{ The roots are}~ \alpha = 8~ \text{and}~ \beta = -5\\\\\text{Equation for the given roots,}\\\\x^2 -(\alpha +\beta )x +\alpha \beta = 0\\\\\implies x^2 -(8-5)x + 8(-5)=0\\\\\implies x^2 -3x -40=0\\\\\text{Hence, the answer is option B}$

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2 years ago

Kim rolls a six-sided number cube labeled from 1 to 6.

makvit [3.9K]

The answer is A) 2/3

5 0

3 years ago

The coordinate plane shows the positions of different places in a town. Each unit on the graph is equal to 1 block. Match the pa

Karolina [17]

Home is located at the point (-5, 5)

The park is located at the point (-2, 3)

Apply the distance formula

$d = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}\\\\d = \sqrt{(-5-(-2))^2 + (5-3)^2}\\\\d = \sqrt{(-5+2)^2 + (5-3)^2}\\\\d = \sqrt{(-3)^2 + (2)^2}\\\\d = \sqrt{9 + 4}\\\\d = \sqrt{13}\\\\d \approx 3.6055513\\\\$

When rounding to the nearest whole number, we get 4. This is the approximate distance (in blocks) from home to the park. I'm not sure why "4 blocks" isn't listed as a possible distance, so there may be a typo somewhere.

You'll apply this idea to the other pairs of points to find the other distances.

8 0

3 years ago

Calculate s f(x, y, z) ds for the given surface and function. g(r, θ) = (r cos θ, r sin θ, θ), 0 ≤ r ≤ 4, 0 ≤ θ ≤ 2π; f(x, y, z)

Triss [41]

$g(r,\theta)=(r\cos\theta,r\sin\theta,\theta)\implies\begin{cases}g_r=(\cos\theta,\sin\theta,0)\\g_\theta=(-r\sin\theta,r\cos\theta,1)\end{cases}$

The surface element is

$\mathrm dS=\|g_r\times g_\theta\|\,\mathrm dr\,\mathrm d\theta=\sqrt{1+r^2}\,\mathrm dr\,\mathrm d\theta$

and the integral is

$\displaystyle\iint_Sx^2+y^2\,\mathrm dS=\int_0^{2\pi}\int_0^4((r\cos\theta)^2+(r\sin\theta)^2)\sqrt{1+r^2}\,\mathrm dr\,\mathrm d\theta$

$=\displaystyle2\pi\int_0^4r^2\sqrt{1+r^2}\,\mathrm dr=\frac\pi4(132\sqrt{17}-\sinh^{-1}4)$

###

To compute the last integral, you can integrate by parts:

$u=r\implies\mathrm du=\mathrm dr$

$\mathrm dv=r\sqrt{1+r^2}\,\mathrm dr\implies v=\dfrac13(1+r^2)^{3/2}$

$\displaystyle\int_0^4r^2\sqrt{1+r^2}\,\mathrm dr=\frac r3(1+r^2)^{3/2}\bigg|_0^4-\frac13\int_0^4(1+r^2)^{3/2}\,\mathrm dr$

For this integral, consider a substitution of

$r=\sinh s\implies\mathrm dr=\cosh s\,\mathrm ds$

$\displaystyle\int_0^4(1+r^2)^{3/2}\,\mathrm dr=\int_0^{\sinh^{-1}4}(1+\sinh^2s)^{3/2}\cosh s\,\mathrm ds$

$\displaystyle=\int_0^{\sinh^{-1}4}\cosh^4s\,\mathrm ds$

$=\displaystyle\frac18\int_0^{\sinh^{-1}4}(3+4\cosh2s+\cosh4s)\,\mathrm ds$

and the result above follows.

4 0

4 years ago