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Lady bird [3.3K]
3 years ago
6

Which number is a factor of 20, but not a multiple of 2? 12, 5, 10 or 4?

Mathematics
2 answers:
melisa1 [442]3 years ago
6 0
5 is your answer

20/4 = 5 however,

2 x 2.5 = 5 (it doesn't work, cannot have decimals)

so 5 is your answer

hope this helps
tia_tia [17]3 years ago
6 0
Factors of 20 are: 1,20:2,10:4,5.
So 1 or 20 is that number
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What is the GFC of 28 and 72
Ivan

the greatest common factor of these numbers is 2

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3 years ago
Find the greatest common factor 32a^3b^2, 44ab^3 and 40a^2b
Ronch [10]
\32a^3b^2 \ , \  44ab^3 \ , \  40a^2b\\


\text {Taking out common factor : } \\ \\
4ab(8a^2b) + 4ab(11b^2) + 4ab(10a)

\text { greatest common factor =  } 4ab
3 0
3 years ago
Using polar coordinates, evaluate the integral which gives the area which lies in the first quadrant below the line y=5 and betw
vfiekz [6]

First, complete the square in the equation for the second circle to determine its center and radius:

<em>x</em> ² - 10<em>x</em> + <em>y</em> ² = 0

<em>x</em> ² - 10<em>x</em> + 25 + <em>y </em>² = 25

(<em>x</em> - 5)² + <em>y</em> ² = 5²

So the second circle is centered at (5, 0) with radius 5, while the first circle is centered at the origin with radius √100 = 10.

Now convert each equation into polar coordinates, using

<em>x</em> = <em>r</em> cos(<em>θ</em>)

<em>y</em> = <em>r</em> sin(<em>θ</em>)

Then

<em>x</em> ² + <em>y</em> ² = 100   →   <em>r </em>² = 100   →   <em>r</em> = 10

<em>x</em> ² - 10<em>x</em> + <em>y</em> ² = 0   →   <em>r </em>² - 10 <em>r</em> cos(<em>θ</em>) = 0   →   <em>r</em> = 10 cos(<em>θ</em>)

<em>y</em> = 5   →   <em>r</em> sin(<em>θ</em>) = 5   →   <em>r</em> = 5 csc(<em>θ</em>)

See the attached graphic for a plot of the circles and line as well as the bounded region between them. The second circle is tangent to the larger one at the point (10, 0), and is also tangent to <em>y</em> = 5 at the point (0, 5).

Split up the region at 3 angles <em>θ</em>₁, <em>θ</em>₂, and <em>θ</em>₃, which denote the angles <em>θ</em> at which the curves intersect. They are

<em>θ</em>₁ = 0 … … … by solving 10 = 10 cos(<em>θ</em>)

<em>θ</em>₂ = <em>π</em>/6 … … by solving 10 = 5 csc(<em>θ</em>)

<em>θ</em>₃ = 5<em>π</em>/6  … the second solution to 10 = 5 csc(<em>θ</em>)

Then the area of the region is given by a sum of integrals:

\displaystyle \frac12\left(\left\{\int_0^{\frac\pi6}+\int_{\frac{5\pi}6}^{2\pi}\right\}\left(10^2-(10\cos(\theta))^2\right)\,\mathrm d\theta+\int_{\frac\pi6}^{\frac{5\pi}6}\left((5\csc(\theta))^2-(10\cos(\theta))^2\right)\,\mathrm d\theta\right)

=\displaystyle 50\left\{\int_0^{\frac\pi6}+\int_{\frac{5\pi}6}^{2\pi}\right\} \sin^2(\theta)\,\mathrm d\theta+\frac12\int_{\frac\pi6}^{\frac{5\pi}6}\left(25\csc^2(\theta) - 100\cos^2(\theta)\right)\,\mathrm d\theta

To compute the integrals, use the following identities:

sin²(<em>θ</em>) = (1 - cos(2<em>θ</em>)) / 2

cos²(<em>θ</em>) = (1 + cos(2<em>θ</em>)) / 2

and recall that

d(cot(<em>θ</em>))/d<em>θ</em> = -csc²(<em>θ</em>)

You should end up with an area of

=\displaystyle25\left(\left\{\int_0^{\frac\pi6}+\int_{\frac{5\pi}6}^{2\pi}\right\}(1-\cos(2\theta))\,\mathrm d\theta-\int_{\frac\pi6}^{\frac{5\pi}6}(1+\cos(2\theta))\,\mathrm d\theta\right)+\frac{25}2\int_{\frac\pi6}^{\frac{5\pi}6}\csc^2(\theta)\,\mathrm d\theta

=\boxed{25\sqrt3+\dfrac{125\pi}3}

We can verify this geometrically:

• the area of the larger circle is 100<em>π</em>

• the area of the smaller circle is 25<em>π</em>

• the area of the circular segment, i.e. the part of the larger circle that is bounded below by the line <em>y</em> = 5, has area 100<em>π</em>/3 - 25√3

Hence the area of the region of interest is

100<em>π</em> - 25<em>π</em> - (100<em>π</em>/3 - 25√3) = 125<em>π</em>/3 + 25√3

as expected.

3 0
3 years ago
An investor invests $2,500 into a mutual fund and earns 5.75% on the principle for each of three years. How much interest has ac
HACTEHA [7]

Answer:

Interest in 3 years = $456.52

Step-by-step explanation:

As we know the the formula of compound interest

Total amount =  A(1+\frac{r}{n})^{nt}

Here n = number of times amount is compounded

r = rate of interest

t = period

Here A = $2500

r = 0.0575

n = 1 (compounded annually)

t = 3 years

Therefore amount after 3 years

P=2500(1+\frac{.0575}{1})^{3}

P =2500(1.0575)³

  = 2500×1.18

  = $2956.52

We have to calculate the interest then

Interest = $2956.52-$2500 = $456.52

So after 3 years interest gained = $456.52

8 0
3 years ago
Read 2 more answers
HELP! WILL GIVE BRAINLIEST!
goblinko [34]

Answer:

(2x+16) + (x) = 180

Step-by-step explanation:

The opposite angles of a quadrilateral inscribed inside a circle will be supplementary angles, meaning that A+C=180, and B+D=180. A+C is not given in the answers below, but B+D is, so that is the correct answer.

Hope this helps! Please give brainliest!!

6 0
3 years ago
Read 2 more answers
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