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2 years ago

If a diameter of a circle with a circumference of 104.48 mm is reduced by 1/2,what is the circumference of the new circle?

Mathematics

1 answer:

klio [65]2 years ago

4 0

All we need to do here is divide the circumference by 2.

104.48 / 2 = 52.24

The new circumference is 52.24 mm.

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Is 5.565656... a rational number

seropon [69]

Answer:

Yes 5.565656 is a rational number

Step-by-step explanation:

How do we know?

Rational: Numbers that end and do not go on forever

Examples:

Decimals that end or repeat (in your case)

Fractions

Whole numbers

Square Roots

7 0

2 years ago

Read 2 more answers

If the probability that a person will die in the next year is 593/100000

melisa1 [442]

Answer:

99407/100000

Step-by-step explanation:

100000 - 593 = 99407

4 0

2 years ago

The baker pays $0.80 per pound for sugar and $1.25 per pound for butter. Write an expression that shows how much the baker will

alekssr [168]

X is sugar
y is butter
z is total money

$0.80x + $1.25y = z

the total money spent if the Baker bought 6 pounds of butter and 20 pounds of sugar would be $23.50.

5 0

2 years ago

Read 2 more answers

Use green's theorem to compute the area inside the ellipse x252+y2172=1. use the fact that the area can be written as ∬ddxdy=12∫

Pavel [41]

The area of the ellipse $E$ is given by

$\displaystyle\iint_E\mathrm dA=\iint_E\mathrm dx\,\mathrm dy$

To use Green's theorem, which says

$\displaystyle\int_{\partial E}L\,\mathrm dx+M\,\mathrm dy=\iint_E\left(\frac{\partial M}{\partial x}-\frac{\partial L}{\partial y}\right)\,\mathrm dx\,\mathrm dy$

( $\partial E$ denotes the boundary of $E$ ), we want to find $M(x,y)$ and $L(x,y)$ such that

$\dfrac{\partial M}{\partial x}-\dfrac{\partial L}{\partial y}=1$

and then we would simply compute the line integral. As the hint suggests, we can pick

$\begin{cases}M(x,y)=\dfrac x2\\\\L(x,y)=-\dfrac y2\end{cases}\implies\begin{cases}\dfrac{\partial M}{\partial x}=\dfrac12\\\\\dfrac{\partial L}{\partial y}=-\dfrac12\end{cases}\implies\dfrac{\partial M}{\partial x}-\dfrac{\partial L}{\partial y}=1$

The line integral is then

$\displaystyle\frac12\int_{\partial E}-y\,\mathrm dx+x\,\mathrm dy$

We parameterize the boundary by

$\begin{cases}x(t)=5\cos t\\y(t)=17\sin t\end{cases}$

with $0\le t\le2\pi$ . Then the integral is

$\displaystyle\frac12\int_0^{2\pi}(-17\sin t(-5\sin t)+5\cos t(17\cos t))\,\mathrm dt$

$=\displaystyle\frac{85}2\int_0^{2\pi}\sin^2t+\cos^2t\,\mathrm dt=\frac{85}2\int_0^{2\pi}\mathrm dt=85\pi$

###

Notice that $x^{2/3}+y^{2/3}=4^{2/3}$ kind of resembles the equation for a circle with radius 4, $x^2+y^2=4^2$ . We can change coordinates to what you might call "pseudo-polar":

$\begin{cases}x(t)=4\cos^3t\\y(t)=4\sin^3t\end{cases}$

which gives

$x(t)^{2/3}+y(t)^{2/3}=(4\cos^3t)^{2/3}+(4\sin^3t)^{2/3}=4^{2/3}(\cos^2t+\sin^2t)=4^{2/3}$

as needed. Then with $0\le t\le2\pi$ , we compute the area via Green's theorem using the same setup as before:

$\displaystyle\iint_E\mathrm dx\,\mathrm dy=\frac12\int_0^{2\pi}(-4\sin^3t(12\cos^2t(-\sin t))+4\cos^3t(12\sin^2t\cos t))\,\mathrm dt$

$=\displaystyle24\int_0^{2\pi}(\sin^4t\cos^2t+\cos^4t\sin^2t)\,\mathrm dt$

$=\displaystyle24\int_0^{2\pi}\sin^2t\cos^2t\,\mathrm dt$

$=\displaystyle6\int_0^{2\pi}(1-\cos2t)(1+\cos2t)\,\mathrm dt$

$=\displaystyle6\int_0^{2\pi}(1-\cos^22t)\,\mathrm dt$

$=\displaystyle3\int_0^{2\pi}(1-\cos4t)\,\mathrm dt=6\pi$

3 0

2 years ago

Which table of values could be generated by the equation 10x + 5y = 15?

Ad libitum [116K]

Write the given equation AS FOLLOWS:
10x + 5y = 15
5y = 15 - 10x
Divide through by 5.
y = 3 - 2x

Test x=0: y = 3 - 2*0 = 3 => (0,3) Correct for B
Test x=1:. y = 3 - 2*1 = 1 => (1,1) Correct for B
Test x=2: y = 3 - 2*2 = -1 => (2,-1) Correct for B

Answer: B

3 0

2 years ago