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3 years ago

Find the area of a circle if its circumference is 10 pi

Mathematics

1 answer:

AleksandrR [38]3 years ago

8 0

Answer:

25π

Step-by-step explanation:

pi's symbol is π, which will be used sometimes to make it easier later

The circumference is equal to diameter multiplied by pi. (Diameter is the length across the circle, radius the center of the circle to an edge point aka. half the diameter, and circumference is the edge length aka. perimeter of the circle.)

We can then remove the pi off the 10, as the diameter multiplied by pi is the circumference, so the diameter is 10.

Half of 10 is 5, the radius.

The formula for area of a circle is radius squared times pi, remember easily by π r ^2

We can plug in the radius into the formula to get

π 5 ^2

And finish it by solving the square root to get

π 25

25π

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Solve the system of equations by substitution. 3/8 x + 1/3 y =17/24 and <br> x + 7y = 8

goblinko [34]

$\left \{ {{ \frac{3}{8}x+ \frac{1}{3}y = \frac{17}{14} } \atop {x+7y=8}} \right.$

To solve this system by substitution, first isolate x in the second equation.

$x+7y=8$
$x+7y-7y=8-7y$
$x=8-7y$

Now, plug this expression ( $8-7y$ ) for x in the top equation to solve for y.

$\frac{3}{8} (8-7y)+ \frac{1}{3} y= \frac{17}{14}$
$3- \frac{21}{8} y+ \frac{1}{3} y= \frac{17}{24}$
$72-63y+8y=17$
$72-55y=17$
$-55y=17-72$
$-55y=-55$
$y=1$

Now that you have y, plug it into the second equation and solve for x.

$x+7y=8$
$x+7(1)=8$
$x+7=8$
$x=1$

Last step is to plug your x- and y-values in to both equations to check your work.

$\frac{3}{8} (1)+ \frac{1}{3} y= \frac{17}{24}$

$\frac{3}{8} * \frac{3}{3} = \frac{9}{24} ; \frac{1}{3} * \frac{8}{8} = \frac{8}{24}$

$\frac{9}{24} + \frac{8}{24} = \frac{17}{24}$ <--True

$1+7(1)=8$
$1+7=8$ <--True

Answer:
$x=1 \\ y=1$

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3 years ago

Jaina and Tomas compare their compound interest accounts to see how much they will have in the accounts after three years. They

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Formula for compound interest is

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Interest = $P(1+r)^{t}$ - P

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t = time in years

For Jaina,

P = $300

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t = 3 yrs

So, Interest = $300(1+0.07)^{3}$ - 300

For Tomas

P = $400

r= 4%

t = 3 yrs

So, Interest = $400(1+0.04)^{3}$ - 400

So pair of equations for Jaina and Tomas are

Interest = $300(1+0.07)^{3}$ - 300

Interest = $400(1+0.04)^{3}$ - 400

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A science teacher has a supply of 5% hydrochloric acid and a supply of 65% hydrochloric acid(HC1). How much of each solution sho

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Assume that the amount needed from the 5% solution is x and that the amount needed from the 65% solution is y.

We are given that, the final solution should be 42 ml, this means that:
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Substitute with equation II in equation III as follows:
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0.05(42-y) + 0.65y = 18.9
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Substitute with y in equation II to get x as follows:
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