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3 years ago

A circle has a radius of 3 units. What is the area of the circle? Round to the nearest hundredth. Use 3.14 for pi.

Mathematics

1 answer:

Troyanec [42]3 years ago

5 0

Answer:

Step-by-step explanation:

Ac=3.14*r^2

Ac=9*3.14=28.27

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Jimmy invests $2500 in an account with a 5% interest rate, making no other deposits or withdrawals. What will Jimmy’s account ba

Alik [6]

Answer:

We conclude that the total amount accrued, principal plus interest, from compound interest on an original principal of $2500 at a rate of 5% per year compounded 6 times per year over 8 years is $3723.38.

Step-by-step explanation:

Given

Principle P = $2500

Interest rate r = 5% = 0.05

Time period t = 8 years

To determine

Accrue Amount A = ?

Using the compound interest equation

$A\:=\:P\left(1\:+\:\frac{r}{n}\right)^{nt}$

where:

A represents the Accrue Amount

P represents the Principal Amount

r represents the interest rate

t represents the time period in years

n represents the number of compounding periods per unit t

Important tip:

Given that the interest is compounded 6 times each year, therefore, the value of n = 6.

now substituting P = 2500, r = 0.05, t = 8 and n = 6 in the equation

$A\:=\:P\left(1\:+\:\frac{r}{n}\right)^{nt}$

$A=2500\left(1+\frac{0.05}{6}\right)^{\left(6\right)\left(8\right)}$

$\:A=2500\left(1+\frac{0.05}{6}\right)^{48}$

$A=2500\times 1.48935$ ∵ $\left(1+\frac{0.05}{6}\right)^{48\:\:}=1.48935$

$A=\:3723.38$ $

Therefore, we conclude that the total amount accrued, principal plus interest, from compound interest on an original principal of $2500 at a rate of 5% per year compounded 6 times per year over 8 years is $3723.38.

8 0

2 years ago

How many gallons of water can fill a pool that is 50 yards by 20 yards and is 9 feet deep? (Assume 7 1/2 gallons per cubic foot.

serg [7]

it would take 10,800 gallons to fill the pool

8 0

3 years ago

Read 2 more answers

What is the solution to 5/6x-1/3>1 1/3

CaHeK987 [17]

Answer:

Step-by-step explanation:

$\frac{5}{6}x-1>1\frac{1}{3}\\\\\frac{5}{6}x-1>\frac{4}{3}\\\\\frac{5}{6}x>\frac{4}{3}+1\\\\\frac{5}{6}x>\frac{4}{3}+\frac{3}{3}\\\\\frac{5}{6}x>\frac{7}{3}\\\\x>\frac{7}{3}*\frac{6}{5}\\\\x>\frac{7*2}{5}\\x>\frac{14}{5}\\\\x>2\frac{4}{5}$

3 0

3 years ago

Find the perimeter of the polygon with vertices A(-6,-4), B(-3,6), C(4,0), and D(2,-1)?

EleoNora [17]

Check the picture below.

so the perimeter of the polygon is the sum of all its sides, namely, AB + BC + CD + DA.

now, let's check how long each side is,

$\bf ~~~~~~~~~~~~\textit{distance between 2 points}\\ \quad \\
\begin{array}{ccccccccc}
&&x_1&&y_1&&x_2&&y_2\\
% (a,b)
&A&(~{{ -6}} &,&{{ -4}}~) 
% (c,d)
&B&(~{{ -3}} &,&{{ 6}}~)
\end{array}
\\\\\\
d = \sqrt{({{ x_2}}-{{ x_1}})^2 + ({{ y_2}}-{{ y_1}})^2}\\\\
-------------------------------\\\\
AB=\sqrt{[-3-(-6)]^2+[6-(-4)]^2}
\\\\\\
AB=\sqrt{(-3+6)^2+(6+4)^2}
\\\\\\
AB=\sqrt{3^2+10^2}\implies \boxed{AB=\sqrt{109}}\\\\
-------------------------------$

$\bf ~~~~~~~~~~~~\textit{distance between 2 points}\\ \quad \\
\begin{array}{ccccccccc}
&&x_1&&y_1&&x_2&&y_2\\
% (a,b)
&B&(~{{ -3}} &,&{{6}}~) 
% (c,d)
&C&(~{{ 4}} &,&{{ 0}}~)
\end{array}
\\\\
-------------------------------\\\\
BC=\sqrt{[4-(-3)]^2+[0-6]^2}\implies BC=\sqrt{(4+3)^2+(0-6)^2}
\\\\\\
BC=\sqrt{7^2+(-6)^2}\implies \boxed{BC=\sqrt{85}}\\\\
-------------------------------$

$\bf ~~~~~~~~~~~~\textit{distance between 2 points}\\ \quad \\
\begin{array}{ccccccccc}
&&x_1&&y_1&&x_2&&y_2\\
% (a,b)
&C&(~{{ 4}} &,&{{0}}~) 
% (c,d)
&D&(~{{ 2}} &,&{{ -1}}~)
\end{array}
\\\\
-------------------------------\\\\
CD=\sqrt{(2-4)^2+(-1-0)^2}\implies CD=\sqrt{(-2)^2+(-1)^2}
\\\\\\
\boxed{CD=\sqrt{5}}\\\\
-------------------------------$

$\bf ~~~~~~~~~~~~\textit{distance between 2 points}\\ \quad \\
\begin{array}{ccccccccc}
&&x_1&&y_1&&x_2&&y_2\\
% (a,b)
&D(~{{ 2}} &,&{{-1}}~) 
% (c,d)
&A&(~{{ -6}} &,&{{ -4}}~)
\end{array}\\\\
-------------------------------\\\\
DA=\sqrt{[-6-2]^2+[-4-(-1)]^2}\\\\\\ DA=\sqrt{(-6-2)^2+(-4+1)^2}
\\\\\\
DA=\sqrt{(-8)^2+(-3)^2}\implies \boxed{DA=\sqrt{73}}$

sum those sides up, and that's the perimeter of the polygon.

6 0

2 years ago

What is the relationship between the center of any circle and the point that lie on the circle?

Arlecino [84]

The distance between the center and any point on the circle is the radius. That's likely what your book or teacher is asking for.

Note: double the radius and you get the diameter

7 0

3 years ago

Read 2 more answers