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3 years ago

Is pi over 2 irrational

Mathematics

1 answer:

Luden [163]3 years ago

3 0

It's irrational.

An irrational number divided by a rational number will result in an irrational number

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X^2 - 4x - 12 = 0 Factor and solve

maxonik [38]

Ax^2+bx+c=0

find what 2 numbers multiply to get c and add to get b
x^2-4x-12
b=-4
c=-12

x times y=-12
x+y=-4
factor -12
-1, 12
-2,6
-3,4
add
-1+12=11
-2+6=4
-3+4=1

the one that works is -2 and 6 because they can be reversed to make -6 and 2 which multiploy to get -12 and add to get -4 so

split it up into

x^2-4x-12=(x-6)(x+2)=0
set each to zero
x-6=0
add 6
x=6

x+2=0
subtract 2
x=-2

x=6 or -2

7 0

3 years ago

Which number is equivalent to 3^4/3^2

s2008m [1.1K]

$\frac{ 3^{4} }{ 3^{2} }$ First, take about the $3^{4}$ and $3^{2}$
$\frac{3 x 3 x 3 x 3}{3 x 3}$ You can cancel out the two 3's on the bottom using two of the threes from the numerator
$\frac{3 x 3}{1}$ Simplify the fraction
3 x 3 Multiply
9

4 0

3 years ago

Question

Gnoma [55]

Given parameters:

y varies directly as w;

This interpreted implies that as y increases, we increases by a certain factor or amount;

So, y ∝ w

y = kw

where k is the constant of proportionality

Now, given that y = 8 and w = 2

Input in the equation to solve for k;

8 = k x 2

Solving k gives, k = 4

Now to the second part,

if v is directly proportional to w;

v = k w

So v = 4w

The equation that relates v to w is v = 4w

3 0

3 years ago

You find an interest rate of 10% compounded quarterly. Calculate how much more money you would have in your pocket if you had us

Elena-2011 [213]

Answer:

see the explanation

Step-by-step explanation:

we know that

step 1

The compound interest formula is equal to

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

where

A is the Final Investment Value

P is the Principal amount of money to be invested

r is the rate of interest in decimal

t is Number of Time Periods

n is the number of times interest is compounded per year

in this problem we have

$r=10\%=10/100=0.10\\n=4$

substitute in the formula above

$A=P(1+\frac{0.10}{4})^{4t}$

$A=P(1.025)^{4t}$

Applying property of exponents

$A=P[(1.025)^{4}]^{t}$

$A=P(1.1038)^{t}$

step 2

The formula to calculate continuously compounded interest is equal to

$A=P(e)^{rt}$

where

A is the Final Investment Value

P is the Principal amount of money to be invested

r is the rate of interest in decimal

t is Number of Time Periods

e is the mathematical constant number

we have

$r=10\%=10/100=0.10$

substitute in the formula above

$A=P(e)^{0.10t}$

Applying property of exponents

$A=P[(e)^{0.10}]^{t}$

$A=P(1.1052)^{t}$

step 3

Compare the final amount

$P(1.1052)^{t} > P(1.1038)^{t}$

therefore

Find the difference

$P(1.1052)^{t} - P(1.1038)^{t}$ ----> Additional amount of money you would have in your pocket if you had used a continuously compounded account with the same interest rate and the same principal.

3 0

3 years ago

Using equivalent ratios, which statements are true about the cost per magnet? Check all that apply.

N76 [4]

Answer:

The true statements are:

The cost of 9 magnets is $3.

The cost of 6 magnets is $2.

The cost of 3 magnets is $1.

Step-by-step explanation:

equivalents ratios are two or more ratios that express the same relationship between the numbers involved. In order to calculate the equivalent ratios that are equal, when the numbers involved are divided, they ought to give the same result. In the answer chosen above the ratios in each case are equivalent because:

if the cost of 9 magnets is $3;

9 magnets = $3

∴ 1 magnet = 3/9 = $ 1/3 = 1:3

if the cost of 6 magnets is $2;

6 magnets = $2

1 magnet = 2/6 = $1/3 = 1:3

if the cost of 3 magnets is $1;

3 magnets = $1

∴ 1 magnet = $ 1/3 = 1:3

From the answers obtained, the equivalent ratio of 1 : 3 is the same in all case.

3 0

3 years ago