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3 years ago

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If you have $1,500, how much money will you have after 40 years in an account that offers 5.9% yearly interest, if the interest

is compounded: a. Monthly: $ b. Quarterly:$ c. Continuously:$

1 answer:

Aneli [31]3 years ago

4 0

$5040 after 40 years
hm... probably continuously i think ,

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Traveling with the current, a boat covers a distance 1.5 times greater than traveling against the current in the same amount of

jeka94

Let the speed of the current equal c
and the speed of the boat in still water equal b.

b + c = 1.5 (b - c)
b + c = 1.5b - 1.5c
0.5b = 2.5c
b = 5c

The speed of the current is 1.5 mph so
b = 5 * 1.5 = 7.5 mph

4 0

3 years ago

(4x + 4)(ax – 1) – x2 +4

Oksana_A [137]

Answer:

b=-3

Step-by-step explanation:

If the expression simplifies to bx that means the $x^{2}$ terms and the constant terms must be cancel out.

Simplify it first.

$(4x+4)(ax-1)-x^{2} +4\\=(4ax^{2} -4x+4ax-4)-x^{2} +4\\=4ax^{2} -x^{2} -4x+4ax-4+4\\=4ax^{2} -x^{2} -4x+4ax$

We know –4 + 4 will cancel out. If we simplify this expression to only an x term, then the $x^{2}$ terms should be cancelled. Therefore, we say that 4ax^2 – x^2 = 0.

$4ax^{2} -x^{2} =0\\x^{2} (4a-1)=0\\4a-1=0\\4a=1\\a=\frac{1}{4}$

If we put a = ¼, then we can find the value of b:

$=4(\frac{1}{4} )x^{2} -x^{2} -4x+4(\frac{1}{4} )x\\=x^{2} -x^{2} -4x+x\\ (cancel out x^{2} terms)\\$

$=-3x$

$bx=-3x\\$ if the expression is equivalent to bx

Therefore, b = –3.

8 0

2 years ago

Marriane can say hello in more than 7 languages. Which number line could represent this situation?

Alina [70]

Answer:

A) x > 7

Step-by-step explanation:

Since it's more than, the inequality would be >

Since it's >, that means it's an open circle

So,

x > 7

8 0

2 years ago

Lim x-> vô cùng ((căn bậc ba 3 (3x^3+3x^2+x-1)) -(căn bậc 3 (3x^3-x^2+1)))

NNADVOKAT [17]

I believe the given limit is

$\displaystyle \lim_{x\to\infty} \bigg(\sqrt[3]{3x^3+3x^2+x-1} - \sqrt[3]{3x^3-x^2+1}\bigg)$

Let

$a = 3x^3+3x^2+x-1 \text{ and }b = 3x^3-x^2+1$

Now rewrite the expression as a difference of cubes:

$a^{1/3}-b^{1/3} = \dfrac{\left(a^{1/3}-b^{1/3}\right)\left(a^{2/3}+a^{1/3}b^{1/3}+b^{2/3}\right)}{\left(a^{2/3}+a^{1/3}b^{1/3}+b^{2/3}\right)} \\\\ = \dfrac{a-b}{a^{2/3}+a^{1/3}b^{1/3}+b^{2/3}}$

Then

$a-b = (3x^3+3x^2+x-1) - (3x^3-x^2+1) \\\\ = 4x^2+x-2$

The limit is then equivalent to

$\displaystyle \lim_{x\to\infty} \frac{4x^2+x-2}{a^{2/3}+(ab)^{1/3}+b^{2/3}}$

From each remaining cube root expression, remove the cubic terms:

$a^{2/3} = \left(3x^3+3x^2+x-1\right)^{2/3} \\\\ = \left(x^3\right)^{2/3} \left(3+\dfrac3x+\dfrac1{x^2}-\dfrac1{x^3}\right)^{2/3} \\\\ = x^2 \left(3+\dfrac3x+\dfrac1{x^2}-\dfrac1{x^3}\right)^{2/3}$

$(ab)^{1/3} = \left((3x^3+3x^2+x-1)(3x^3-x^2+1)\right)^{1/3} \\\\ = \left(\left(x^3\right)^{1/3}\right)^2 \left(\left(3+\dfrac3x+\dfrac1{x^2}-\dfrac1x\right)\left(3-\dfrac1x+\dfrac1{x^3}\right)\right)^{1/3} \\\\ = x^2 \left(9+\dfrac6x-\dfrac1{x^3}+\dfrac4{x^4}+\dfrac1{x^5}-\dfrac1{x^6}\right)^{1/3}$

$b^{2/3} = \left(3x^3-x^2+1\right)^{2/3} \\\\ = \left(x^3\right)^{2/3} \left(3-\dfrac1x+\dfrac1{x^3}\right)^{2/3} \\\\ = x^2 \left(3-\dfrac1x+\dfrac1{x^3}\right)^{2/3}$

Now that we see each term in the denominator has a factor of <em>x</em> ², we can eliminate it :

$\displaystyle \lim_{x\to\infty} \frac{4x^2+x-2}{a^{2/3}+(ab)^{1/3}+b^{2/3}} \\\\ = \lim_{x\to\infty} \frac{4x^2+x-2}{x^2 \left(\left(3+\dfrac3x+\dfrac1{x^2}-\dfrac1{x^3}\right)^{2/3} + \left(9+\dfrac6x-\dfrac1{x^3}+\dfrac4{x^4}+\dfrac1{x^5}-\dfrac1{x^6}\right)^{1/3} + \left(3-\dfrac1x+\dfrac1{x^3}\right)^{2/3}\right)}$

$=\displaystyle \lim_{x\to\infty} \frac{4+\dfrac1x-\dfrac2{x^2}}{\left(3+\dfrac3x+\dfrac1{x^2}-\dfrac1{x^3}\right)^{2/3} + \left(9+\dfrac6x-\dfrac1{x^3}+\dfrac4{x^4}+\dfrac1{x^5}-\dfrac1{x^6}\right)^{1/3} + \left(3-\dfrac1x+\dfrac1{x^3}\right)^{2/3}}$

As <em>x</em> goes to infinity, each of the 1/<em>x</em> ⁿ terms converge to 0, leaving us with the overall limit,

$\displaystyle \frac{4+0-0}{(3+0+0-0)^{2/3} + (9+0-0+0+0-0)^{1/3} + (3-0+0)^{2/3}} \\\\ = \frac{4}{3^{2/3}+(3^2)^{1/3}+3^{2/3}} \\\\ = \frac{4}{3\cdot 3^{2/3}} = \boxed{\frac{4}{3^{5/3}}}$

8 0

2 years ago

Answer this question due soon

In-s [12.5K]

Answer:

isosceles triangle means all equal sides and sum of interior angles of a triangle have to add to 180deg. if you draw a triangle with 3 equal 60 deg angles and draw a line from the top angle straight down to the bottom line, basically dividing the triangle into two even ones. then you can say the line or bisector line from the angle makes a 90deg with the bottom line across from angle the line is drawn out of. so then that makes two even and equal triangles, then the measure of the angles will be 90deg from bisector line + 60deg from angle untouched + 30deg from bisector angle = 180 degs for sum of interior angles in both triangles now proving the altitude from the base of an isosceles triangle is also the angle bisector of that angle.

Step-by-step explanation:

3 0

2 years ago