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2 years ago

12

2a^3+a^2–17–3a^2+a^3–a –80

1 answer:

adelina 88 [10]2 years ago

3 0

Answer:

=3a^3−2a^2−a−97

Step-by-step explanation:

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Kristen invests $5,745 in a bank. The bank pays 6.5% interest compounded monthly. How long must she leave the money in the bank

s344n2d4d5 [400]

formula is $A=P(1-\frac{r}{n})^{nt}$

where A=final amount

P=principal

r=interest rate in decimal

n=number of times per year it is compounded

t=time in years

we want to find where

A=2P

and P=5745

and r=6.5%=0.065

n=monthly=12

remember that $ln(x^a)=a(ln(x))$

also that $(a^b)^c=a^{bc}$

$2(5745)=5745(1+\frac{0.065}{12})^{12t}$ , solving for t

divide both sides by 5745 to simplify things a bit

$2=(1+\frac{0.065}{12})^{12t}$ I'd rather not simplify this because it give us a decimals and those aren't exact, if we combine, we get 12.065/12 for inside parenthases

$2=(\frac{12.065}{12})^{12t}$

take ln of both sides

$ln(2)=ln((\frac{12.065}{12})^{12t})$

$ln(2)=(12t)ln(\frac{12.065}{12})$

divide both sides by $12ln(\frac{12.065}{12})$

$\frac{ln(2)}{12ln(\frac{12.065}{12})}=t$

using our calculator, t≈10.6927

so rounded, we get 10.7 years

3 0

3 years ago

Dimensions of a building are 740 feet by 800 feet. If 1 inch represents 8 feet, what are the dimensions of the building on the d

Scrat [10]

The dimensions of the building on the drawing would be 92.5 inches by 100 inches.
Explanation:
if 1 inch = 8 feet, then you just subtract 8 by 740 and 800 to get the dimensions.

4 0

3 years ago

Read 2 more answers

A store is going out of business. Everything is marked down 40%. How much do you pay now for an item that used to cost $150?

barxatty [35]

Answer : $60

Steps for Solving :

$150/10 (to get 10 parts)
=15

15•4 (to get 40%)
=60

6 0

3 years ago

1+4=52+5=123+6=218+11=?

Nikolay [14]

1+4=5
2+5=7
3+6=9
8+11=19
hope this helped:)

4 0

3 years ago

Read 2 more answers

Rewrite the statement in mathematical notation. (Let y be the distance from the top of the ladder to the floor, x be the distanc

In-s [12.5K]

Answer:

$\frac{dy}{dt}=\frac{6y}{x}\text{ ft per sec}$

Step-by-step explanation:

Let L be the length of the ladder,

Given,

x = the distance from the base of the ladder to the wall, and t be time.

y = distance from the base of the ladder to the wall,

So, by the Pythagoras theorem,

$L^2 = y^2 + x^2$

$\implies L = \sqrt{y^2 + x^2}$ ,

Differentiating with respect to time (t),

$\frac{dL}{dt}=\frac{d}{dt}(\sqrt{x^2 + y^2})$

$=\frac{1}{2\sqrt{x^2 + y^2}}\frac{d}{dt}(x^2 + y^2)$

$=\frac{1}{2\sqrt{x^2 + y^2}}(2x\frac{dx}{dt}+2y\frac{dy}{dt})$

$=\frac{1}{\sqrt{x^2 +y^2}}(x\frac{dx}{dt}+y\frac{dy}{dt})$

Here,

$\frac{dy}{dt}=-6\text{ ft per sec}$

Also, $\frac{dL}{dt} = 0$ ( Ladder length = constant ),

$\implies \frac{1}{\sqrt{x^2 +y^2}}(x(-6)+y\frac{dy}{dt})=0$

$-6x + y\frac{dy}{dt}=0$

$y\frac{dy}{dt}=6x$

$\implies \frac{dy}{dt}=\frac{6y}{x}\text{ ft per sec}$

Which is the required notation.

8 0

3 years ago