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3 years ago

Help pls I have more

Mathematics

2 answers:

IgorC [24]3 years ago

7 0

Answer:

$\frac{5}{10} \times \frac{2}{1} = \frac{10}{10} = 1$

$\frac{1}{10} \times \frac{8}{3} = \frac{8}{30} = \frac{4}{15}$

$\frac{2}{6} \times \frac{12}{6} = \frac{24}{36} = \frac{2}{3}$

$\frac{1}{4} \times \frac{1}{3} = \frac{1}{12}$

$\frac{1}{5} \times \frac{1}{1} = \frac{1}{5}$

earnstyle [38]3 years ago

3 0

Answer:

Step-by-step explanation:

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Name three decimals with a product that is about 40

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The circumference of the circle is increasing at a rate of 0.5 meters per minute. What's the rate of change of the area of the c

morpeh [17]

Answer:

The rate of change of the area of the circle when the radius is 4 meters = 2 meters²/minute ⇒ answer 4

Step-by-step explanation:

* Lets revise the chain rule in the derivative

- If dy/da = m and dx/da = n, and you want to find dy/dx

∴ dy/dx = dy/da ÷ dx/da = m ÷ n = m/n

* In our problem we have

- The rate of increasing of the circumference dC/dt = 0.5 meters/minute

- We need the find the rate of change of the area of the circle

when the radius is 4 meters

- The common element between the circumference and the area

of the circle is the radius of the circle

* We must to find dC/dr and dA/dr and use the chain rule to

find dA/dr

- Find the rate of change of the radius dr/dt

∵ C = 2πr

- Find the derivative of C with respect to r

∴ dC/dr = 2π ⇒ (1)

∵ dC/dt = 0.5 meters/minute ⇒ (2)

- Divide (1) by (2) to get dr/dt by using chain rule

∵ dC/dt ÷ dC/dr = 0.5 ÷ 2π

∴ dC/dt × dr/dC = 0.5 × 1/2π ⇒ cancel dC together and change

0.5 to 1/2

∴ dr/dt = 1/2 × 1/2π = 1/4π ⇒ (3)

- Find the rate of change of the area dA/dt

∵ A = πr²

- Find the derivative of A with respect to r

∴ dA/dr = 2πr

∵ r = 4

∴ dA/dr = 2π(4) = 8π ⇒ (4)

- Multiply (4) by (3) to get dA/dt by using chain rule

∵ dA/dr × dr/dt = 8π × 1/4π ⇒ divide 8 by 4 and cancel π

∴ dA/dt = 2 meters²/minute

* The rate of change of the area of the circle when the radius is

4 meters = 2 meters²/minute

3 0

3 years ago

A sum of money is invested at 12% compounded quarterly. About how long will it take for the amount of money to double?

iVinArrow [24]

I'll use my own formula (similar to yours tho)

$A=P(1+ \frac{r}{n})^{nt}$
A=future amount
p=invested
r=rate in decimal
n=number of times per year compounded
t=time in years

so
when will A=2P
subsitute 2P for A
also quarterly means 4 times a year or n=4
and 12%=0.12=r
so

$2P=P(1+ \frac{0.12}{4})^{(4*t)}$
divide both sides by P
$2=(1+ \frac{0.12}{4})^{(4*t)}$
simplify
$2=(1+ 0.03)^{4t}$
$2=(1.03)^{4t}$
take the ln of both sides
$ln(2)=ln(1.03)^{4t}$
$ln(2)=4tln(1.03)$
$ln(2)=t(4ln(1.03))$
divide both sides by 4ln(1.03)
$\frac{ln(2)}{4ln(1.03)}=t$
use calculator
5.86244=t
about 5.9 years

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Yakvenalex [24]

Answer: x=6

Step-by-step explanation:

3(x-2)=12

3x-6=12

3x=18

x=6

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Help pls I have more ​

Help pls I have more