What is the simplified expression for 4 power 4 multiplied by 4 power 3 over 4 power 5

Write the following ratio in their simplest form (a)150minutes:1 1/2 hours (b) 150cm:1060mm

spayn [35]

Answer:

a) 5:3

b) 7.5:5.3

Step-by-step explanation:

150min : 90min (1 and a half hour)

10 : 6

5 : 3

150 × 10 mm : 1060 mm

1500 : 1060

750 : 530

7.5 : 5.3

7 0

2 years ago

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

How does 5+66+5429 what does it equal

elixir [45]

Answer:

i think 5 500 ..........

6 0

3 years ago

Read 2 more answers

Which letter is the correct answer and why

Julli [10]

Answer:

<h2>Option C</h2>

Step-by-step explanation:

Here,

[Taking 'A' = 'a']

$a \: = \: 4\pi {r}^{2}$

Then for 'r',

$= > 4\pi {r}^{2} = a$

$= > {r}^{2} = \frac{a}{4\pi}$

$= > r = \sqrt{\frac{a}{4\pi} }$

$= > r = \frac{1}{2}\sqrt{ \frac{a}{\pi} }$

Hence,

Option C is correct .

3 0

3 years ago

The temperature was recorded for four straight days.The temperatures was recorded for the first three days were -2°,10°,and 7°.W

lubasha [3.4K]

Answer:

$-19^{\circ}$

Step-by-step explanation:

Let x represent temperature on 4th day.

We have been given that the temperatures was recorded for the first three days were -2°,10°,and 7°.

The total temperature on f days would be $-2^{\circ}+10^{\circ}+7^{\circ}+x$ .

We have been given that total temperature change was -4°. We can represent this information in an equation as:

$-2^{\circ}+10^{\circ}+7^{\circ}+x=-4^{\circ}$

$15^{\circ}+x=-4^{\circ}$

$x=-4^{\circ}-15^{\circ}$

$x=-19^{\circ}$

Therefore, the temperature on 4th day must be equal to $-19^{\circ}$ .

7 0

3 years ago