What is equivalent to 9^2•9^6

Mathematics

1 answer:

Jet001 [13]4 years ago

6 0

So remember the rule with multiplying exponents of the same base: $x^m*x^n=x^{m+n}$

In this case:

$9^2*9^6=9^{2+6}=9^8$

<u>The equivalent of 9^2 × 9^6 is 9^8.</u>

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Ratios Help easyyy plzz help me !!!!!

schepotkina [342]

The first one states that there are 6 cups of orange juice for every _ cups of punch

There are 6 cups of orange juice and 4 cups of cranberry in 10 cups of juice because 6 c orange + 4 c cranberry = 10 cups total punch

So for 6 cups of orange juice there would be 10 cups of punch.

The 3rd one states that the ratio of cranberry juice to punch is _:_

Punch is cranberry and orange combined- at the ratio of 4:6

So for 4 cups of cranberry, there would be 10 cups punch (4 c cranberry + 6 c orange = 10 c punch)

So the ratio would be 4:10, it can be simplified like fractions as 2:5

I don't know is you have to but if you do, don't forget to simplify the ratios.

Good luck!

7 0

3 years ago

A weight suspended by a spring vibrates vertically according to the function D D given by D(t)=2sin(4π(t+18)) D ( t ) = 2 sin (

STALIN [3.7K]

Answer:

21.75 cm/s

Step-by-step explanation:

1 cm above central position means D = 1, so we plug in 1 into D(t) and find the time and which this occurs.

$D(t)=2Sin (4\pi(t+18))\\1=2Sin (4\pi(t+18))\\\frac{1}{2}=Sin(4\pi t +72\pi)\\4\pi t + 72 \pi = \frac{\pi}{6}\\4\pi t = \frac{\pi}{6}-72\pi\\t=\frac{\frac{\pi}{6}-72\pi}{4\pi}$

This is the time at which this occurs.

To find instantaneous rate of change, we differentiate D(t) and plug in this t we found. Remembering that d/dt (Sin t) = Cos t

$D(t)=2Sin (4\pi(t+18))\\D(t)=2Sin(4\pi t + 72\pi)\\D'(t)=2Cos(4\pi t + 72\pi)(4\pi)$

Now putting t:

$D'(t)=2Cos(4\pi t + 72\pi)(4\pi)\\D'(\frac{\frac{\pi}{6}-72\pi}{4\pi})=2Cos(4\pi (\frac{\frac{\pi}{6}-72\pi}{4\pi}) + 72\pi)(4\pi)\\=8\pi Cos(\frac{\pi}{6})\\=21.75$