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tamaranim1 [39]
3 years ago
15

2.What is the solution of the solution of the equation 5^3x=15? Round to the nearest ten thousandth.

Mathematics
1 answer:
sveta [45]3 years ago
8 0
Hmm
remember
a^c=b can translate to log_a(b)=c
so

5^{3x}=15 can translate to log_5(15)=3x
divide both sides by 3
(1/3)log_5(15)=x
log_5(15^{1/3})=x
use calculator, if you can't use change of base formula to do it
log_a(b)= \frac{log_c(b)}{log_c(a)} so
log_5(10^{1/3})= \frac{log_{10}(15^{1/3})}{log_{10}(5)}=x
evaluate using base 10 on your calculator
0.560869=x
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3 years ago
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BartSMP [9]

Answer:

  3.33×10⁴

Step-by-step explanation:

You can use the hint, or you can use a common exponent. Here is the latter case.

  (3.9×10⁴) -(5.7×10³) = (3.9×10⁴) -(0.57×10⁴) = (3.9 -0.57)×10⁴

  = 3.33×10⁴

_____

With a little practice, you can see the effect on exponents of moving the decimal point. Here, we have ...

  5.7×10³ = (0.57×10)×10³ = 0.57×(10×10³) = 0.57×10⁴

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When adding or subtracting in scientific notation, all that is required is that the exponents of all the numbers be the same. The hint says make all the exponents be 0. Above, we have chosen to make them all be 4. You could also use 3:

  (3.9×10⁴) -(5.7×10³) = (39×10³) -(5.7×10³) = (39 -5.7)×10³

  = 33.3×10³ = 3.33×10⁴

6 0
3 years ago
A machine wheel spins at a rate of 500 revolutions per minute. If the wheel has a diameter of 80 centimeters, what is the angula
Setler [38]

The angular speed of the wheel is calculated as 52.36 radians per second

<h3>How to solve for the angular speed</h3>

The revolution of this wheel is said to be at 500 in a minute

This is also called the frequency of this wheel.

This can be written as

500rev in 60 seconds. 500/60 = 8.333 per second

Angular speed is given as

pi = 22/7

f = 8.333

Formular for angular speed = ω = 2*pi*f

w = 2 * 22/7 * 8.333

= 52.36 radians per second

Read more on angular speed here:

brainly.com/question/6860269

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2 years ago
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Since the volume of a rectangular prism is V=lwh, we can isolate for h to obtain that h=V/(lw).

So, for the first prism, the height is 117/(4*6.5) = 4.5

Similarly, for the second prism, the height is 175.5/(6.5 * 4) = 6.75

So, the difference in heights is 6.75-4.5=2.25 = 2 1/4 inches
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