Rewrite using a single exponent.
(6^3)5
(6^3)^5
that is wrong
Apologies for the confusion. The correct way to rewrite (6^3)5 using a single exponent is 6^(3*5), which can also be simplified to 6^15.
Solve for u.
5/7=u+2/8
To solve for u, we'll manipulate the equation to isolate the variable.
First, let's simplify both sides of the equation. On the left side, 5/7 cannot be simplified further. On the right side, 2/8 simplifies to 1/4:
5/7 = u + 1/4
Next, let's get rid of the fraction on the right side by finding a common denominator. The common denominator between 7 and 4 is 28:
(5/7) * 4/4 = u + 1/4 * 7/7
20/28 = u + 7/28
Combining the fractions on the left side:
20/28 = u + 7/28
Now, let's subtract 7/28 from both sides to isolate u:
20/28 - 7/28 = u + 7/28 - 7/28
13/28 = u
Therefore, the solution for u is u = 13/28.
The sum of two numbers is 42. One number is 2 times as large as the other. What are the numbers?
Let's call the smaller number x. Since the larger number is 2 times as large as the smaller number, we can represent the larger number as 2x.
According to the problem, the sum of these two numbers is 42:
x + 2x = 42
Next, we'll combine like terms:
3x = 42
To isolate x, we'll divide both sides of the equation by 3:
x = 42/3
x = 14
Therefore, the smaller number is 14. Now, we can find the larger number by substituting this value back into the equation:
2x = 2 * 14 = 28
So, the larger number is 28.
In conclusion, the two numbers are 14 and 28.
Solve 216=y^3, where is a real number.
Simplify your answer as much as possible.
To solve the equation 216 = y^3, we can take the cube root of both sides to isolate y:
∛216 = ∛y^3
The cube root of 216 is 6, since 6 * 6 * 6 = 216. Therefore, we have:
6 = y
So, the simplified answer is y = 6.
(a) An astronomer's infrared telescope is able to detect radiation with a wavelength of 8.35*10^-5 meters. Write this number in standard notation.
(b) The diameter of Venus at its equator is approximately 12100 kilometers. Write this number in scientific notation.