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.
(a) To write 8.35*10^-5 in standard notation, we can simply move the decimal point 5 places to the left since the exponent is negative. This gives us:
0.0000835
(b) To write 12100 kilometers in scientific notation, we need to express it as a number between 1 and 10 multiplied by a power of 10. The diameter of Venus at its equator is 12100 kilometers, which can be represented as:
1.21*10^4 kilometers
A tank at a factory contains water. Workers are draining the tank at a constant rate. After 31 minutes of being drained, the tank contains 536 liters of water. After 51 minutes, the tank contains 256 liters of water.
To determine the rate at which the tank is being drained, we need to find the change in water volume divided by the change in time.
Let's denote the initial volume of water in the tank as V0, and the rate of drainage as R.
From the given information:
After 31 minutes, the volume of water is V1 = 536 liters.
After 51 minutes, the volume of water is V2 = 256 liters.
The change in volume is: ΔV = V2 - V1 = 256 - 536 = -280 liters.
The change in time is: Δt = 51 - 31 = 20 minutes.
The rate of drainage is given by: R = ΔV / Δt = -280 / 20 = -14 liters per minute.
Therefore, the tank is being drained at a rate of 14 liters per minute. Note that the negative sign indicates a decrease in volume.
Calculate.
(5.6*10^5)-(4.4*10^5)
To calculate (5.6*10^5) - (4.4*10^5), we can subtract the coefficients while keeping the same exponent:
(5.6 - 4.4) * 10^5 = 1.2 * 10^5
So, (5.6*10^5) - (4.4*10^5) simplifies to 1.2 * 10^5.
Solve for u.
u+4/8=6/7
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, u + 4/8 can be simplified to u + 1/2:
u + 1/2 = 6/7
Next, let's get rid of the fraction on the right side by finding a common denominator. The common denominator between 2 and 7 is 14:
(u + 1/2) * 7/7 = 6/7 * 2/2
7(u + 1/2) = 12/14
Combining the fractions on the right side:
7(u + 1/2) = 6/7 * 12/14
Now, let's simplify the right side:
7(u + 1/2) = 72/98
Next, let's distribute 7 to the terms on the left side:
7u + 7/2 = 72/98
To eliminate the fraction on the left side, multiply both sides of the equation by 2:
2(7u + 7/2) = 2(72/98)
Simplifying both sides:
14u + 7 = 144/98
Now, let's subtract 7 from both sides to isolate u:
14u + 7 - 7 = 144/98 - 7
Simplifying the fractions on the right side:
14u = 144/98 - 686/98
14u = -542/98
To simplify further, both the numerator and denominator of the right side can be divided by their greatest common divisor, which is 98, resulting in:
14u = -542/98 = -271/49
Finally, let's divide both sides of the equation by 14 to solve for u:
u = (-271/49) / 14
Simplifying the right side:
u = -271/49 / 14 = -271/49 * 1/14 = -271/686 = -0.3959 (rounded to four decimal places)
Therefore, the solution for u is approximately u = -0.3959.