Find the surface area of a cylinder with a radius of 6 inches and a height of 14 inches. Use the approximation 3.14 for pi.
The formula for the surface area of a cylinder is given by the equation:
Surface Area = 2πr^2 + 2πrh
where r is the radius of the cylinder and h is its height.
Plugging in the given values, we have:
Surface Area = 2π(6^2) + 2π(6)(14)
Surface Area = 2π(36) + 2π(6)(14)
Surface Area = 2π(36) + 2π(84)
Surface Area = 72π + 168π
Using the approximation 3.14 for π, we can compute:
Surface Area ≈ 72(3.14) + 168(3.14)
Surface Area ≈ 226.08 + 527.52
Surface Area ≈ 753.6
Therefore, the surface area of the cylinder is approximately 753.6 square inches.
If a triangle has a 25 degree angle and a 45 degree angle, what is the third angle measure?
The sum of the angles in a triangle is always 180 degrees.
Let's denote the third angle as x. Therefore, we can write the following equation:
25 + 45 + x = 180
Combining like terms, we have:
70 + x = 180
To isolate x, we need to subtract 70 from both sides of the equation:
x = 180 - 70
x = 110
Therefore, the third angle measures 110 degrees.
Use the Product Rule of Exponents to simplify the expression 6^4 x 6^-2
The Product Rule of Exponents states that when multiplying two numbers with the same base, you add the exponents.
In this case, we have 6^4 multiplied by 6^(-2). Using the Product Rule of Exponents, we add the exponents to simplify the expression:
6^4 x 6^(-2) = 6^(4+(-2))
The sum of 4 and (-2) is equal to 2:
6^(4+(-2)) = 6^2
Therefore, the expression 6^4 x 6^(-2) simplifies to 6^2.
Which of the following is rational?
A. 78.345
B. 4.82415461....
C. π
D. √8
A rational number is any number that can be expressed as the quotient or fraction of two integers. Rational numbers can be written in the form p/q, where p and q are integers and q is not equal to 0.
From the given options:
A. 78.345 is a decimal number, but it can also be expressed as 78345/1000. This can be written as a fraction, so it is rational.
B. 4.82415461... is an irrational number because it has a decimal expansion that does not terminate or repeat. It cannot be expressed as a fraction, so it is not rational.
C. π (pi) is an irrational number because it has a decimal expansion that does not terminate or repeat. It cannot be expressed as a fraction, so it is not rational.
D. √8 is an irrational number because it cannot be expressed as the quotient of two integers. It cannot be written as a fraction, so it is not rational.
Therefore, the only given option that is rational is A. 78.345.