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mathematics oral study guide
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Terms in this set (12)
what formula is used to find the area of a circle?
A=0.7854•D²
or,
A=π•R².
what formula is used to find the volume of a cylinder?
V = 0.7854 x D squared x H
What formula is used to find the area of a rectangle?
A = L x W
What formula is used to find the volume of a rectangular solid?
V = L x W x H
what formula is used to find the area of a triangle?
A = (B x H) / 2
what is the significance of the constant pi?
Pi is the ratio of the circumference to the diameter of any circle.
what is the value of the constant pi?
Pi = 3.1416
What is meant by the root of a number?
The root of a number is one of two or more equal numbers that, when multiplied together, will produce the number.
what is the 8th power of 2?
256
what is the square root of 4,096?
64
what is it meant by a negative number?
A number less than 0, or a number that is preceded by a minus sign.
what is it meant by a ratio and how is a ratio expressed?
A fraction that compares one number to another; for an example, 6:2 is a ratio
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Verified questions
question
Use the Modiﬁed Euler method to approximate the solutions to each of the following initial-value problems, and compare the results to the actual values. a. $y^{\prime}=t e^{3 t}-2 y, \quad 0 \leq t \leq 1, \quad y(0)=0, \text { with } h=0.5$ actual solution $y(t)=\frac{1}{5} t e^{3 t}-\frac{1}{25} e^{3 t}+ \frac{1}{25} e^{-2 t}$ b. $y^{\prime}=1+(t-y)^{2}, \quad 2 \leq t \leq 3, \quad y(2)=1, \text { with } h=0.5;$ actual solution $y(t)=t+\frac{1}{1-t}$ c. $y^{\prime}=1+y / t, \quad 1 \leq t \leq 2, \quad y(1)=2, \text { with } h=0.25;$ actual solution $y(t)=t \ln t+2 t$ d. $y^{\prime}=\cos 2 t+\sin 3 t, \quad 0 \leq t \leq 1, \quad y(0)=1, \text { with } h=0.25;$ actual solution $y(t) = \frac{1}{2} \sin 2 t-\frac{1}{3} \cos 3 t+\frac{4}{3}$
calculus
Find the derivative of the function. $y=\log _{10}\left(x^{2}+6 x\right)$
algebra
Simplify: $\left(\frac{3 x^2 y^{-2}}{y^3}\right)^{-2} \cdot($
algebra
Solve each equation, giving both exact solutions and approximate solutions to the nearest hundredth. $$ 3 x^2=60 $$
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