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What is a corollary in geometry?

An example of a corollary is that an equilateral triangle is always equiangular because it is known that on a triangle, angles that oppose two congruent sides are always congruent. Because the triangle has all congruent or equal sides, it is equilateral. Because the angles are congruent, the triangle is equiangular, or with equal angles. Therefore, the corollary is known as true by the original statement or theorem.

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How should you find the circumference of a circle?

Find the radius of the circleThe radius extends from the center of a circle to its outer edge. To find the radius of a circle, locate its center. Then, measure the distance from the center to the outer edge of the circle. This distance is the radius.Recall the circumference formulaThe circumference of a circle is two times pi times the radius. Algebraically, C = 2 x pi x r, where "C" is the circumference, "pi" is 3.14159 and "r" is the radius.Perform the necessary calculationsFor a circle with a radius of 4 meters, the circumference is given by 2 x 3.14 x 4 meters, which equals 25.12 meters.

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How many four-digit palindromiic number are there?

A palindromic number refers to a numeric value that remains unchanged when its digits are written backwards or forwards. Some examples of four-digit palindromes include 1001, 6886, 4334 and 9559. The term palindromic is derived from palindrome, which is also used to refer to words whose spelling remains the same when its letters are written backwards like "rotor" or "radar." Palindromes can be found in other numeral system other than decimal. There are several palindromic binary numbers, such as 1111 and 1001.

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What is the volume of a rectangular prism?

A rectangular prism has 12 edges and eight vertices. In this rectangular and solid shape, the opposite faces have equal measurements and also are parallel. Square prisms and cubes are special kinds of rectangular prisms. A rectangular prism is also known as a cuboid, and it is box-shaped. Another useful formula for a rectangular prism is its surface area. The formula is that the surface area (SA) = 2(w * h) + (l * w) + (l * h).

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What is the antiderivative of sec(x)?

The antiderivative of sec(x) is equal to the antiderivative of sec(x) * ([sec(x) + tan(x])/[sec(x) + tan(x)]). Using substitution, the variable u replaces sec(x) + tan(x), and the derivative of u, du, is (sec(x) * tan(x) + sec^2(x)) dx. Substituting u and du into the equation for the integral of ([sec^2(x) + sec(x) * tan (x) dx]/[sec(x) + tan(x)]) results in the integral of du/u. Solving that integral gives ln |u| + C, and substituting back in for u gives the above solution.

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How do you find the line of best fit?

Estimate the direction of the line of best fitGraph the points of the data. Set a pipe cleaner or piece of dry spaghetti in a position that appears to be as close as possible to as many of the points. Mark points on the graph paper at the beginning and end of the pipe cleaner or piece of spaghetti.Find the equation of the estimated lineWrite the coordinates of the two endpoints as (x1, y1) and (x2, y2). Find the slope of the line by plugging the coordinates into this formula: slope (m) = (y2-y1)/(x2-x1). Write the equation using point-slope format (y-y1 = m(x-x1)).Predict further points in the..

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Is the rounding whole numbers a difficult concept to learn?

The second digit to the right is in the 10's place, the third is in the 100's place and the pattern continues. The first thing you need to know about rounding is to what place value you are rounding. Take the number 1,857. To round this number to the nearest 100's value, find the digit in the 100's place. It is eight. Find the digit to the immediate right. If its value is four or less, the eight remains an eight, and the numbers to the right all become zeros. If the value of the digit is five or higher, the eight becomes nine, and the numbers to the right become zeros. The ..

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What are real roots in math?

However, the solution to an equation can be real roots, complex roots or imaginary roots. While an imaginary root given as (i) is sqrt (-1), a complex number is a combination of a real number and an imaginary number like (3+4i).\nWhen one needs to find the roots of an equation, such as for a quadratic equation, one can use the discriminant to see if the roots are real, imaginary, rational or irrational.\nTo find the roots of the quadratic equation a x^2 +bx + c =0, where a, b, and c represent constants, the formula for the discriminant is b^2 -4ac. When the discriminant equals zero, then there..

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How do you calculate the surface area of a right cylinder?

Determine your variablesIn order to calculate the surface area of the right cylinder, you will need the height (represented as h in the formula) and the radius of the base and lid (represented as r).Compute the formulasThe formula for the surface area of this cylinder is 2?r^2 + 2?rh, but factoring 2?r from each term, the simpler formula 2?r(r + h) is derived. Multiply the two terms to determine the surface areaOnce the terms in Step 2 are calculated, simple multiplication gives the answer.

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How can you use base-10 blocks to teach basic math concepts?

Introduce the base-10 blocks by explaining that single cubes represent the number one, the long bars represent 10 and the large squares represent 100. Students experiment with creating numbers using the blocks, such as using a 100 square, three bars and five single cubes to show 135. Practice exchanging smaller blocks for larger ones. Ten long bars turn into a 100 square, and 13 individual cubes turn into a 10 bar and three singles.\n\nTo learn addition, students represent two different numbers with the blocks and push them together. They exchange smaller blocks for larger blocks as needed. St..

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