Tutor profile: Animesha K.
Yo aconsejo que tú _____ (ir) al doctor. Fill in the blank with the best conjugation of the verb in parentheses.
Our answer would be: vayas. We know we need the tú form of the word ir. Next, we need to find the tense of the verb. Since we're switching from yo to tú, and since we are giving a suggestion, we need the subjunctive tense of the verb. So the tú conjugation of ir in the subjunctive tense is: vayas.
An equilateral hexagon ABCDEF is inscribed within a circle Z. Each side of the hexagon is 2 units in length. What is the length of arc DEF?
We know that equilateral hexagons have sides of all equal length. We also know that an equilateral hexagon is made up of 6 equilateral triangles, where each side of the hexagon is the base of each triangle. Since we know AB (or any other side) is two units long, we know that ZA is also two units long (length from center to a vertex of the hexagon). This is because ZA is also a side of the equilateral triangle, and is 2 units long. We know that because the hexagon has been inscribed, each of the vertices of the hexagon is also a point on the circle. As a result, ZA is also a radius of the circle. To find the circumference: C = 2*pi*r C = 4*pi Now, we can also determine that the arc corresponding to each side of the hexagon (i.e. arc AB and side AB) makes up 1/6 of the circumference as each vertex divides the circle into sixths. So, arc DE is 1/6 of C and EF is also 1/6 of C, summing to 2/6 or 1/3 of C. We can solve this as follows: arcDEF = (1/3)*(4*pi) arcDEF = (4/3)*pi Our final answer is (4/3)*pi units.
3x + 6y = 15 Write (2^x)/(2^y) in terms of a single variable.
According to the properties of exponents: (2^x)/(2^y) = 2^(x-y) We can also find x in terms of y based on the initial equation: 3x + 6y = 15 3x = 15 - 6y (divide by 3) x = 5 - 2y We can substitute this new value in for x to get: 2^((5 - 2y) - y) = 2^(5 - 3y) So the final answer is: 2^(5 - 3y)
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