Math Exercise Solutions

Extract

[...] Trigonometry, Equations and Functions Exercise 1 « Question Calculate the area of triangle ADE. It is known that: is perpendicular to and F are aligned. Or: A triangle with two sides perpendicular is a right triangle. So: ADE is a right triangle. It is known that: ADE is a right triangle. AD = 6,825 cm ED = 14 cm Or : The formula for the calculation of the area of a right triangle is: Area = * / 2 with a and b different from the hypotenuse. [...]

[...] Statement n° 'Bob took less than 3h15 min to finish his marathon' Let the formula for the speed be: Speed = distance / time So time = distance / speed So t = 42 / 12 T = 7/2 T = 3 + 1/2 T = 3h 30 min Bob took 3h30 to run his marathon. The statement is false. « 4. The following Scratch program is considered. Statement number 'If we choose 2 as the starting number the result is By choosing we have Step 3 * 2 = 6 Step 2 - 4 = Result = Step 1 * Step 2 = 6 * = -12 By taking we indeed get - 12 because it amounts to doing * = -12 The statement is true « 5. [...]

[...] It is known that: and are perpendicular to Or: If two lines are perpendicular to the same line, then these two lines are parallel to each other. Therefore: and are parallel. « Question Calculate CB. It is known that : The points E and D are aligned in the same order. Or : According to Thales' theorem, we have : AB/AD = AC/AE = BC/DE 3,9/6,825 = AC/15,575 = BC/14 Therefore 3.9/6.825 = BC/14 Therefore : BC = (3.9/6.825) * 14 = 8 CB is 8 cm. [...]

[...] What is the result obtained with program A if we choose as the starting number? We have the number On multiply by which gives: * = 15 On add 7 which gives 15 + 7 = 22 We get 22 by taking the number in the program A « b. What is the result obtained with program B if we choose 9 as the starting number ? We have the digit 9 We subtract 6 from this number which gives: 9-6 = 3 We multiply by 4 the result: 3*4 = 12 We add 11 to this result: 12 + 11 = 23 We obtain 23 by taking the number 9 in the program B « 2. [...]

[...] It is known that: and are affine functions of the form y = ax + b The coefficients a and b for the function f and g are respectively - and -13 Or: The coefficient b is called the Y-intercept, which means it is the value for x=0 Hence, to identify the two curves, it is enough to look at the point of intersection between the y-axis and the plot of the curve and So: The curve cuts the y-axis at which means that is the graphical representation of and by elimination is the graphical representation of f(x). cuts the y-axis at y = 7 which confirms the answer above. « b. By graphical reading, give, as precisely as possible, the number whose image is the same by the function f and the function g. » By graphical reading, the number whose image is the same by the function f and the function g seems to be 2.25 « 4. Determine by calculation the starting number for which programs A and B give the same result. [...]