1. D bc switch the 1/3 into 3/1, then 4 time 3/1 = 12. Basically 4 times 3 =12
2. D
Answer:
(a) 36
(b) y = 36x-31
Step-by-step explanation:
(a) dy/dx = 18x
slope of tangent at (2, 41) = 18(2)
= 36
(b) using y-y1 = m(x-x1)
y-41 = 36(x-2)
y = 36x-31
Answer:
Neither
Explanation:
The slope-intercept form of the equation of a line is generally given as;

where m = the slope of the line
b = the y-intercept of the line
Two lines are said to be parallel if they have the same slope. Looking at the two given equations below, we see that the slope of the 1st one, 5/7, is different from the slope of the 2nd one, 7/5;

Two lines are said to be perpendicular if their slopes are negative reciprocals of each other, let's go ahead and compare their slopes;

So the two lines are not perpendicular to each other. It, therefore, means that the correct answer will be Neither.
(3 cos x-4 sin x)+(3sin x+4 cos x)=5
(3cos x+4cos x)+(-4sin x+3 sin x)=5
7 cos x-sin x=5
7cos x=5+sin x
(7 cos x)²=(5+sinx)²
49 cos²x=25+10 sinx+sin²x
49(1-sin²x)=25+10 sinx+sin²x
49-49sin²x=25+10sinx+sin²x
50 sin² x+10sinx-24=0
Sin x=[-10⁺₋√(100+4800)]/100=(-10⁺₋70)/100
We have two possible solutions:
sinx =(-10-70)/100=-0.8
x=sin⁻¹ (-0.8)=-53.13º (360º-53.13º=306.87)
sinx=(-10+70)/100=0.6
x=sin⁻¹ 0.6=36.87º
The solutions when 0≤x≤360º are: 36.87º and 306.87º.
B.C. counts down to 0, and that's when A.D. starts counting up. That means you can add 582 and 1643, to get their difference. Pythagoras and Newton were born 2,225 years apart.