The differentiable functions xxx and yyy are related by the following equation: \sin(x)+\cos(y)=\sqrt{2}sin(x)+cos( y)=
2

sine, left parenthesis, x, right parenthesis, plus, cosine, left parenthesis, y, right parenthesis, equals, square root of, 2, end square root
Also, \dfrac{dx}{dt}=5
dt
dx

=5start fraction, d, x, divided by, d, t, end fraction, equals, 5.
Find \dfrac{dy}{dt}
dt
dy

start fraction, d, y, divided by, d, t, end fraction when y=\dfrac{\pi}{4}y=
4
π

y, equals, start fraction, pi, divided by, 4, end fraction and 0 2
π

0, is less than, x, is less than, start fraction, pi, divided by, 2, end fraction.

The data shown in the table below represents the weight, in pounds, of a little girl, recorded each year on her birthday. age (in years) weight (in pounds) 2 32 6 47 7 51 4 40 5 43 3 38 8 60 1 23 part a: create a scatter plot to represent the data shown above. sketch the line of best fit. label at least three specific points on the graph that the line passes through. also include the correct labels on the x-axis and y-axis. part b: algebraically write the equation of the best fit line in slope-intercept form. include all of your calculations in your final answer. part c: use the equation for the line of best fit to approximate the weight of the little girl at an age of 14 years old.

In the 30-60-90 triangle below side s has a length of and side r has a length

The function a represents the cost of manufacturing product a, in hundreds of dollars, and the function b represents the cost of manufacturing product b, in hundreds of dollars. a(t) = 5t + 2 b(t) = 7t - 2t +4 find the expression that describes the total cost of manufacturing both products, a(t) + b(t). a. 7t^2 - 7t + 2 b. 7t^2 + 3 +6 c. 7t^2 + 7t - 6 d. 7t^2 - 3t + 6