Mike likes to canoe he can paddle 150 feet per minute he is planning a river trip that will take him to a destination about 30.000 upstream that is against the current)the speed of the current will work against the speed that he can paddle be the speed of the current in feel per minute mike wants to know how long it will take him to travel the 30.000 leet upstream which expression, t(s) represents the time in minutes
since the volume of gas and the cube of its radius vary directly, we can set up an initial equation to find the constant of variation:
v = kr³, where v=volume, r=radius and k=contant of variation
given that a balloon with a radius of 3 inches can hold a volume of 81 cubic inches, we can plug these values into the equation and solve for 'k':
81 = k3³ or 81 = 27k or k = 3
given 'k', now we can find the volume of the balloon with a radius of 2:
v = (3)(2³) = 24 in³
since the question asked how much gas must be released to reduce the radius, we would find the difference of 81 and 24:
81 - 24 = 57 in³
to find a side length of similar triangles, write two equal ratios and set them equal in a proportion. the ratios should be written using the side lengths in each triangle which correspond to each other.
this proportion compares the short side of the largest triangle to its hypotenuse and compares the short side of the smallest triangle to its hypotenuse. to solve for x, cross multiply by multiplying numerator and denominator.
options a and d are right.
the given function is of the above form
we have here a=1/4 : b=1 : p = -pi/3: and k=-1
hence we have an amplitude of 1/4, horizontal shift of pi/3 to the right,vertical shift of 1 unit down and vertical shrink of 1/4
hence the correct choices would be
1) it has amplitude 1/4
d) horizontal shift of pi/3 to the left
other options are false
let's use x as an unknown variable. you know that this amount was twice what she spent. this statement means the amount is equal to 2x. however, the amount is also 12 dollars less. so, the equation would now become 2x-12. lastly, you know that the amount she spent on jeans was 36 dollars so the equation would equal 36 dollars: 2x-12=36 hope this !