If a and B are angles which tan a= 3/4 and cos B= 8/17. Determine the exact value of cos(a-B)

Life table of males at age 30. Probability of dying between ages x and x+1

total population:  

29–30 . . . . . . . . . . . . . . . . . . . . . . . . 0.001030

30–31 . . . . . . . . . . . . . . . . . . . . . . . . 0.001061

males:  

29–30 . . . . . . . . . . . . . . . . . . . . . . . . 0.001420

30–31 . . . . . . . . . . . . . . . . . . . . . . . . 0.001448

white population

29–30 . . . . . . . . . . . . . . . . . . . . . . . . 0.001005

30–31 . . . . . . . . . . . . . . . . . . . . . . . . 0.001037

white males

29–30 . . . . . . . . . . . . . . . . . . . . . . . . 0.001372

30–31 . . . . . . . . . . . . . . . . . . . . . . . . 0.001399

non Hispanic white population

29–30 . . . . . . . . . . . . . . . . . . . . . . . . 0.001083

30–31 . . . . . . . . . . . . . . . . . . . . . . . . 0.001116

non Hispanic white males

29–30 . . . . . . . . . . . . . . . . . . . . . . . . 0.001477

30–31 . . . . . . . . . . . . . . . . . . . . . . . . 0.001503

Jacob, non Hispanic white male. 30 years old.

Probability that Jacob lives to be 30 years old.  

Since the given probabilities are probabilities of dying, I think we simply subtract it from 1 to get the probability of living. We will use the probability of non Hispanic white male.

                                         Probability of living to be 30 y.o.

29 - 30 : 1 - 0.001477 = 0.998523

30 - 31 : 1 - 0.001503 = 0.998497

Step-by-step explanation:

Life table of males at age 30. Probability of dying between ages x and x+1

total population:  

29–30 . . . . . . . . . . . . . . . . . . . . . . . . 0.001030

30–31 . . . . . . . . . . . . . . . . . . . . . . . . 0.001061

males:  

29–30 . . . . . . . . . . . . . . . . . . . . . . . . 0.001420

30–31 . . . . . . . . . . . . . . . . . . . . . . . . 0.001448

white population

29–30 . . . . . . . . . . . . . . . . . . . . . . . . 0.001005

30–31 . . . . . . . . . . . . . . . . . . . . . . . . 0.001037

white males

29–30 . . . . . . . . . . . . . . . . . . . . . . . . 0.001372

30–31 . . . . . . . . . . . . . . . . . . . . . . . . 0.001399

non Hispanic white population

29–30 . . . . . . . . . . . . . . . . . . . . . . . . 0.001083

30–31 . . . . . . . . . . . . . . . . . . . . . . . . 0.001116

non Hispanic white males

29–30 . . . . . . . . . . . . . . . . . . . . . . . . 0.001477

30–31 . . . . . . . . . . . . . . . . . . . . . . . . 0.001503

Jacob, non Hispanic white male. 30 years old.

Probability that Jacob lives to be 30 years old.  

Since the given probabilities are probabilities of dying, I think we simply subtract it from 1 to get the probability of living. We will use the probability of non Hispanic white male.

                                         Probability of living to be 30 y.o.

29 - 30 : 1 - 0.001477 = 0.998523

30 - 31 : 1 - 0.001503 = 0.998497

lol we need to see what the question is asking about

step-by-step explanation:

answer: ratio of volume of cone (with 3 times the height and equal diameter) to volume of cylinder is 2 to 1. the value of π is not used.

step-by-step explanation:

radius is diameter/2 = 4.

area of circle is π r^2.

volume of cylinder is height × area of base = hπr^2 = 3(4^2) π = 48π cubic inches.

not knowing the formula for volume of cone, i calculate it using calculus (which is for calculating things).

volume of cone is integral 0 to h area(y) dy. area(y) is π r(y)^2. r(y) runs r to zero as y runs zero to h, r(0) = r, r(h) = 0.

r(y) = r - r/h y

area(y) = π (r - r/h y)^2 = π (r^2 - 2r^2y/h + r^2y^2/h^2) = π r^2(1-2y/h+y^2/h^2)

antiderivative area(y) = π r^2 (y-y^2/h+y^3/(3h^2))

integral 0 to h = π r^2(h-h^2/h+h^3/(3h^2) - (0)) = π r^2(h - h + h/3) = π r^2(h/3) = π/3 r^2 h

volume of this cone is π/3(4^2)18 cubic inches.

= 6 16 π = 96π cubic inches.

cone has twice the volume, 96/48.

cone height is 6 times the cylinder.

ratio of volume formula: π r^2 cancels.

cone over cylinder ratio is 6h/3 to h, 2 to 1.