D is directly proportional to t2 When t = 4, D = 8 Find the positive value of t when D = 50

t = 10

Step-by-step explanation:

Proportions

D is directly proportional to t squared. This can be written as:

Where k is the proportionality constant. It can be calculated by substituting the given condition in the formula, when t=4, D=8:

Solving for k:

Thus, the proportional relationship is:

When D=50, the value of t can be found by solving for t:

Multiplying by 2:

Taking the square root:

The positive value of t is:

t = 10

the equation cos(35) =a/25 can be used to find the length of bc what is the length of bc? round to the nearest tenth

step-by-step explanation:

we have three similar triangles, because each has a right angle and shares an angle.   let's write the angles in order: opposite to short leg, long leg, hypotenuse.

cab similar to bad similar to cbd

or as ratios,

ca: ab: cb = ba: ad: bd = cb: bd: cd

we also know

ac = ad + cd

(ad+cd): ab: cb = ba: ad: bd = cb: bd: cd

(ad+cd)/cb=cb/cd

we have cb=6, ad=5 and seek x=cd.

we reject the negative root and conclude x=4

answer: 4