Given circle E with diameter CD and radius EA. AB is tangent to E at A. if AD = 15 and EC = 14, solve for AC.

AC ≈ 23.6 units

Step-by-step explanation:

m∠CAD = 90°

CD = 2×14 = 28 , AD = 15

CD² = AD² + AC² ⇒ AC² = CD² - AD²

AC² = 28² - 15² = ( 28 - 15 )( 28 + 15 ) = 13 × 43 = 559

AC ≈ 23.6

The answer is in the image 

For every 8 cars there are 7 trucks

Therefore,

Cars:Truck=8:7

Answer is B)8:7

The answer is in the image 

Speed=Distance/time

Here,

distance=15m

time=1sec

speed=15/1=15m/sec

Distance=Speed*time

time=15min=15*60sec=900sec

Distance travelled in 15 min=15*900=13,500m

=13500/1000 km=13.5Km

The wood before starting =12 feet

Left wood=6 feet

Wood used till now=12-6=6 feet

Picture frame built till now= 6/(3/4)

=8 pieces

Therefore, till now 8 pieces have been made.

The answer is in the image 

30% of 420 are first year students

first year students = (30/100 )*420

=126 students

Student who are not in first year = 420-126

=294 students  

Area of rectangle= L*b

here,

L=12.4 cm

b= 8.8 cm

A= L*b

= 12.4 * 8.8 = 109.12 cm^2

Let the father's age be x and son's be y

10 years before-

Father age=x-10

sons age=y-10

Given,

x-10=10(y-10)

x-10=10y-100

Given present age of father=40

therefore,

x=40

40-10=10y-100

10y-100=30

10y=130

y=130/10

y=13

Therefore present age of son=13years