Answer:
7.45
Step-by-step explanation:
We are given a right triangle with one side length known and an angle know so we can use some trigonometry.
You need to find the hypotenuse so you are going to use either sine or cosine.
Since the adjacent from the angle is given (SOH-CAH-TOA) we can use cosine so,
cos(20) = 7/h
=>h = 7/cos(20)
=> 7.44924
=> 7.45
Answer:
25
Step-by-step explanation:
b=4x+1 h=x+1 A=175
A=bh
Substitute: 175=(4x+1)(x+1)
Expand: 175=4x^2+5x+1
Subtract 175
4x^2+5x-174=0
Solve w/quadratic formula
(-5 <u>+</u> sqrt(25+2784))/8
Simplify: x=6 or -29/4
Distance is positive, so x=6
4x+1=4*6+1=25
Answer:
13 ft/s
Step-by-step explanation:
t seconds after the boy passes under the balloon the distance between them is ...
d = √((15t)² +(45+5t)²) = √(250t² +450t +2025)
The rate of change of d with respect to t is ...
dd/dt = (500t +450)/(2√(250t² +450t +2025)) = (50t +45)/√(10t² +18t +81)
At t=3, this derivative evaluates to ...
dd/dt = (50·3 +45)/√(90+54+81) = 195/15 = 13
The distance between the boy and the balloon is increasing at the rate of 13 ft per second.
_____
The boy is moving horizontally at 15 ft/s, so his position relative to the spot under the balloon is 15t feet after t seconds.
The balloon starts at 45 feet above the boy and is moving upward at 5 ft/s, so its vertical distance from the spot under the balloon is 45+5t feet after t seconds.
The straight-line distance between the boy and the balloon is found as the hypotenuse of a right triangle with legs 15t and (45+5t). Using the Pythagorean theorem, that distance is ...
d = √((15t)² + (45+5t)²)
Answer:
sorry if I'm wrong but I think its a=1/6
Cant see the question clearly
