9514 1404 393
Answer:
y +3 = 1/2(x +4)
Step-by-step explanation:
The slope is given by the formula ...
m = (y2 -y1)/(x2 -x1)
m = (1 -(-3))/(4 -(-4)) = 4/8 = 1/2
The point-slope form of the equation for a line is ...
y -y1 = m(x -x1)
Filling in the known values, this is ...
y -(-3) = 1/2(x -(-4))
y +3 = 1/2(x +4)
Answer:
Step-by-step explanation:
(96 minutes)/(32 sculptures) = (96/32 minutes)/sculpture = (3 minutes)/sculpture
It takes 3 minutes to make one sculpture.
(160 balloons)/(32 sculptures) = (160/32 balloons)/sculpture = (5 balloons)/sculpture
It takes 5 balloons to make one sculpture.
(160 balloons)/(96 minutes) ≈ 1.7 balloons used per minute.
To determine how much silk Amanda has at the end we need to substract the amount each pice need from the original amount:
Therefore Amanda has 11 17/28 yards of silk left.
<span> Sketch this, assuming the Earth is a sphere with radius R, so a plane slice through the periscope, ship and center of the Earth is a circle of radius R. Draw the lines out from the center (O) of the circle to point A at the top of the periscope and point B at the top of the ship. so that line AB is tangent to the circle at point C. That makes triangles OAC and OBC right triangles, each having the right angle at C. </span>
<span>From the problem, the lengths OA = R+5, OC = R, and OB=R+50. Label the lengths AC = p and BC= q, then use Pythagoras: </span>
<span>R² + p² = (R + 5)² </span>
<span>R² + q² = (R + 50)² </span>
<span>Solve those: </span>
<span>p² = (R + 5)² - R² = 10R - 25 </span>
<span>p = √(10R + 25) </span>
<span>q² = (R + 50)² - R² = 100R + 2500 </span>
<span>q = √(100R + 2500) </span>
<span>Find a good value for the radius R (in ft. units!) and calculate. The distance from periscope top to ship top is (p + q) feet. Convert that to miles for your answer.</span>