Answer:
0.75 feet per second.
Step-by-step explanation:
Please find the attachment.
We have been given that a 25-ft ladder is leaning against a wall. We can see from the attachment that ladder forms a right triangle with respect to wall and ground.
So we can set a Pythagoras theorem as:


Now, we need to find the derivative of above equation with respect to time.

Since the adder is moving toward the wall at a rate of 1 ft/sec for 5 sec, so x after 5 seconds would be: 
Let us solve for y using Pythagoras theorem.




Take positive square root:


Upon substituting our given values in derivative equation, we will get:






Therefore, the ladder is moving up at a rate of 0.75 feet per second.
In geometry, it is always advantageous to draw a diagram from the given information in order to visualize the problem in the context of the given.
A figure has been drawn to define the vertices and intersections.
The given lengths are also noted.
From the properties of a kite, the diagonals intersect at right angles, resulting in four right triangles.
Since we know two of the sides of each of the right triangles, we can calculate their heights which in turn are the segments which make up the other diagonal.
From triangle A F G, we use Pythagoras theorem to find
h1=A F=sqrt(20*20-12*12)=sqrt(256)=16
From triangle DFG, we use Pythagoras theorem to find
h2=DF=sqrt(13*13-12*12)=sqrt(25) = 5
So the length of the other diagonal equals 16+5=21 cm
Answer:
The probability that no flaws occur in a certain portion of wire of length 5 millimeters = 1.1156 occur / millimeters
Step-by-step explanation:
<u>Step 1</u>:-
Given data A copper wire, it is known that, on the average, 1.5 flaws occur per millimeter.
by Poisson random variable given that λ = 1.5 flaws/millimeter
Poisson distribution 
<u>Step 2:</u>-
The probability that no flaws occur in a certain portion of wire

On simplification we get
P(x=0) = 0.223 flaws occur / millimeters
<u>Conclusion</u>:-
The probability that no flaws occur in a certain portion of wire of length 5 millimeters = 5 X P(X=0) = 5X 0.223 = 1.1156 occur / millimeters
Answer: 50%
Step-by-step explanation:
In 2010, there were only 2 bike manufacturers and they had market shares of 30% and 70%.
A new manufacturer joins the market and captures 10% of the market share and Splendor increases to 40% of market share.
Market shares:
Yamaha = 10%
Splendor = 40%
Passion = 100% - 10% - 40%
= 50%