Answer:
The measures of angles of triangle MNP are
Step-by-step explanation:
<u><em>The picture of the question in the attached figure</em></u>
step 1
Find the measure of arcs AB, BC and AC
we know that
The inscribed angle is half that of the arc it comprises.
so
step 2
Find the measure of angle M
we know that
The measurement of the outer angle is the semi-difference of the arcs it encompasses.
![M=\frac{1}{2}[arc\ AB+arc\ BC-arc\ AC]](https://tex.z-dn.net/?f=M%3D%5Cfrac%7B1%7D%7B2%7D%5Barc%5C%20AB%2Barc%5C%20BC-arc%5C%20AC%5D)
substitute
![M=\frac{1}{2}[2\gamma+2\alpha-2\beta]\\M=[\gamma+\alpha-\beta]](https://tex.z-dn.net/?f=M%3D%5Cfrac%7B1%7D%7B2%7D%5B2%5Cgamma%2B2%5Calpha-2%5Cbeta%5D%5C%5CM%3D%5B%5Cgamma%2B%5Calpha-%5Cbeta%5D)
step 3
Find the measure of angle N
we know that
The measurement of the outer angle is the semi-difference of the arcs it encompasses.
![N=\frac{1}{2}[arc\ AC+arc\ BC-arc\ AB]](https://tex.z-dn.net/?f=N%3D%5Cfrac%7B1%7D%7B2%7D%5Barc%5C%20AC%2Barc%5C%20BC-arc%5C%20AB%5D)
substitute
![N=\frac{1}{2}[2\beta+2\alpha-2\gamma]\\N=[\beta+\alpha-\gamma]](https://tex.z-dn.net/?f=N%3D%5Cfrac%7B1%7D%7B2%7D%5B2%5Cbeta%2B2%5Calpha-2%5Cgamma%5D%5C%5CN%3D%5B%5Cbeta%2B%5Calpha-%5Cgamma%5D)
step 4
Find the measure of angle P
we know that
The measurement of the outer angle is the semi-difference of the arcs it encompasses.
![P=\frac{1}{2}[arc\ AC+arc\ AB-arc\ BC]](https://tex.z-dn.net/?f=P%3D%5Cfrac%7B1%7D%7B2%7D%5Barc%5C%20AC%2Barc%5C%20AB-arc%5C%20BC%5D)
substitute
![P=\frac{1}{2}[2\beta+2\gamma-2\alpha]\\P=[\beta+\gamma-\alpha]](https://tex.z-dn.net/?f=P%3D%5Cfrac%7B1%7D%7B2%7D%5B2%5Cbeta%2B2%5Cgamma-2%5Calpha%5D%5C%5CP%3D%5B%5Cbeta%2B%5Cgamma-%5Calpha%5D)
The answer is 15
To find the answer set up an equation like this
a2 + b2 = c2 (2 means squared)
Here we are trying to find the value of a so we know the values of b and c.
a2 + 20(squared) = 25(squared)
20 squared equals 400
25 squared equals 625
a2 + 400 = 625
Subtract 400 from 625 which equals 225.
Now we find the square root or closest square root of 225.
The square root of 225 is 15. 15 x 15 = 225
Answer:
<h2>The slope of the line tangent to the function at x = 1 is 2.01 ≅2.</h2>
Step-by-step explanation:
Using the formula of derivative, it can be easily shown that,
where
.
Here we need to show that as per the instructions in the given table.
Δy = f(x + Δx) - f(x) = f(1 + 0.01) - f(1) =
.
In the above equation, we have put x = 1 because we need to find the slope of the line tangent at x = 1.
Hence, dividing Δy by Δx, we get,
.
Let's examine this taking a smaller value.
If we take Δx = 0.001, then Δy =
.
Thus,
.
The more smaller value of Δx is taken, the slope of the tangent will be approach towards the value of 2.
What would you like help with?
Answer:
There would be 7 swan boat rides out of which 6 will carry 6 people each but the last swan boat ride carries 4 people. 2 more people can join the swan boat ride.
Step-by-step explanation:
We are given the following information in the question:
A park guide plans the swan boat ride for 40 people.
Total number of people = 40
Number of people that can ride in 1 boat = 6
Number of boats required =

This can also be represented with the modulo function which gives the remainder.

Thus, there would be 7 swan boat rides out of which 6 will carry 6 people each but the last swan boat ride carries 4 people.
2 more people can join the swan boat ride.