1. Points Q,R,S, and T lie on a circle with center P. If the radius of the circle is 1, what is the value of PQ+PR+PS+PT?
2. If 10^ab= 10,000, where a and b are positive integers, what is one possible value of a?
3. In the plane, the line 2x-3y=c passes through the point (5, -1). What is the value of c?
I really have no clue as to what to do on these problems. Please help (explain). Thanks
1. They are all the length of the radius. 1+1+1+1 = 4
2. Since 10^4 = 10,000, a = 0
3. 2(5)-3(-1) = c
1. To find the value of PQ + PR + PS + PT, we need to apply the properties of a circle.
Since the points Q, R, S, and T lie on a circle with center P, the distance from P to any of these points is equal to the radius of the circle. In this case, the radius of the circle is given as 1.
Hence, we can say that PQ = PR = PS = PT = 1.
Now, to find the total value of PQ + PR + PS + PT, we just add up these individual values:
PQ + PR + PS + PT = 1 + 1 + 1 + 1 = 4.
Therefore, the value of PQ + PR + PS + PT is 4.
2. To find a possible value of a in the equation 10^ab = 10,000, we can start by expressing 10,000 as a power of 10.
10,000 can be written as 10^4.
Now, let's equate the two expressions: 10^ab = 10^4.
Since the bases are the same, the exponents must also be equal: ab = 4.
Since a and b are positive integers, we need to find two numbers that multiply together to give 4.
Possible combinations are:
- a = 4, b = 1
- a = 2, b = 2
Therefore, one possible value of a is 4.
3. To find the value of c in the equation 2x - 3y = c when the line passes through the point (5, -1), we substitute the given values into the equation.
We have the equation 2(5) - 3(-1) = c.
Simplifying this expression, we get: 10 + 3 = c.
Thus, c = 13.
Therefore, the value of c is 13.