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what is the smaller angle formed by the minute and hour hands at 3: 30pm?

75°

Step-by-step explanation:

Calculate the angle of the minute hand (θm)

The clock face is a circle of 360°, and there are 60 min in 1h,

So, the minute hand travels 6° in 1 min.

In 30 min, the minute hand will travel

θm = 30 × 6

     = 180°

Calculate the angle of the hour hand (θh)

The hour hand travels 360° in 12 h, so it travels 30° in 1 h and 0.5° in 1 min.

It has travelled for 3 h + 30 min

θh = (3 × 30) + (30 × 0.5)

    = 90 + 15

    = 105°

Calculate the angle between the hands

θ =  θm -  θh

  = 180 - 105

  = 75°

The angle between the hands is 75°.

answer: all of the odd numbers were opened

the first person was the one that was opening all of the lockers. since one is odd, this causes all of the odd number lockers to be opened in the end.

center (1,3) with radius 6

step-by-step explanation:

we must complete the square to find the center and radius of the circle.

first make sure the x and y squared terms have 1 as their coefficients. we also make sure x and y terms together.

we now create space between the x and y terms with parenthesis.

we complete the square by taking the middle terms -2x and the -6y - divide each and square them.

we add the squares to both sides.

simplify.

and write the quadratics in factored form.

the center is (h,k) or (1,3). the radius is the square root of 36 which is 6.