Solotion let p: rn+1∖{0}→rk+1∖{0} be a smooth function, and suppose that for some d∈z, p(λx)=λdp(x) for all λ∈r∖{0} and x∈rn+1∖{0}. (such a function is said to be homogeneous of degree d.) show that the map p~: rpn→rpk defined by p~([x])=[p(x)] is well defined and smooth.

the formula for the equation of a circle is (x – h)2+ (y – k)2 = r2, where (h, k) represents the coordinates of the center of the circle, and r represents the radius of the circle. if a circle is tangent to the x-axis at (3,0), this means it touches the x-axis at that point.

there are 70 more legs than eyes at the dog show (196 – 126 = 70). dogs have two more legs than eyes, and humans have the same number of legs as eyes. thus 70 is twice the number of dogs at the show, so the number of dogs is half of 70, which is 35. to get the number of humans, subtract 35 from 63: 63 – 35 = 28.

step-by-step explanation:

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step-by-step explanation: