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Blizzard [7]
2 years ago
7

I need help with this!!

Mathematics
2 answers:
leonid [27]2 years ago
6 0

Answer:

c = 12.5

Step-by-step explanation:

Pythagorean Theorem:

c^2 = 10^2 + (7.5)^2

c = 12.5

Leviafan [203]2 years ago
4 0

Answer:

c = 12.5

Step-by-step explanation:

a² + b² = c²

10 and 7.5 are bases of the triangle, that means they stand for a and b

the equation would be

10² + 7.5² = c²

square the numbers

100 + 56.25 = c²

156.25 = c²

√156.25 = √c²

12.5 = c

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Use the Pythagorean Theorem to find the distance to the nearest tenth, between F(9, 5) and G(-2, 2). (Hint: Place F and G on the
artcher [175]
Put a point H on (9, 2).  Sketch a triangle out of the three points.  Distance between (-2, 2) and (9, 2) is going to be 11.  Distance between (9, 2) and (9, 5) is going to be 3.    These correspond to the a and b of the Pythagorean Theorem
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3 years ago
(c). Under a set of controlled laboratory conditions, the size of the population P of a certain bacteria culture at time t (in s
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(i) Since P(t) gives the population of the culture after t seconds, the population after 1 second is

P(1) = 3•1² + 3e¹ + 10 = 13 + 3e ≈ 21.155

In Mathematica, it's convenient to define a function:

P[t_] := 3t^2 + 3E^t + 10

(E is case-sensitive and must be capitalized. Alternatively, you could use Exp[t]. You can also specify that the argument t must be non-negative by entering a condition via P[t_ ;/ t >= 0], but that's not necessary.)

Then just evaluate P[1], or N[P[1]] or N <at symbol> P[1] or P[1] // N to get a numerical result.

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(P(b) - P(a))/(b - a)

Then the ARoC between t = 2 and t = 6 is

(P(6) - P(2))/(6 - 2) ≈ 321.030

In M,

(P[6] - P[2])/(6 - 2)

and you can also include N just as before.

(iii) You want the instantaneous rate of change of P when t = 60 (since 1 minute = 60 seconds). Differentiate P :

P'(t) = 6t + 3e^t

Evaluate the derivative at t = 60 :

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The approximate value is quite large, so I'll just leave its exact value.

In M, the quickest way would be P'[60], or you can differentiate and replace (via ReplaceAll or /.) t with 60 as in D[P[t], t] /. t -> 60.

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2 years ago
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