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2 years ago

Evaluate the expression without using a calculator Tan(arccos3/4)

Mathematics

1 answer:

julia-pushkina [17]2 years ago

6 0

9514 1404 393

Answer:

(√7)/3

Step-by-step explanation:

The relationship between tangent and cosine is ...

tan(α) = √(1/cos(α)² -1)

The cosine of the angle is given as 3/4, so the tangent is ...

tan(arccos(3/4)) = √(1/(3/4)² -1) = √(16/9 -1) = √(7/9)

tan(arccos(3/4)) = (√7)/3

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(7p+8)-(5p-2) combine like terms

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The answer is:

= 2p+10

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2 years ago

The number of bacteria in a refrigerated food product is given by N ( T ) = 22 T 2 − 123 T + 40 , 6 < T < 36 , where T is

antoniya [11.8K]

Answer:

$N(T(t)) = 1408t^2 - 385.6t - 105.52$

Time for bacteria count reaching 8019: t = 2.543 hours

Step-by-step explanation:

To find the composite function N(T(t)), we just need to use the value of T(t) for each T in the function N(T). So we have that:

$N(T(t)) = 22 * (8t + 1.7)^2 - 123 * (8t + 1.7) + 40$

$N(T(t)) = 22 * (64t^2 + 27.2t + 2.89) - 984t - 209.1 + 40$

$N(T(t)) = 1408t^2 + 598.4t + 63.58 - 984t - 169.1$

$N(T(t)) = 1408t^2 - 385.6t - 105.52$

Now, to find the time when the bacteria count reaches 8019, we just need to use N(T(t)) = 8019 and then find the value of t:

$8019 = 1408t^2 - 385.6t - 105.52$

$1408t^2 - 385.6t - 8124.52 = 0$

Solving this quadratic equation, we have that t = 2.543 hours, so that is the time needed to the bacteria count reaching 8019.

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3 years ago

List 2 integers that are congruent to 4 modulo 14.

vivado [14]

Answer:

32, 46

Step-by-step explanation:

Remember, a is congruent to b modulo d if d divides a-b.

Now, the problem says that b=4 and d=14.

Let a=32. Observe that a-b=28 and $\frac{28}{14}=2$ , then 32 is congruent to 4 modulo 14.

Let a=46. Observe that a-b=46-4=42 and $\frac{42}{14}=3$ , then 46 is congruent to 4 modulo 14.

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3 years ago

What is the circumference of the largest circle that can fit a rectangle with dimension 8 x 12?

Minchanka [31]

The number that will fit there is 93

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3 years ago

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