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3 years ago

Find the maximum and minimum values by evaluating the equation

Mathematics

1 answer:

dezoksy [38]3 years ago

7 0

Answer:

min = -9

max =3

Step-by-step explanation:

C = x-3y

x ≥0

x≤3

y≥0

y≤3

The minimum will be be when x is smallest and y is at its max

x =0 and y = 3

C = 0 - 3(3)

C = 0-9 = -9

The minimum is -9

The maximum occurs when x is largest and y is smallest

x =3 and y = 0

C = 3 - 3(0)

C = 3-0 = 3

The max is 3

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Cube root of - 1000p^12q^3

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\qquad (p^4)^3
\end{cases}\implies \sqrt[3]{(-1)^3(10)^3(p^4)^3q^3}
\\\\\\
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3 years ago

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3 years ago

Write the sum using summation notation, assuming the suggested pattern continues.

Usimov [2.4K]

Answer:

Sum of the sequence will be 648

Step-by-step explanation:

The given sequence is representing an arithmetic sequence.

Because every successive term of the sequence is having a common difference d = -3 - (-9) = -3 + 9 = 6

3 - (-3) = 3 + 3 = 6

Since last term of the sequence is 81

Therefore, by the explicit formula of an arithmetic sequence we can find the number of terms of this sequence

$T_{n}=a+(n-1)d$

where a = first term of the sequence

d = common difference

n = number of terms

81 = -9 + 6(n - 1)

81 + 9 = 6(n - 1)

n - 1 = $\frac{90}{6}=15$

n = 15 + 1 = 16

Now we know sum of an arithmetic sequence is represented by

$\sum_{n=1}^{n}(a_{n})=\frac{n}{2}(a_{1}+a_{n})$

Now we have to find the sum of the given sequence

$S_{16}=\frac{16}{2}[-9 + (16-1)6]$

= 8[-9 + 90]

= 8×81

= 648

Therefore, sum of the terms of the given sequence will be 648.

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3 years ago

The point (−3, 1) is on the terminal side of angle Θ, in standard position. What are the values of sine, cosine, and tangent of

inn [45]

The angle is in the second quadrant so only the sine is positive .
Length of the hypotenuse = sqrt (-1^2 + 3^2) = sqrt10
sine = 1/sqrt10 = 0.3162 to 4 dec places
tangent = 1 / -3 = -0.3333 to 4 d p's
cosine = -3/sqrt10 = -0.9487 to 4 d, p's.

8 0

3 years ago

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