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Mathematics

1 answer:

ruslelena [56]3 years ago

7 0

|12| ÷ 2 • |-5|
= 12 ÷ 2 • 5
= 6 • 5
= 30
Absolute values just make the number positive if it is negative. The number stays positive if it’s positive.

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If cos x=8/17, and 270° < x < 360°<br> what is cos(2x)?

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Answer: $\bold{-\dfrac{161}{289}}$

<u>Step-by-step explanation:</u>

Given: cos x = $\dfrac{8}{17}$ , x is in Quadrant 4

Use Pythagorean Theorem to find sin x:

8² + y² = 17²

y² = 17² - 8²

y² = 289 - 64

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→ sin x = $-\dfrac{15}{17}$

Use the double angle formula to find cos (2x):

$cos (2x) = cos^2 x - sin^2 x\\\\.\qquad=\bigg(\dfrac{8}{17}\bigg)^2-\bigg(-\dfrac{15}{17}\bigg)^2\\\\\\.\qquad=\dfrac{64}{289}-\dfrac{225}{289}\\\\\\.\qquad=-\dfrac{161}{289}$

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myrzilka [38]

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Step-by-step explanation:

Finding an equation of a tangent line to that function requires that we find the derivative of the function at that point. Since this is an absolute value function with its cusp at (2, 5), the function is not differentiable here.

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3 years ago

express the limit as a definite integral on the given interval. lim n → [infinity] n ∑ i = 1 cos x i x i δ x , [ 2 π , 4 π ]

Lemur [1.5K]

The limit as a definite integral on the interval $\lim _{n \rightarrow \infty} \sum_{i=1}^n \frac{\cos x_i}{x_i} \Delta x$ on [2π , 4π] is $\int_{2\pi}^{4 \pi} \frac{\cos x}{x} d x$$ .

<h3>What is meant by definite integral?</h3>

A definite integral uses infinitesimal slivers or stripes of the region to calculate the area beneath a function. Integrals can be used to represent a region's (signed) area, the cumulative value of a function changing over time, or the amount of a substance given its density.

Definite integral, a term used in mathematics. is the region in the xy plane defined by the graph of f, the x-axis, and the lines x = a and x = b, where the area above the x-axis adds to the total and the area below the x-axis subtracts from the total.

If an antiderivative F exists for the interval [a, b], the definite integral of the function is the difference of the values at points a and b. The definite integral of any function can also be expressed as the limit of a sum.

Let the equation be

$\int_a^b f(x) d x=\lim _{n \rightarrow \infty} \sum_{i=1}^n f\left(x_i\right) \Delta x$