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3 years ago

Use the quadratic formula to solve the equation 25x^2-30x+25=0

Mathematics

1 answer:

Reika [66]3 years ago

8 0

Answer: $x=\frac{3}{5}+i\frac{4}{5},\:x=\frac{3}{5}-i\frac{4}{5}$

Step-by-step explanation:

$25x^2-30x+25=0$

$x_{1,\:2}=\frac{-\left(-30\right)\pm \sqrt{\left(-30\right)^2-4\cdot \:25\cdot \:25}}{2\cdot \:25}$

$\sqrt{\left(-30\right)^2-4\cdot \:25\cdot \:25}$

$=\sqrt{30^2-4\cdot \:25\cdot \:25}$

$=\sqrt{30^2-2500}$

$=i\sqrt{2500-30^2}$

$=40i$

$x_{1,\:2}=\frac{-\left(-30\right)\pm \:40i}{2\cdot \:25}$

$x_1=\frac{-\left(-30\right)+40i}{2\cdot \:25},\:x_2=\frac{-\left(-30\right)-40i}{2\cdot \:25}$

$x=\frac{3}{5}+i\frac{4}{5},\:x=\frac{3}{5}-i\frac{4}{5}$

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Step-by-step explanation:

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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

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

substitute the values in the above equation, we get

= $\lim _{n \rightarrow \infty} \sum_{i=1}^n \frac{\cos x_i}{x_i} \Delta x$ on [2π, 4π],

simplifying the above equation

$\int_{2\pi}^{4 \pi} \frac{\cos x}{x} d x$$

To learn more about definite integral refer to:

brainly.com/question/24353968

#SPJ4

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2 years ago