Veronica put a $400 necklace on layaway by making a 10% down payment

Mathematics

1 answer:

AnnZ [12.3K]3 months ago

7 0

7 weeks APEX LEARNING

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The name of the lesson is "Using Trigonometric Laws" The two non-parallel sides of an isosceles trapezoid are each 7 feet long.

AnnZ [12381]

The diagonal measures 20.68 ft; the shorter base is 17.21 ft. To understand this, we recognize that with base angles summing to 140°, each angle is 70°, given the isosceles trapezoid's properties. We can apply the Law of Cosines to find the diagonal's length, denoted as d. The length of the diagonal determines to be d = 20.68 ft. Determining the shorter base is somewhat more complex. By drawing an altitude from the upper vertices to the base, which measures 22 ft, we create two similar smaller right triangles requiring us to find the height and base measures related to each of the 70-degree angles and the hypotenuse of 7. By working through the calculations for height and base from one triangle, we subsequently find that 22 minus twice the base measure gets us to the shorter base's measure, arriving at x = 17.21 ft.

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2 months ago

1. X^4(dy/dx) +x^3y =- sec (xy)<br><br>Integral by separation of variables? <br>

PIT_PIT [12445]

Answer:

Step-by-step explanation:

Considering the differential equation x^4(dy/dx) + x^3y = -sec(xy). We will solve it employing the method of separation of variables;

$x^{4} \frac{dy}{dx} +x^{3}y = -sec(xy)\\x^{3}(x\frac{dy}{dx} + y) = -sec(xy)\\let \ v=xy\\\frac{dv}{dx} = x\frac{dy}{dx} + y(implicit \ in\ nature)\\$

By substituting v and dv/dx into the previous equation, we acquire;

$x^{3}\frac{dv}{dx} = -secv$

We then separate the variables:

$-\frac{dv}{secv} = \frac{dx}{x^{3} }$

$-cosvdv = x^{-3}dx\\ integrating\ both\ sides\\-\int\limits {cosv} \, dv = \int\limits {x^{-3} } \, dx\\-sinv = \frac{x^{-2} }{-2} + C\\since\ v = xy\\-sinxy = \frac{x^{-2} }{-2} + C\\2sin(xy) = x^{-2} -2C\\2 sin(xy) = \frac{1}{x^{2} } -K (where\ K = 2C)\\$

The end expression provides the solution to the differential equation.

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3 months ago

Emerson drives 135 miles at 60 miles per hour to get to the train station. He waits 20 minutes for a train. Then he travels 350

Inessa [12570]

Response: 4.4

Detailed breakdown:

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2 months ago

Ray CE is the angle bisector of ACD. Which statement about the figure must be true? mECD = mECB mACE = mACD ACE DCB

Leona [12618]

Answer:

ACE = ECD is the solution

Step-by-step explanation:

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2 months ago