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Genrish500 [490]

3 years ago

7

Help me please i need help on geometry to passthe 10th grade

1 answer:

Leokris [45]3 years ago

4 0

EZ = 8 because E is the midpoint of BZ

Triangles DBE and ABZ are similar because DE is parallel to AZ

therefore by property of similar triangles
8 / (8+8) = 9 / ZA

1/2 = 9/ZA

ZA = 18

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Find the exact length of the curve. x=et+e−t, y=5−2t, 0≤t≤2 For a curve given by parametric equations x=f(t) and y=g(t), arc len

Rama09 [41]

The length of a curve <em>C</em> parameterized by a vector function <em>r</em><em>(t)</em> = <em>x(t)</em> i + <em>y(t)</em> j over an interval <em>a</em> ≤ <em>t</em> ≤ <em>b</em> is

$\displaystyle\int_C\mathrm ds = \int_a^b \sqrt{\left(\frac{\mathrm dx}{\mathrm dt}\right)^2+\left(\frac{\mathrm dy}{\mathrm dt}\right)^2} \,\mathrm dt$

In this case, we have

<em>x(t)</em> = exp(<em>t</em> ) + exp(-<em>t</em> ) ==> d<em>x</em>/d<em>t</em> = exp(<em>t</em> ) - exp(-<em>t</em> )

<em>y(t)</em> = 5 - 2<em>t</em> ==> d<em>y</em>/d<em>t</em> = -2

and [<em>a</em>, <em>b</em>] = [0, 2]. The length of the curve is then

$\displaystyle\int_0^2 \sqrt{\left(e^t-e^{-t}\right)^2+(-2)^2} \,\mathrm dt = \int_0^2 \sqrt{e^{2t}-2+e^{-2t}+4}\,\mathrm dt$

$=\displaystyle\int_0^2 \sqrt{e^{2t}+2+e^{-2t}} \,\mathrm dt$

$=\displaystyle\int_0^2\sqrt{\left(e^t+e^{-t}\right)^2} \,\mathrm dt$

$=\displaystyle\int_0^2\left(e^t+e^{-t}\right)\,\mathrm dt$

$=\left(e^t-e^{-t}\right)\bigg|_0^2 = \left(e^2-e^{-2}\right)-\left(e^0-e^{-0}\right) = \boxed{e^2-\frac1{e^2}}$

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2 years ago

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Nat2105 [25]

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2 years ago

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Lunna [17]

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Step-by-step explanation:

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2 years ago

A line with a slope of 5 passes through the points (3,8).which of the following is the value of the y-intercept

alexira [117]

Answer:

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Step-by-step explanation:

7 0

2 years ago

Please help me this looks easy but I don’t understand it tho

Tems11 [23]

Let's call the unknown amount of money <em>x</em>

Betty spend 5/12 of her money (5/12)x and had 42 dollars left. Translated,

$x - \frac 5{12} x = 42$

Solving,

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$x = \dfrac{12}{7} \cdot 42 = 72$

Answer: $72

4 0

2 years ago