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3 years ago

9

Complete the following theorem.

2 answers:

NISA [10]3 years ago

7 0

: If all of the angles in both triangles are congruent then the triangles are SIMILAR not necessarily congruent. They can be congruent by using a theorem called ASA, SSS, or SAS. The "S" stands for Side and the "A" stands for angle.

Arlecino [84]3 years ago

4 0

If two angles in a triangle are congruent to two angles in another triangle, then the third angles are also congruent.
(Third Angle Theorem)

hope this helped!
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4. 30% to 50% of the money is for frozen food, a

strojnjashka [21]

Answer:

Step-by-step explanation:

It said the greatest amount,

So change 50% to .50

120x.50=60

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2 years ago

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Answer:

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3 years ago

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Suppose a class of 50 students has 20 males and 30 females. The insturctor will pick 1 (different) student to compete in 3 diffe

Pie

Answer:

Step-by-step explanation:

Total = 50

Males = 20

Females = 30

a) P(exactly 1 female) = P(1 female , 2 male)

(30C1 * 20C2) / (50C3) = 30*190/19,600 = 0.2908

b) P(at least 2 males) = 1 - (P(0 males) + P(1 males))

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3 years ago

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Factor completely:<br> z^9-d^6

jeka57 [31]

Answer: with the power of 9 − 1 with the power of 6

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2 years ago

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Find, correct to four decimal places, the length of the curve of intersection of the cylinder 4x2 1 y2 − 4 and the plane x 1 y 1

charle [14.2K]

<u>Answer-</u> Length of the curve of intersection is 13.5191 sq.units

<u>Solution-</u>

As the equation of the cylinder is in rectangular for, so we have to convert it into parametric form with

x = cos t, y = 2 sin t (∵ 4x² + y² = 4 ⇒ 4cos²t + 4sin²t = 4, then it will satisfy the equation)

Then, substituting these values in the plane equation to get the z parameter,

cos t + 2sin t + z = 2

⇒ z = 2 - cos t - 2sin t

∴ $\frac{dx}{dt} = -\sin t$

$\frac{dy}{dt} = 2 \cos t$

$\frac{dz}{dt} = \sin t-2cos t$

As it is a full revolution around the original cylinder is from 0 to 2π, so we have to integrate from 0 to 2π

∴ Arc length

$= \int_{0}^{2\pi}\sqrt{(\frac{dx}{dt})^{2}+(\frac{dy}{dt})^{2}+(\frac{dz}{dt})^{2}$

$=\int_{0}^{2\pi}\sqrt{(-\sin t)^{2}+(2\cos t)^{2}+(\sin t-2\cos t)^{2}$

$=\int_{0}^{2\pi}\sqrt{(2\sin t)^{2}+(8\cos t)^{2}-(4\sin t\cos t)$

Now evaluating the integral using calculator,

$=\int_{0}^{2\pi}\sqrt{(2\sin t)^{2}+(8\cos t)^{2}-(4\sin t\cos t)$ $= 13.5191$

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3 years ago