Which statement must be true?

Mathematics

2 answers:

STatiana [176]2 years ago

5 0

Answer:

Option C.

Step-by-step explanation:

Given information: ST = TU, ∠STV=88°, ∠UTV=92°.

In triangle STV and UTV

ST = TU (Given)

VT = VT (Reflection property)

∠STV=88° and ∠UTV=92° (Given)

If two corresponding sides of two triangles are congruent, then the third side of triangles depends on the including angle of congruent sides.

The larger included angle has larger opposite side.

∠STV < ∠UTV

∠SV < ∠UV

It can be written as

∠VS < ∠VU

Therefore, the correct option is C.

poizon [28]2 years ago

4 0

Vs<vu
cause smaller sides have smaller angels in front ofthem

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Ksju [112]

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exis [7]

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Then the integral becomes

$\displaystyle \iint_{R'} 4x^2 \, dA = 768 \iint_R u^2 \, du \, dv$

where $R'$ is the unit circle,

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so that

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Now you could evaluate the integral as-is, but it's really much easier to do if we convert to polar coordinates.

$\begin{cases} u = r\cos(\theta) \\ v = r\sin(\theta) \\ u^2+v^2 = r^2\\ du\,dv = r\,dr\,d\theta\end{cases}$

Then

$\displaystyle 768 \int_{-1}^1 \int_{-\sqrt{1-v^2}}^{\sqrt{1-v^2}} u^2\,du\,dv = 768 \int_0^{2\pi} \int_0^1 (r\cos(\theta))^2 r\,dr\,d\theta \\\\ ~~~~~~~~~~~~ = 768 \left(\int_0^{2\pi} \cos^2(\theta)\,d\theta\right) \left(\int_0^1 r^3\,dr\right) = \boxed{192\pi}$