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Lunna [17]
3 years ago
10

What is the value of x? Enter your answer in the box

Mathematics
1 answer:
Marina CMI [18]3 years ago
6 0

Answer:

x = 45º

Step-by-step explanation:

well since a triangle has to equal 180º

then we just have to subtract 88º and 55º from 180º

180 - 80 - 55 = 45

therefore, x = 45

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A flat circular plate has the shape of the region x squared plus y squared less than or equals 1x2+y2≤1. the​ plate, including t
vredina [299]

You're looking for the extreme values of x^2+3y^2+13x subject to the constraint x^2+y^2\le1.

The target function has partial derivatives (set equal to 0)

\dfrac{\partial(x^2+3y^2+13x)}{\partial x}=2x+13=0\implies x=-\dfrac{13}2

\dfrac{\partial(x^2+3y^2+13x)}{\partial y}=6y=0\implies y=0

so there is only one critical point at \left(-\dfrac{13}2,0\right). But this point does not fall in the region x^2+y^2\le1. There are no extreme values in the region of interest, so we check the boundary.

Parameterize the boundary of x^2+y^2\le1 by

x=\cos u

y=\sin u

with 0\le u. Then t(x,y) can be considered a function of u alone:

t(x,y)=t(\cos u,\sin u)=T(u)

T(u)=\cos^2u+3\sin^2u+13\cos u

T(u)=3+13\cos u-2\cos^2u

T(u) has critical points where T'(u)=0:

T'(u)=-13\sin u+4\sin u\cos u=\sin u(4\cos u-13)=0

(1)\quad\sin u=0\implies u=0,u=\pi

(2)\quad4\cos u-13=0\implies\cos u=\dfrac{13}4

but |\cos u|\le1 for all u, so this case yields nothing important.

At these critical points, we have temperatures of

T(0)=14

T(\pi)=-12

so the plate is hottest at (1, 0) with a temperature of 14 (degrees?) and coldest at (-1, 0) with a temp of -12.

4 0
2 years ago
Kevin drew a diagonal inside a quadrilateral. He realizes the it always make 2 congruent isosceles triangleso. What kind of quad
olya-2409 [2.1K]

Answer:

The square is the quadrilateral.

Step-by-step explanation:

A quadrilateral is a 2 dimensional geometric shape. It has four sides which may be or may not be equal.

If a quadrilateral is a square and we make its diagonal so that we get two triangles.

These two triangles are isosceles triangle as the two sides are equal and the square has four equal sides and the triangles are congruent to each  other.  

here, the triangles ABC and ADC are congruent and isosceles.

7 0
3 years ago
No clue what to do here. Can anyone help???
ICE Princess25 [194]

Answer:

try the app socratic Step-by-step explanation:

8 0
3 years ago
Beaker A contains 4 1/3 fluid ounces, while beaker B contains 4 3/10 of water . Which beaker has the smaller amount of water
kirill [66]
Beaker  A contains more water.
First,find equivalent fraction.
Next,compare the amounts you will see Beaker A contains more water.
Therefore,Beaker A contains more water.
8 0
2 years ago
Explain why 1/2 and 3/6 are equivalent fractions
hodyreva [135]

Answer:

3/6 is equal

Step-by-step explanation:

because, if you had 3/6 of a pizza, you would have half of a pizza

8 0
3 years ago
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