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2 years ago

Line segment TV is a midsegment of ∆QRS. What is the value of n in the triangle pictured?

Mathematics

1 answer:

Elis [28]2 years ago

4 0

Answer:

D. 3.2

Step-by-step explanation:

Mid-segment Theorem of a triangle states that the Mid-segment in a triangle is half of the third side of the triangle.

Based on this theorem, we have: TV = ½(RS)

TV = 3n - 2

RS = n + 12

Substitute

3n - 2 = ½(n + 12)

Multiply both sides by 2

2(3n - 2) = (n + 12)

6n - 4 = n + 12

Collect like terms

6n - n = 4 + 12

5n = 16

Divide both sides by 5

5n/5 = 16/5

n = 3.2

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Find the volume of the solid whose base is the region Ix I Iy I < 1 and whose vertical cross sections perpendicular to the y-

gavmur [86]

Answer:

volume of the solid = $\frac{\pi }{3}$

Step-by-step explanation:

As given , the region : |x| + |y| $\leq$ 1

when y $\geq$ 0 ,

|x| + y = 1

⇒|x| = 1 - y

when y ≤ 0 ,

|x| - y = 1

⇒|x| = 1 + y

The given region is the rectangle with sides (0, 5) , (0, -5), (5, 0), (-5, 0)

As given , the vertical cross section are semicircle

As we know that the area of semi circle = $\frac{1}{2}$ $\pi x^{2}$

Now,

Volume = $\int\limits^0_-1 {\frac{\pi }{2} (1+y)^{2} } \, dy$ + $\int\limits^1_0 {\frac{\pi }{2} (1-y)^{2} } \, dy$

= $\frac{\pi }{2} (\frac{(1+y)^{3} }{3} )$ - $\frac{\pi }{2} (\frac{(1-y)^{3} }{3} )$

= $\frac{\pi }{6}$ [1-0] - $\frac{\pi }{6}$ [0-1]

= $\frac{\pi }{6} + \frac{\pi }{6} = 2\frac{\pi }{6} = \frac{\pi }{3}$

⇒volume of the solid = $\frac{\pi }{3}$

4 0

2 years ago

The hypotenuse and one of the legs of a right triangle form an angle that has a cosine of 2 2 . what is the measure of the angle

creativ13 [48]

The correct question is
The hypotenuse and one of the legs of a right triangle form an angle that has a cosine of √2/2 .
What is the measure of the angle?

Let
∅--------> the angle
cos ∅=√2/2
cos ∅=[distance of one of the leg/hypotenuse]
[distance of one of the leg/hypotenuse]=√2/2

I could say that
distance of one of the leg=√2
and
hypotenuse=2
so
applying the Pythagorean theorem
c=hypotenuse=2
a=√2
b=?
c²=a²+b²-------> b²=c²-a²------> b²=2²-(√2)²-----> b²=2-----> b=√2

therefore
if a=b
then
the angle ∅=45°

the answer is the option
b.45 degrees

7 0

2 years ago

On a coordinate plane, a line is drawn from point A to point B. Point A is at (negative 8, negative 13) and point B is at (4, 11

juin [17]

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2 years ago

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What is the area of this shape?

m_a_m_a [10]

Step-by-step explanation:

idk the answer but find the area of a circle with the radius of 45 m and then find the area of the rectangle then add them together.