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2 years ago

Hi please help !!! With steps as well please!

Mathematics

1 answer:

Scrat [10]2 years ago

7 0

Answer:

a) m = 60°, n = 30°

b) m = 20°, n = 45°

Step-by-step explanation:

The top and bottom horizontal lines are parallel, so angle m is an alternate interior angle congruent to the interior angle(s) of the equilateral triangle. Those angles are all 60°.

Angle n is the complement of angle m, so is 90°-60° = 30°

m = 60°, n = 30°

The base angles of the isosceles right triangle are n = 45°. (This should be a memorized fact. It is computed as (180° -90°)/2 = 45°.)

The base angles of the isosceles acute triangle are (180°-50°)/2 = 65°. Angle m is the difference between one of these and angle n.

m = 65° -45° = 20°

m = 20°, n = 45°

_____

<em>Additional comment</em>

The sum of angles of a triangle is 180°. The "base" angles of an isosceles triangle (one with two equal sides) are equal. If 'a' is the third angle, and 'b' are the base angles, you have ...

a + 2b = 180°

2b = 180° -a

b = (180° -a)/2 . . . . . . the relation used above

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Describe in words the region of R3 reperesented by the equations or inequalities y2+z2=16

Anastasy [175]

Answer:

It represents an infinite cylinder of radius 4.

Step-by-step explanation:

The first thing to notice is that

$y^2+z^2=4^2$

<u>represents a circle of radius 4</u>, with its center in the origin of a plane yz, of cartesians coordinates.

Starting from here, we have to put the coordinate x, for all values of x, to complete the space R³. <em>This will enlarge this circle we had on the plane, to infinity</em> (positive and negative on the x-axis).

Finally, we have that this region is a cylinder of radius 4, with center in y=0 and z=0, and of infinite length in the x coordinates.

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3 years ago

Find, correct to four decimal places, the length of the curve of intersection of the cylinder 16x2 + y2 = 16 and the plane x + y

Yuri [45]

Let the curve C be the intersection of the cylinder

$16x^2+y^2=16$

and the plane

$x+y+z=1$

The projection of C on to the x-y plane is the ellipse

$16x^2+y^2=16$

To see clearly that this is an ellipse, le us divide through by 16, to get

$\frac{x^2}{1}+ \frac{y^2}{16}=1$

$\frac{x^2}{1^2}+ \frac{y^2}{4^2}=1$ ,

We can write the following parametric equations,

$x=cos(t), y=4sin(t)$

for

$0\le t \le 2\pi$

Since C lies on the plane,

$x+y+z=1$

it must satisfy its equation.

Let us make z the subject first,

$z=1-x-y$

This implies that,

$z=1-sin(t)-4cos(t)$

We can now write the vector equation of C, to obtain,

$r(t)=(cos(t),4sin(t),1-cos(t)-4sin(t))$

The length of the curve of the intersection of the cylinder and the plane is now given by,

$\int\limits^{2\pi}_0 {|r'(t)|} \, dt$

But

$r'(t)=(-sin(t),4cos(t),sin(t)-4cos(t))$

$|r'(t)|=\sqrt{(-sin(t))^2+(4cos(t))^2+(sin(t)-4cos(t))}$

$\int\limits^{2\pi}_0 {\sqrt{2sin^2(t)+32cos(t)-8sin(t)cos(t)} }\, dt=24.08778184$

Therefore the length of the curve of the intersection intersection of the cylinder and the plane is 24.0878 units correct to four decimal places.

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3 years ago

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zlopas [31]

Answer:

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Step-by-step explanation:

Unit of measure

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For this reason is importatn to include the units of meausre with the plots since with that we have a point of reference for the variables used.

And satisfy the condition "A standard of measure for a physical quantity and is included as part of the x and y axes labels on a line graph."

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posledela

Answer:

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Step-by-step explanation:

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2 years ago

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Answer:

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Step-by-step explanation:

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1min=60sec

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3 years ago