Simplify 4.510. 4.51 1 0 −1

1 answer:

8 0

(4.51)(0.4)(0.511)−1=−0.078156

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Directions: Complete each proof using the properties of equality. Not all rows be used.

kicyunya [14]

The answers for 13 and 14 are attached in the file.

7 0

3 years ago

Consider the vitamin capsule below.

shusha [124]

Answer:

We have a cylinder and two semispheres.

The volume of a cylinder is equal to:

Vc =h*pi*r^2

where h is the height, r is the radius, and pi = 3.14

We know that the diameter is d = 8.4 mm, and the radius is half of that:

r = 8.4mm/2 = 4.2mm

Then the volume of the cylinder is:

Vc = 15.2mm*3.14*(4.2mm)^2 = 841.9 mm^3

The volume of a sphere is:

Vs = (3/4)*pi*r^3

The radius of the sphere is the same as the radius of the cylinder, and for a semisphere, we have half of the volume written above,

Vss = (3/8)*3.14*(4.2mm)^2 = 87.2mm^3

and we have two of those, so the total volume is:

Vt = 841.9 mm^3 + 2*87.2mm^3 = 1016.3 mm^3

The surface area of the figure is equal to the curved surface of the cylinder plus the surface of the two semispheres.

The curved surface of the cylinder is:

Sc = 2*pi*r*h = 2*3.14*4.2mm*15.2mm = 400.9 mm^2

The surface of a sphere is:

Ss = 4*pi*r^2

and for each semisphere, we can find the surface by dividing the previous equation by two, but we have two semispheres, so we can jump a step and think the two semispheres as only one sphere.

Ss = 4*3.14*(4.2mm)^2 = 221.6mm^2

The total surface is St = 221.6mm^2 + 400.9 mm^2 = 622.5 mm^2

7 0

3 years ago

15 points!!! GEOMETRY help please!! Questions attached!

dolphi86 [110]

3. Look at the picture.

We have the right angle triangle. We know the sum of measures of angles in triangle is equal 180°. Therefore:

$x^o+90^o+43^o=180^o\\\\x^o+133^o=180^o\ \ \ |-133^o\\\\x^o=47^o$

$Answer:\ \boxed{47^o}$

4.
Look at the picture.

Use Pythagorean theorem:

$x^2+14^2=(10+x)^2\\\\x^2+196=10^2+2\cdot10\cdot x+x^2\ \ \ \ |-x^2\\\\196=100+20x\ \ \ |-100\\\\20x=96\ \ \ |:20\\\\x=4.8$

$Used:\ (a+b)^2=a^2+2ab+b^2$

$Answer:\ \boxed{4.8\ units}$

5.
TRUE: 1; 2; 4

6.
We find a slope of the line OP:

$m=\dfrac{y_2-y_1}{x_2-x_1}\\\\O(2;\ 6)\to x_1=2;\ y_1=6\\\\P(4;\ 3)\to x_2=4;\ y_2=3\\\\m=\dfrac{3-6}{4-2}=\dfrac{-3}{2}$

We have: $OP:\ y=-\dfrac{3}{2}x+b$

Now, we must find the slope of the line perpendicular to the line OP.
We know:

$k:y=m_1x+b;\ l:y=m_2x+c\\\\k\ \perp\ l\iff m_1m_2=-1$

therefore

$-\dfrac{3}{2}m_2=-1\ \ \ |\cdot\left(-\dfrac{2}{3}\right)\\\\m_2=\dfrac{2}{3}$

So. We have the answer! :)

$Answer:\ \boxed{y=\dfrac{2}{3}x+\dfrac{1}{3}}$