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3 years ago

How to find components of a vector given magnitude and angle?

1 answer:

3 0

1. Find the magnitude and direction angle of the vector.
2. Find the component form of the vector given its magnitude and the angle it makes with the positive x-axis.
3. Find the component form of the sum of two vectors with the given direction angles.

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A gumball has a diameter that is 66 mm. The diameter of the gumball's spherical hollow core is 58 mm. What is the volume of the

grigory [225]

Answer:

Volume of gumball without including its hollow core is 48347.6 cubic mm.

Step-by-step explanation:

Given:

Diameter of Gumball = 66 mm

Since radius is half of diameter.

Radius of gumball = $\frac{diameter}{2}=\frac{66}{2} =33 \ mm$

Now We will first find the Volume of Gumball.

To find the Volume of Gumball we will use volume of sphere which is given as;

Volume of Sphere = $\frac{4}{3}\pi r^3$

Now Volume of Gumball = $\frac{4}{3}\times3.14 \times (33)^3 = 150456.24 \ mm^3$

Also Given

Diameter of gumball's spherical hollow core = 58 mm

Since radius is half of diameter.

Radius of gumball's spherical hollow core = $\frac{diameter}{2}=\frac{58}{2} =29 \ mm$

Now We will find the Volume of gumball's spherical hollow core.

Volume of Sphere = $\frac{4}{3}\pi r^3$

So Volume of gumball's spherical hollow core = $\frac{4}{3}\times3.14 \times (29)^3 = 102108.61 \ mm^3$

Now We need to find volume of the gumball without including its hollow core.

So, To find volume of the gumball without including its hollow core we would Subtract Volume of gumball spherical hollow core from Volume of Gumball.

volume of the gumball without including its hollow core = Volume of Gumball - Volume of gumball's spherical hollow core = $150456.24\ mm^3 - 102108.61\ mm^3 = 48347.63\ mm^3$

Rounding to nearest tenth we get;

volume of the gumball without including its hollow core = $48347.6\ mm^3$

Hence Volume of gumball without including its hollow core is 48347.6 cubic mm.

8 0

3 years ago

Which shows the best use of the associative and commutative to make simplifying 3/4-5+9-2/4+2 easier

ziro4ka [17]

Answer:

(not this) 3/4-5+9-2/4+2

Step-by-step explanation:

1 1/3 instead of 3/4 and 2/4

3 0

3 years ago

Aaliyah is working two summer jobs, making $7 per hour walking dogs and making $10 per hour tutoring. In a given week, she can w

Minchanka [31]

Answer:

140 >/ 7x + 10y (read as 140 is greater than or equal to 7x plus 10y)

x + y /< 17 - to represent the number of hours she can work

she will work at least 10 hours walking dogs and at least 7 tutoring

Step-by-step explanation:

4 0

3 years ago

What is the slope of the line on the graph? Enter your answer in the box.

Olenka [21]

Look at points (0, -1) and (1, 5).

m = (y2 - y1)/(x2 - x1) = (5 - (-1))/(1 - 0) = 6/1 = 6

Slope = 6

Answer: 6

6 0

3 years ago

A circle is inscribed in a square. A point in the figure is selected at random. Find the probability that the point will be in t

hram777 [196]

P of selecting point on the shaded region = shaded area/whole area
P( selecting point on the shaded ) = ( the four shaded circles ) / the whole square 
P of selecting point on the shaded = ( 4 * ( π * r^2 ) )/ x^2 
P of selecting point on the shaded = ( 4 * ( π * (x/4)^2 ) )/ x^2 
P of selecting point on the shaded = ( 4 * ( π * x^2/16 ) )/ x^2 
P of selecting point on the shaded = ( π * x^2/4 )/ x^2 
P of selecting point on the shaded = x^2( π/4 )/ x^2 
P( selecting point on the shaded ) = π/4 ≈ 0.7854 ≈ 79%
=80%
D is right option hope this helps

4 0

4 years ago