Answer:
1.44m^3
Step-by-step explanation:
Given data
Number of balls= 8
Diameter of ball = 70cm = 0.7m
Radius= 35cm= 0.35m
We know that a ball has a spherical shape
The volume of a sphere is
V= 4/3πr^3
substitute
V= 4/3*3.142*0.35^3
V= 0.18m^3
Hence if 1 ball has a volume of 0.18m^3
Then 8 balls will have a volume of
=0.18*8
=1.44m^3
First, find slope of point A and B using slope formula:
<u>y2-y1</u> = <u>7-0 </u>= <u>-7</u>
x2-x1 3-8 5
Next, use the point-slope formula to find the equation (pick either point A or B to substitute into this equation; the answer will be the same either way):
y-y1=m(x-x1)
y-7=<u>-7</u>(x-3) (I used point B here)
5
y=<u>-7x</u> +<u>56</u> so the y-intercept is <u>56</u>. Hurray! Part 1 down!
<span> 5 5 5
Now to answer part 2. Since AB ll CD, they have the same slope: <u>-7</u>
5
Therefore, you can use the handy point-slope equation to calculate the equation of line CD. (Remember you only need one of the points to use this equation if you already have the slope.) Since the only point given is D(5,5), we'll use that one:
</span>y-y1=m(x-x1)
y-5=<u>-7</u>(x-5)
<span> 5
</span>y=<u>-7x</u> + 12 Yay! That's the answer to part 2; the equation of line CD
<span> 5</span>
Answer:
See below.
Step-by-step explanation:
<u>Simplify</u>
y - 2 = 5(x - 6)
y - 2 = 5x - 30
y = 5x - 28
Points which lie on the line
(6, 2)
(5, -3)
(7, 7)
Answer: x = 30°
Concept:
Here, we need to know the idea of an isosceles triangle and the vertical angle theorem.
An <u>isosceles triangle</u> is a triangle that has any two of its sides equal to each other. Also, the angles opposite these equal sides are equal, which is basically the base angles.
The <u>vertical angle theorem</u> states that two vertical angles formed when two lines intersect each other are always equal to each other.
Solve:
<u>Find the other base angle of the isosceles triangle.</u>
Since there are two equal sides, we know that this is an isosceles triangle.
Since the definition said that the base angles are equal, the other base angle would also be x.
<u>Find the value of x</u>
According to the vertical angle theorem, two vertical angles formed by intersection are equal.
Just as angle x and 30°, are vertical angles formed by intersection, therefore, 
Hope this helps!! :)
Please let me know if you have any questions
