Answer:
Radius = 8.575 cm
Step-by-step explanation:
Formula for volume of a pyramid is;
V_p = ½Ah
Where A is area of base and h is height
Also, formula for volume of cone is given as;
V_c = ⅓πr²h
Now, we are told that V_p = V_c and that h is the same for both shapes.
Thus ;
½Ah = ⅓πr²h
h will cancel out to give;
½A = ⅓πr²
Cross multiply to give;
3A/2π = r²
Base area of pyramid is given as 154 cm². Thus;
(3 × 154)/2π = r²
r = √((3 × 154)/2π
r = 8.575 cm
Step-by-step explanation:
The point-slope form of an equation of a line:
m - slope
We ahve the slope m = 1/2 and the point (-2, 1). Substitute:
- point-slope form
Covert to the slope-intercept form (y = mx + b):
<em>use the distributive property</em>
<em>add 1 to both sides</em>
- slope-intercept form
Convert to the standard form (Ax + By = C):
<em>multiply both sides by 2</em>
<em>subtract x from both sides</em>
<em>change the signs</em>
- standard form
Convert to the general form (Ax+By+C=0):
<em>add 4 to both sides</em>
- general form
In a parallelogram sum of the adjacent angles
equals supplementary.
opposite angles are equal.
Let the smaller angle = x°
larger angle = twice the smaller angle - 30°
=2x° - 30°
x° +2 x° - 30 = 180°
3x° = 180 + 30
3x = 210
x = 210 / 3
x = 70°
Therefore,
smaller angle = x = 70°
larger angle = 2x - 30
= 2 × 70 - 30
= 140 - 30
= 110°
Required parallelogram angles are 70° , 110° ,
70° , 110°
I hope this helps you.
Answer:
= 8√15
Step-by-step explanation:
Steps
2√3 x 4√5
Apply radical rule: √a√b=√ab.
√3 √5 = √3x 5
=2√3x 5 x 4
Multiply the numbers: 3 x 5= 15
=2√15 x 4
Multiply the numbers: 2 x 4 =8
= 8√15
2√3 x 4√5 = 8√15 (Decimal: 30.98386..)
