Simplify the following:
-5×1×11×4
-5×1 = -5:
-5×11×4
-5×11 = -55:
-55×4
-55×4 = -220:
Answer: -220
Answer:
8820
Step-by-step explanation:
Prime factorization of 294,
→ 2 × 3 × 7 × 7
Prime factorization of 1260,
→ 2 × 2 × 3 × 3 × 5 × 7
LCM of 294 and 1260,
→ 2 × 2 × 3 × 3 × 5 × 7 × 7
→ 8820
Hence, the LCM is 8820.
We can see that revolving the region formed by intersecting 3 lines, we will get 2 cones that are connected their bases.
Volume of the cone V=1/3 *πr²*h
1) small cone has r=5, and h=5
Volume small cone V1= 1/3 *π*5²*5 = 5³/3 *π
2) large cone has r=5, and h=21-6=15, h=15
Volume large cone V2= 1/3 *π*5²*15 = 5³*π
3) whole volume
5³/3 *π + 5³*π=5³π(1/3+1)=((5³*4)/3)π=(500/3)π≈166.7π≈523.6
Area
we see 2 right triangles,
Area of the triangle=1/2*b*h, where b -base, h -height
1) small one, b=5, h=5
A1=(1/2)*5*5=25/2
2)large one, b=5, h=15
A2=(1/2)*5*15=75/2
3)
whole area=A1+A2=25/2+75/2=100/2=
50
The area of a trapezoid is basically the average width times the altitude, or as a formula:
Area = h ·
b 1 + b 2
2
where
b1, b2 are the lengths of each base
h is the altitude (height)
Recall that the bases are the two parallel sides of the trapezoid. The altitude (or height) of a trapezoid is the perpendicular distance between the two bases.
In the applet above, click on "freeze dimensions". As you drag any vertex, you will see that the trapezoid redraws itself keeping the height and bases constant. Notice how the area does not change in the displayed formula. The area depends only on the height and base lengths, so as you can see, there are many trapezoids with a given set of dimensions which all have the same area.