9514 1404 393
Answer:
- base area: 21 ft²
- volume 105 ft³
Step-by-step explanation:
The area of a triangle is given by the formula ...
A = (1/2)bh
The base and height of a right triangle can be taken to be the leg lengths, since each is perpendicular to the other.
A = (1/2)(6 ft)(7 ft) = 21 ft² . . . . base area
__
The volume is the product of the base area and the height:
V = Bh
V = (21 ft²)(5 ft) = 105 ft³ . . . . volume
Standard form : Ax + By = C
12y = 9x - 30
-9x + 12y = -30 ....some teachers accept this, with A being negative
but if not, then it is this :
9x - 12y = 30
Answer:
y= 1/3x - 1
Step-by-step explanation:
1/3 is slope so m and -1 is the y-intercept
Step-by-step explanation:
it filled up half the circle (up to the center point) - if we had a full circle. but a little bit is cut off (below AB).
what we see is that the shaded area is the sum of the area of the triangle AOB and 2 equally sized circle segment areas left and right of AOB.
since we are dealing with a half-circle, we have 180° in total. 120° are taken by AOB, so, that leaves us with 180-120 = 60° for both circle segments (so, one has an angle of 30°).
and 2×30° = 1×60°, so we can calculate the area of one 60° segment instead of two 30° segments.
AOB is an isoceles triangle (the legs are equally long, and therefore also the 2 side angles are equal).
the area of this triangle AOB is
1/2 × a × b × sin(C) = 1/2 × 3 × 3 × sin(120) =
= 3.897114317... m²
a circle segment area of 60° is 60/360 = 1/6 of the full circle area (as a full circle = 360°).
so, it's area is
pi×r² × 1/6 = pi×3²/6 = pi×3/2 = 4.71238898... m²
so, the total area of the shaded area is
3.897114317... m² + 4.71238898... m² =
= 8.609503297... m²
Answer: 1⁵/₈ pints
Step-by-step explanation:
First can contained 3¹/₄ pints and second can contained 6¹/₂.
To make them equal, first find the different;
= 6¹/₂ - 3¹/₄
= 6.5 - 3.25
= 3.25
Divide this difference by 2;
= 3.25/2
= 1.625
= 1⁶²⁵/₁₀₀₀
= 1⁵/₈ pints
If Carson pours 1⁵/₈ pints from the second Can, it would increase the first can to 4⁷/₈ pints whilst reducing the second can to 4⁷/₈ pints as well.
