Answer:
14. A
15. C
16. B
17. B
Step-by-step explanation:
Answers:
<span>
55 deg 30 Minutes = 55.5 degrees
sin = opp/hyp
sin(55.5) = altitude/10
Altitude = 10*sin(55.5)
Altitude = 10 * sin(55.5) = 8.241261886
Rounded to nearest 10th
Altitude = 8.2 cm
b. for base use Low of Cosines
Let C = base
Side A and B = length 10 Cm
c^2 = 2*a^2 -2a^2*cos(<C)
<C = 180 - 2*55.5 = 180 -111 = 69 degrees
c = sqrt ( 2a^2 - 2a^2*cos(<C)
c = sqrt ( 2*100- 200*cos(69))
c = sqrt (200 - 200*cos(69) ) = 11.32812474
Answer base
c = 11.3 cms
c.
Area = (1/2)*b * h
Area = (1/2)*(answer a * answer b)
Area = (1/2)* 11.32812474* 8.241261886 = 46.67902132
Area = 46.7 (rounded)
Area = ( 1/2) * a*b*sin(<C) = (1/2)*10*10*sin(69) =
Area = 50* sin(69) = 46.67902132
Area = 46.7 (rounded)</span>
Answer:
87 packages
Step-by-step explanation:
First we need to find the volume of the cone-shaped vase.
The volume of a cone is given by:
V_cone = (1/3) * pi * radius^2 * height
With a radius of 9 cm and a height of 28 cm, we have:
V_cone = (1/3) * pi * 9^2 * 28 = 2375.044 cm3
Each package of sand is a cube with side length of 3 cm, so its volume is:
V_cube = 3^3 = 27 cm3
Now, to know how many packages the artist can use without making the vase overflow, we just need to divide the volume of the cone by the volume of the cube:
V_cone / V_cube = 2375.044 / 27 = 87.9646 packages
So we can use 87 packages (if we use 88 cubes, the vase would overflow)
Answer:
f(x) = 1.2x
Step-by-step explanation:
Given:
f(x - 5) = 1.2x - 6
Required:
Find f(x)
To solve f(x), we have to express f(x - 5) in terms of f(x).
This is done as follows
f(x - 5) = 1.2x - 6
Factorize the expression at the right hand side
f(x - 5) = 1.2(x - 5)
Now we can solve for f(x) by substituting x for x - 5 in the above expression (on the right hand side and the left hand side)
f(x) = 1.2x
Hence, if f(x - 5) = 1.2x - 6 then f(x) = 1.2x