Given:
Two identical parallelograms total area = 9 1/3 yd²
Each parallelogram has height 1 1/3 yd
Area formula: area = base × height
Split the total area equally to find each parallelogram's area.
Convert 9 1/3: (9*3)+1 = 28/3
Divide by 2: 28/3 × 1/2 = 28/6 yd², which is 4 4/6 yd² → 4 2/3 yd²
So each parallelogram's area is 4 2/3 yd²
Set up base × 1 1/3 yd = 4 2/3 yd²
Convert and divide: 14/3 yd² ÷ 4/3 yd = base
Multiply: 14/3 × 3/4 = base
Compute: 14*3 / 3*4 = base
42 / 12 = base
Which simplifies to 3 6/12 yd = base
or 3 1/2 yd = base
a) Each parallelogram has a base of 3 1/2 yards
b) If the two parallelograms form a rectangle:
Rectangle area = length × width
Length = 3 1/2 yd × 2 = 7 yds
Width = 3 1/2 yds
Area = 7 yd × 3 1/2 yd
Area = 7 × 7/2 yd²
Area = 7*7 / 2 yd²
Area = 49 / 2 yd²
Area = 24 1/2 yd²
Let's sketch the triangle.
The sides are a= 37.674 miles
b= 11.164 miles
c= 36.318 miles
We'll apply the cosine rule for angle calculations
(since the sine law cannot be employed without knowing any angle measurements).
The cosine law is given by
Substituting the values results in
C = 74.48°
We can find angle A using the sine law
A= 
A = 87.38°
The third angle B can be determined by calculating 180° minus the sum of angles A and C
B = 180 - 161.86
B = 18.14°
Thus, we have calculated all three angles (as shown in the attached figure).
Respuesta:
la cantidad de elemento restante después de 14 minutos = 7.091 g =~ 10 g
Explicación paso a paso:
Después de cada minuto, la cantidad que queda será
(100 - 26.9) % es decir, 73.1 %
lo que equivale a 0.731 veces la cantidad inicial.
Si el tiempo transcurrido se representa como t, la función f(t) indica la masa del elemento restante, nuestra ecuación será
f(t) = 570(0.731) ^ t
t= 14 minutos
f(14) = 570 (0.731) ^ 14
= 7.091 g =~ 10 g
1,107 cc
The scanning consists of 10 intervals:
[0,1.5), [1.5,3), [3,4.5), [4.5,6), [6,7.5), [7.5,9), [9,10.5), [10.5,12), [12,13.5), [13.5,15)
To estimate the volume using the Midpoint Rule, n should be set to 10.
Given that we will use n=5, we will split the range [0,15] into five intervals of lengths 3 each:
[0,3], [3,6], [6,9], [9,12], [12,15] and calculate their midpoints:
1.5, 4.5, 7.5, 10.5, and 13.5.
Next, we will determine the volume V from the five cylinders, where each has a height h=3 and the base area A corresponds to the calculated midpoints' intervals:
Cylinder 1
Midpoint=1.5, corresponding to the 2nd interval
A = 18, V= height * area of the base = 18*3 = 54 cc
Cylinder 2
Midpoint=4.5, corresponding to the 4th interval
A = 78, V= height * area of the base = 78*3 = 234 cc
Cylinder 3
Midpoint=7.5, corresponding to the 6th interval
A = 106, V= height * area of the base = 106*3 = 318 cc
Cylinder 4
Midpoint=10.5, corresponding to the 8th interval
A = 129, V= height * area of the base = 129*3 = 387 cc
Cylinder 5
Midpoint=13.5, corresponding to the 10th interval
A = 38, V= height * area of the base = 38*3 = 114 cc
Thus, the estimated volume is
54 + 234 + 318 + 387 + 114 = 1,107
