Volume of cube = side^3
= 15^3
= 3375
Volume of pyramid= length x width x height/3
= 15 x 15 x 9
= 675
Total volume = 3375 + 675
= 4050 cubic feet
Answer:
The area of the triangle is 28 square units
Step-by-step explanation:
First we have to calculate the length of the base of the triangle and the length of the height
To calculate the base we have to subtract point (-1 , 2) from point (7 , 2)
(7 , 2) - (-1 , 2) = ((7 - (-1)) , (2 - 2)) = (8 , 0)
because it has no component in y this means that the length of the base is 8
b = 8
To calculate the height we have to subtract point (-1 , 2) from point (-1 , 9)
(-1 , 9) - (-1 , 2) = (((-1) - (-1)) , (9 - 2)) = (0 , 7)
because it has no component in x this means that the length of the base is 7
h = 7
To calculate the area of a triangle we have to multiply the base by the height and then divide it by 2
a = (b * h)/2
a = (8 * 7)/2
a = 56/2
a = 28
The area of the triangle is 28 square units
Slope = 2/1
Work is attached in the image provided.
Answer:
<h3>π/2</h3>
Step-by-step explanation:
Given the expression;
secθ − tan θ = cosθ
We are to find the solution in the interval [0, 2π).This is as shown;
From trigonometry identity;
secθ = 1/cosθ
tanθ = sinθ/cosθ
Substitute into the formula;
secθ − tan θ = cosθ
1/cosθ-sinθ/cosθ = cosθ
Multiply through by cosθ
1 - sinθ = cos²θ
1-sinθ = (1-sin²θ)
1-sin²θ-1+sinθ =0
-sin²θ+sinθ = 0
sin²θ = sinθ
sinθ = 1
θ = arcsin 1
θ = 90
θ = π/2
Hence the solution is π/2
