Answer:
424 ft and 3 inches
Step-by-step explanation:
To calculate the diagonal of a square, multiply the length of the side by the square root of 2 --> d = a√2
a² + a² = diagonal²
diagonal = √(a² + a²) = √(2 x a²) which simplifies to diagonal = a√2
If area is given --> d = √(2*area)
Knowing square perimeter --> d = (perimeter/4)*√2
Answer:
1/3
Step-by-step explanation:
-1/3 divided by 3/5 = -5/9
-2/9 - -5/9 = 1/3
∫(t = 2 to 3) t^3 dt
= (1/4)t^4 {for t = 2 to 3}
= 65/4.
----
∫(t = 2 to 3) t √(t - 2) dt
= ∫(u = 0 to 1) (u + 2) √u du, letting u = t - 2
= ∫(u = 0 to 1) (u^(3/2) + 2u^(1/2)) du
= [(2/5) u^(5/2) + (4/3) u^(3/2)] {for u = 0 to 1}
= 26/15.
----
For the k-entry, use integration by parts with
u = t, dv = sin(πt) dt
du = 1 dt, v = (-1/π) cos(πt).
So, ∫(t = 2 to 3) t sin(πt) dt
= (-1/π) t cos(πt) {for t = 2 to 3} - ∫(t = 2 to 3) (-1/π) cos(πt) dt
= (-1/π) (3 * -1 - 2 * 1) + [(1/π^2) sin(πt) {for t = 2 to 3}]
= 5/π + 0
= 5/π.
Therefore,
∫(t = 2 to 3) <t^3, t√(t - 2), t sin(πt)> dt = <65/4, 26/15, 5/π>.
Answer:
2 m
Step-by-step explanation:
Here the area and the lengths of the two parallel sides of this trapezoid are given:
A = 7m^2, b1 = 3 m and b2 = 4 m. What's missing is the width of the trapezoid.
First we write out the formula for the area of a trapezoid:
b1 + b2
A = --------------- * w, where w represents the width of the figure.
2
We need to solve this for the width, w. Multiplying both sides of the above equation by
2
------------
b1 + b2
results in
2A
------------ = w
b1 + b2
Substituting 7 m^2 for A, 3 m for b1 and 4 m for b2 results in
2(7 m^2) 14 m^2
w = ------------------ = ---------------- = 2 m
(3 + 4) m 7 m
The missing dimension is the width of the figure. This width is 2 m.
