5. Combien de paires de nombres naturels peut-on former dont : a) la somme est 23? b) la différence est 100?
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Answer:
49 ft
Step-by-step explanation:
h(t) = 56t - 16t²
This is the equation of a parabola.
We must solve the equation to find the time (t) when the ball reaches its maximum height (h).
The coefficient of t² is negative, so the parabola opens downward, and the vertex is a maximum.
One way to solve this problem is to convert the equation to the vertex form.
We do that by completing the square.
Calculation:
h = -16t² + 56t
Divide both sides by -16 to make the coefficient of t² equal to 1.
(-1/16)h = t² - ⁷/₂t
Square half the coefficient of t
(-7/4)² = 49/16
Add and subtract it on the right-hand side
(-1/16)h = t² - ⁷/₂t + 49/16 - 49/16
Write the first three terms as the square of a binomial
(-1/16)h = (t - ⁷/₄)² - 49/16
Multiply both sides by -16
h = -16(t - ⁷/₄)² + 49
You have converted your equation to the vertex form of a parabola:
y = a(t - h)² + k = 0,
where (h, k) is the vertex.
h = ⁷/₄ and k = 49, so the vertex is at (⁷/₄, 49).
The time to reach maximum height is ⁷/₄ s = 1.75 s.
The graph below shows that the ball reaches a maximum height of 49 ft after 1.75 s.
<u>Given</u>:
The base of the triangle is b = 3 feet.
The height of the triangle is h = 4 feet.
The other side of the triangle is 5 feet.
The height of the triangular prism is 20 feet.
We need to determine the surface area of the triangular prism.
<u>Surface area of the triangular prism:</u>
The surface area of the triangular prism is given by the formula,
where b is the base of the triangle,
h is the height of the triangle,
s₁ , s₂ and s₃ are the sides of the triangle and
H is the height of the triangular prism.
Substituting the values, we get;
Thus, the surface area of the triangular prism is 252 ft²
