Divide 105 by 7 to get 15
The final answer is x = -19/6. The first step is to reduce the expression to
2/3 * 3(5-3x)= 29. This will make the equation much easier. The next step is to simplify by cancelling out the 3 in 2/3 with the 3 multiplying 5-3x so it leaves you with 2(5-3x)=29. Then you would remove the parenthesis by using the distributive property and simplifying 2(5-3x) to 10-6x= 29. Then subtract 10 from both sides, which leaves you with -6x = 19. Divide by -6 on both sides and you get x= -19/6. Hope this helps
Answer:
1) 13.3 cm
2) 48.3 cm
Step-by-step explanation:
1) Right angled triangle ODC and right angled triangle OAB are similar because AB//DC. The two triangles have the same proportion and are equiangular (having equal angles) but have different lengths.
Let OB = x, OC = OB + BC = x + 8
Therefore:
The height of triangle ODC = OC = x + 8 = 5.3 + 8 = 13.3 cm
2) Using Pythagoras theorem:
OD² = OC² + DC²
OD² = 13.3² + 15²
OD² = 401.89
OD = √401.89 = 20 cm
2) perimeter of triangle ODC = OD + OC + DC = 20 + 13.3 + 15 =48.3 cm
Answer:
120
Step-by-step explanation:
Answer:
I = ∫₀¹ eˣ dx
I = ∫₀¹ e⁻ˣ dx
Step-by-step explanation:
Trapezoidal rule will be an overestimate if the function is concave up.
We can determine this by looking at the graph, or by evaluating the second derivative. If the second derivative is positive on the interval, the function is concave up.
f(x) = eˣ
f'(x) = eˣ
f"(x) = eˣ
On the interval [0, 1], f(x) is concave up.
f(x) = e⁻ˣ
f'(x) = -e⁻ˣ
f"(x) = e⁻ˣ
On the interval [0, 1], f(x) is concave up.
f(x) = √x = x^½
f'(x) = ½ x^(-½)
f"(x) = -¼ x^(-³/₂)
On the interval [0, 1], f(x) is concave down.
f(x) = sin x
f'(x) = cos x
f"(x) = -sin x
On the interval [0, 1], f(x) is concave down.
