Answer:
(x, y) = (- 2, 5)
Step-by-step explanation:
given the 2 equations
3y = 11 - 2x → (1)
3x = y - 11 → (2)
Rearrange (2) expressing y in terms of x
add 11 to both sides
y = 3x + 11 → (3)
Substitute y = 3x + 11 into (1)
3(3x + 11) = 11 - 2x
9x + 33 = 11 - 2x ( add 2x to both sides )
11x + 33 = 11 ( subtract 33 from both sides )
11x = - 22 ( divide both sides by 11 )
x = - 2
Substitute x = - 2 in (3) for corresponding value of y
y = (3 × - 2) + 11 = - 6 + 11 = 5
As a check
substitute x = - 2, y = 5 into (1) and (2) and if the left side equals the right side then these values are the solution.
(1) : left side = (3 × 5) = 15
right side = 11 - (2 × - 2) = 11 + 4 = 15 ⇒ left = right
(2) : left side = (3 × - 2 ) = - 6
right side = 5 - 11 = - 6 ⇒ left = right
solution = (- 2, 5 )
Answer:
B) -3.464
Step-by-step explanation:
∫₀³ g'(x) cos²(2g(x) + 1) dx
Using u substitution:
u = 2g(x) + 1
du = 2g'(x) dx
½ du = g'(x) dx
When x = 0, u = 11.
When x = 3, u = -3.
½ ∫₁₁⁻³ cos²(u) du
You can use a calculator to solve this, or you can evaluate algebraically.
Use power reduction formula:
½ ∫ (½ + ½ cos(2u)) du
¼ ∫ du + ¼ ∫ cos(2u) du
¼ ∫ du + ⅛ ∫ 2 cos(2u) du
¼ u + ⅛ sin(2u) + C
Evaluating from u = 11 to u = -3:
[¼ (-3) + ⅛ sin(-6) + C] − [¼ (11) + ⅛ sin(22) + C]
-⁷/₂ + ⅛ sin(-6) − ⅛ sin(22)
−3.464
Answer:
The answer would be 9.12
Step-by-step explanation:
Answer:
The distance from his starting point is <u>6.7 m</u>.
Step-by-step explanation:
Given:
Shane marched 3 m East and 6 m north.
Now, to get the distance from his starting point.
Let the distance from the starting point be
Now, to solve using pythagorean theorem:
<em>Using square root on both sides we get:</em>
<u>So, the distance from the starting point nearest to tenth is 6.7 m.</u>
Therefore, he is 6.7 m from his starting point.
Answer:
The volume of the rectangular prism is 352 ft. The total surface area is 328 ft.
Step-by-step explanation:
Volume:
V = whl
V = 8 x 4 x 11
V = 352 ft
For finding surface area you have to find the lateral surface area: 152 ft, top surface area: 88 ft, and the bottom surface area: 88 ft. Add all that up and you get 328 ft.