Answer:
Step-by-step explanation:
3(x+7)=-36
x+7=-12
x=-19
There are 4 triangles and the formula for the area of a triangle is 1/2BH so 11x10 is 110 and then take half of that and you’ll get 55. Since there are 4 triangles you need to then multiply that by 4 to get 220. And then you have to find the area of the square base which is 11x11 which will come out to 121. So you add the 220 and 121 to get 341.
Answer:4/21
Step-by-step explanation:divide 6 by both sides
Answer:
y(t) = c₁ e^(-1/2 t) cos(√3/2 t) + c₂ e^(-1/2 t) sin(√3/2 t) + 1
Step-by-step explanation:
y" + y' + y = 1
This is a second order nonhomogenous differential equation with constant coefficients.
First, find the roots of the complementary solution.
y" + y' + y = 0
r² + r + 1 = 0
r = [ -1 ± √(1² − 4(1)(1)) ] / 2(1)
r = [ -1 ± √(1 − 4) ] / 2
r = -1/2 ± i√3/2
These roots are complex, so the complementary solution is:
y = c₁ e^(-1/2 t) cos(√3/2 t) + c₂ e^(-1/2 t) sin(√3/2 t)
Next, assume the particular solution has the form of the right hand side of the differential equation. In this case, a constant.
y = c
Plug this into the differential equation and use undetermined coefficients to solve:
y" + y' + y = 1
0 + 0 + c = 1
c = 1
So the total solution is:
y(t) = c₁ e^(-1/2 t) cos(√3/2 t) + c₂ e^(-1/2 t) sin(√3/2 t) + 1
To solve for c₁ and c₂, you need to be given initial conditions.
Answer:
D.
Step-by-step explanation:
1. Answer A:
15 students signed up for violin lessons (4 boys + 11 girls)
15 / 70 = approx. 21% of the class.
Answer A says 28%, so this is incorrect.
2. Answer B:
17 students signed up for drum lessons (11 boys + 6 girls)
17/70 = approx. 24%
B says 17% signed up for drums, so this is incorrect.
3. Answer C.
Wrong because more girls signed up for piano lessons (15 girls, whereas only 9 boys signed up for piano)
4. D. The same percent of boys and girls are taking guitar lessons.
Get the total number of boys and girls in the class (just add the results for each separately for all instruments)
Boys: 11 + 6 + 9 + 4 = 30
Girls: 6+8+15+11 = 40
6 out of 30 boys signed up for guitar
6/30= 20%
8 out of 40 girls signed up for guitar
8/40 = 20%
Answer is D
