Answer:
x=3
Step-by-step explanation:
5x+6=21
5x=15
x=3
Answer:
25/11 divided by 5/22 = 10
Step-by-step explanation:
Step 1:
Start by setting it up with the divisor 11 on the left side and the dividend 25 on the right side like this:
1 1 ⟌ 2 5
Step 2:
The divisor (11) goes into the first digit of the dividend (2), 0 time(s). Therefore, put 0 on top:
0
1 1 ⟌ 2 5
Step 3:
Multiply the divisor by the result in the previous step (11 x 0 = 0) and write that answer below the dividend.
0
1 1 ⟌ 2 5
0
Step 4:
Subtract the result in the previous step from the first digit of the dividend (2 - 0 = 2) and write the answer below.
0
1 1 ⟌ 2 5
- 0
2
Step 5:
Move down the 2nd digit of the dividend (5) like this:
0
1 1 ⟌ 2 5
- 0
2 5
Step 6:
The divisor (11) goes into the bottom number (25), 2 time(s). Therefore, put 2 on top:
0 2
1 1 ⟌ 2 5
- 0
2 5
Step 7:
Multiply the divisor by the result in the previous step (11 x 2 = 22) and write that answer at the bottom:
0 2
1 1 ⟌ 2 5
- 0
2 5
2 2
Step 8:
Subtract the result in the previous step from the number written above it. (25 - 22 = 3) and write the answer at the bottom.
0 2
1 1 ⟌ 2 5
- 0
2 5
- 2 2
3
You are done, because there are no more digits to move down from the dividend.
The answer is the top number and the remainder is the bottom number.
Therefore, the answer to 25 divided by 11 calculated using Long Division is:
The first solution is quadratic, so its derivative y' on the left side is linear. But the right side would be a polynomial of degree greater than 1, so this is not the correct choice.
The third solution has a similar issue. The derivative of √(x² + 1) will be another expression involving √(x² + 1) on the left side, yet on the right we have y² = x² + 1, so that the entire right side is a polynomial. But polynomials are free of rational powers, so this solution can't work.
This leaves us with the second choice. Recall that
1 + tan²(x) = sec²(x)
and the derivative of tangent,
(tan(x))' = sec²(x)
Also notice that the ODE contains 1 + y². Now, if y = tan(x³/3 + 2), then
y' = sec²(x³/3 + 2) • x²
and substituting y and y' into the ODE gives
sec²(x³/3 + 2) • x² = x² (1 + tan²(x³/3 + 2))
x² sec²(x³/3 + 2) = x² sec²(x³/3 + 2)
which is an identity.
So the solution is y = tan(x³/3 + 2).
Answer:
answers are A & C
Step-by-step explanation:
because the '-' sign indicates it's under 0 and common sense shows the rest.
