Answer:
5mm
Step-by-step explanation:
using the formula of volume of cone i.e. 1/3 ×πr²h
1/3 × πr²h = 314
or, r²= (314×3)/ (π×h)
or, r² = 25
r= 5 mm
Answer: Variant C
Step-by-step explanation:
f(x) = 3x^2 − 4
For finding f(-2) just replace x with - 2 like this:
f(-2)=3*((-2))^2-4=3*4-4=12-4=8
Simplify \frac{5}{3}x35x to \frac{5x}{3}35x
x-\frac{5x}{3}<3x−35x<3
2
Simplify x-\frac{5x}{3}x−35x to -\frac{2x}{3}−32x
-\frac{2x}{3}<3−32x<3
3
Multiply both sides by 33
-2x<3\times 3−2x<3×3
4
Simplify 3\times 33×3 to 99
-2x<9−2x<9
5
Divide both sides by -2−2
x>-\frac{9}{2}x>−29
Answer: 11
Step-by-step explanation: The sum of 15 and six times t will be 15 + 6t = 81.
Now, you subtract 15 from both sides to isolate the constants from the variables on the left side and on the other side and you will end up with 6t = 66. Then, you divide 6 from both sides to finally isolate the numbers from the variable and 66 divided by 6 would equal 11
Hope this Helps :)
Answer:
∫((cos(x)*dx)/(√(1+sin(x)))) = 2√(1 + sin(x)) + c.
Step-by-step explanation:
In order to solve this question, it is important to notice that the derivative of the expression (1 + sin(x)) is present in the numerator, which is cos(x). This means that the question can be solved using the u-substitution method.
Let u = 1 + sin(x).
This means du/dx = cos(x). This implies dx = du/cos(x).
Substitute u = 1 + sin(x) and dx = du/cos(x) in the integral.
∫((cos(x)*dx)/(√(1+sin(x)))) = ∫((cos(x)*du)/(cos(x)*√(u))) = ∫((du)/(√(u)))
= ∫(u^(-1/2) * du). Integrating:
(u^(-1/2+1))/(-1/2+1) + c = (u^(1/2))/(1/2) + c = 2u^(1/2) + c = 2√u + c.
Put u = 1 + sin(x). Therefore, 2√(1 + sin(x)) + c. Therefore:
∫((cos(x)*dx)/(√(1+sin(x)))) = 2√(1 + sin(x)) + c!!!
