Answer:
C = 5.
Step-by-step explanation:
First, you need to remember that:
For the function:
h(x) = Sinh(k*x)
We have:
h'(x) = k*Cosh(k*x)
and for the Cosh function:
g(x) = Cosh(k*x)
g'(x) = k*Cosh(k*x).
Now let's go to our problem:
We have f(x) = A*cosh(C*x) + B*Sinh(C*x)
We want to find the value of C such that:
f''(x) = 25*f(x)
So let's derive f(x):
f'(x) = A*C*Sinh(C*x) + B*C*Cosh(C*x)
and again:
f''(x) = A*C*C*Cosh(C*x) + B*C*C*Sinh(C*x)
f''(x) = C^2*(A*cosh(C*x) + B*Sinh(C*x)) = C^2*f(x)
And we wanted to get:
f''(x) = 25*f(x) = C^2*f(x)
then:
25 = C^2
√25 = C
And because we know that C > 0, we take the positive solution of the square root, then:
C = 5
In one display case there are 5 shelves in it. It was said that 4 shelves stores equal number of juice cans in it while the other one has only 3 cans. As a whole, Ari has 35 cans of juice. By placing 3 in one of the shelves, we can deduct it from 35 or (35 minus 3) so what we now have is 32 pieces of juice cans left to be equally distributed in the 4 shelves left. The equation will now be 32 divided 4 or 32/4 which will be equal to 8. So in each shelf from the 4 shelves will store 8 cans of juice equally.
Answer:
m arc ACD =310
m arc AC = 130
Step-by-step explanation:
drawing the figure helps
if you do, should get something like the figure below
filling in arc ad as 50 degrees tells you that the angle describing it is also 50 degrees; it's a central angle.
and we know that 1/2 of a circle is 180 degrees. so if you subtract 50 from 180 you'll get 130 which will be your measurement for arc AC (because it is a central angle and AC
+AD completes the 180 half.).
as well as that to get ACD, well 1st we know that arc AC is within arc ACD. that would mean that ACD has to be more than 130.
what you can do is subtract 50 from 360. the entire circle is 360, but seeing as the arc is ACD (The rest of the circle excluding arc AD since we aren't looking for that measurement) we can just subtract.
subtracting 50 from 360 will give you 310
Answer:
p<8
Step-by-step explanation:
We multiply both sides by -1 to get
But remember, when you do that you reverse it, so we turn > into a <
2p<16
we divide both sides by 2
p<8
Hope this helps :)
Answer:
- (12, 12, 156) and (9, 9, 162)
Step-by-step explanation:
<u>Since AB = AC and the triangle is isosceles:</u>
- ∠ABC ≅ ∠ACB
- 3x² - 2x + 4 = 9x - 6
- 3x² - 11x + 10 = 0
- x = (11 ± √(121 - 4*3*10)/6
- x = (11 ± 1) / 6
- x = 2, x = 10/6
<u>The angles:</u>
- m∠B = m∠C = 9*2 - 6 = 12°
- m∠A = 180 - 2(12) = 156°
- m∠B = m∠C = 9(10/6) - 6 = 9°
- m∠A = 180 - 2(9) = 162°
