Answer:
∠L = 43°
∠M = 121°
∠N = 16°
Step-by-step explanation:
<u>Start by setting all sides equal to 180</u>
3x - 5 + 7x + 9 + x = 180
<u>Add like terms</u>
11x + 4 = 180
<u>Solve for x</u>
11x + 4 = 180
- 4 - 4
11x = 176
/ 11 /11
x = 16
<u>Now, plug in 16 for all instances of x on the triangle and solve.</u>
∠L = 43°
∠M = 121°
∠N = 16°
Answer:
B=45
Step-by-step explanation:
Multiply 8 by 5
Add 40 and 5 together
This is quite a complex problem. I wrote out a really nice solution but I can't work out how to put it on the website as the app is very poorly made. Still, I'll just have to type it all in...
Okay so you need to use a technique called logarithmic differentiation. It seems quite unnatural to start with but the result is very impressive.
Let y = (x+8)^(3x)
Take the natural log of both sides:
ln(y) = ln((x+8)^(3x))
By laws of logarithms, this can be rearranged:
ln(y) = 3xln(x+8)
Next, differentiate both sides. By implicit differentiation:
d/dx(ln(y)) = 1/y dy/dx
The right hand side is harder to differentiate. Using the substitution u = 3x and v = ln(x+8):
d/dx(3xln(x+8)) = d/dx(uv)
du/dx = 3
Finding dv/dx is harder, and involves the chain rule. Let a = x+ 8:
v = ln(a)
da/dx = 1
dv/da = 1/a
By chain rule:
dv/dx = dv/da * da/dx = 1/a = 1/(x+8)
Finally, use the product rule:
d/dx(uv) = u * dv/dx + v * du/dx = 3x/(x+8) + 3ln(x+8)
This overall produces the equation:
1/y * dy/dx = 3x/(x+8) + 3ln(x+8)
We want to solve for dy/dx, achievable by multiplying both sides by y:
dy/dx = y(3x/(x+8) + 3ln(x+8))
Since we know y = (x+8)^(3x):
dy/dx = ((x+8)^(3x))(3x/(x+8) + 3ln(x+8))
Neatening this up a bit, we factorise out 3/(x+8):
dy/dx = (3(x+8)^(3x-1))(x + (x+8)ln(x+8))
Well wasn't that a marathon? It's a nightmare typing that in, I hope you can follow all the steps.
I hope this helped you :)
Answer:
H. 3 units
Step-by-step explanation:
In order to answer this question, we have to apply the formula for the sphere volume. The formula is:
Plugging the given number into V, we calculate that:
If π=3.14, the radius is:
r ≈ 3 units.
Answer:
The correct option is c which is if this test was one-tailed instead of two-tailed, you would reject the null.
Step-by-step explanation:
a: This statement cannot be true as the p-value for a 1 tailed test is dependent on the level of significance and other features.
b: This statement cannot be true as there is no valid mathematical correlation between the p-value of the one-tailed test and the current p-value.
c: This statement is true because due to the enhanced level of significance, the null hypothesis will not be rejected.
d: This statement is inverse of statement c which cannot be true.
e: The statement cannot be true as there is no correlation between the current p-value and the p-value of 1 tailed test. The correlation exists between the values of one-tailed and two-tailed p-values.
