Answer:
2. ![x = \frac{\pi }{4} , \frac{3\pi }{4}, \frac{5\pi }{4}, \frac{7\pi }{4}](https://tex.z-dn.net/?f=x%20%3D%20%5Cfrac%7B%5Cpi%20%7D%7B4%7D%20%2C%20%5Cfrac%7B3%5Cpi%20%7D%7B4%7D%2C%20%5Cfrac%7B5%5Cpi%20%7D%7B4%7D%2C%20%5Cfrac%7B7%5Cpi%20%7D%7B4%7D)
3. -0.28
4. a. ![- \frac{\pi }{6}](https://tex.z-dn.net/?f=-%20%5Cfrac%7B%5Cpi%20%7D%7B6%7D)
b. ![\frac{3\pi }{4}](https://tex.z-dn.net/?f=%5Cfrac%7B3%5Cpi%20%7D%7B4%7D)
Step-by-step explanation:
2. Given that
⇒
or
Since x belongs to [0,2π).
Therefore,
(Answer)
3. Given that,
⇒
Degrees
{Since
is in first quadrant}
So,
(Answer)
4. a. Given
b.
(Answer)
Answer:
The answer is below
Step-by-step explanation:
The horizontal asymptote of a function f(x) is gotten by finding the limit as x ⇒ ∞ or x ⇒ -∞. If the limit gives you a finite value, then your asymptote is at that point.
![\lim_{x \to \infty} f(x)=A\\\\or\\\\ \lim_{x \to -\infty} f(x)=A\\\\where\ A\ is\ a\ finite\ value.\\\\Given\ that \ f(x) =25000(1+0.025)^x\\\\ \lim_{x \to \infty} f(x)= \lim_{x \to \infty} [25000(1+0.025)^x]= \lim_{x \to \infty} [25000(1.025)^x]\\=25000 \lim_{x \to \infty} [(1.025)^x]=25000(\infty)=\infty\\\\ \lim_{x \to -\infty} f(x)= \lim_{x \to -\infty} [25000(1+0.025)^x]= \lim_{x \to -\infty} [25000(1.025)^x]\\=25000 \lim_{x \to -\infty} [(1.025)^x]=25000(0)=0\\\\](https://tex.z-dn.net/?f=%5Clim_%7Bx%20%5Cto%20%5Cinfty%7D%20f%28x%29%3DA%5C%5C%5C%5Cor%5C%5C%5C%5C%20%5Clim_%7Bx%20%5Cto%20-%5Cinfty%7D%20f%28x%29%3DA%5C%5C%5C%5Cwhere%5C%20A%5C%20is%5C%20a%5C%20finite%5C%20value.%5C%5C%5C%5CGiven%5C%20that%20%5C%20f%28x%29%20%3D25000%281%2B0.025%29%5Ex%5C%5C%5C%5C%20%5Clim_%7Bx%20%5Cto%20%5Cinfty%7D%20f%28x%29%3D%20%5Clim_%7Bx%20%5Cto%20%5Cinfty%7D%20%5B25000%281%2B0.025%29%5Ex%5D%3D%20%5Clim_%7Bx%20%5Cto%20%5Cinfty%7D%20%5B25000%281.025%29%5Ex%5D%5C%5C%3D25000%20%5Clim_%7Bx%20%5Cto%20%5Cinfty%7D%20%5B%281.025%29%5Ex%5D%3D25000%28%5Cinfty%29%3D%5Cinfty%5C%5C%5C%5C%20%5Clim_%7Bx%20%5Cto%20-%5Cinfty%7D%20f%28x%29%3D%20%5Clim_%7Bx%20%5Cto%20-%5Cinfty%7D%20%5B25000%281%2B0.025%29%5Ex%5D%3D%20%5Clim_%7Bx%20%5Cto%20-%5Cinfty%7D%20%5B25000%281.025%29%5Ex%5D%5C%5C%3D25000%20%5Clim_%7Bx%20%5Cto%20-%5Cinfty%7D%20%5B%281.025%29%5Ex%5D%3D25000%280%29%3D0%5C%5C%5C%5C)
![Since\ \lim_{x \to -\infty} f(x)=0\ is\ a\ finite\ value,hence:\\\\Hence\ the\ horizontal\ asymtotes\ is\ at\ y=0](https://tex.z-dn.net/?f=Since%5C%20%20%5Clim_%7Bx%20%5Cto%20-%5Cinfty%7D%20f%28x%29%3D0%5C%20is%5C%20a%5C%20finite%5C%20value%2Chence%3A%5C%5C%5C%5CHence%5C%20the%5C%20horizontal%5C%20asymtotes%5C%20is%5C%20at%5C%20y%3D0)
Answer: t₇ = 17 t₃₀ = 63 S₁₀ = 140
<u>Step-by-step explanation:</u>
t₇ = 2(7) + 3
= 14 + 3
= 17
t₃₀ = 2(30) + 3
= 60 + 3
= 63
S₁₀ = (t₁ + t₁₀)/2 × 10
= (5 + 23)/2 × 10
= 28/2 10
= 14 × 10
= 140
Answer:
y=-5/8x-11/4
Step-by-step explanation:
y-y1=m(x-x1)
y-6=-5/8(x-(-14))
y-6=-5/8(x+14)
y=-5/8x-70/8+6
y=-5/8x-11/4
First we should figure out the volume of the prism (ignoring the cylinder at the moment)
(base * height/2)*depth
We need to find the height of the triangle which can be done with pythagoras because this is a right angled triangle (as shown by the little square at the bottom)
12 is the hypotenuse.
√12²-10² =6.63 (rounded)
Now we have the height of the triangle and can find the volume.
12*6.63/2*15=596.7
Now we find the volume of the cylinder.
area of circle * depth
area=3.14*1.5²
3.14*2.25
7.065
7.065*15=105.975
Now we subtract the volume of the cylinder from the volume of the prism and you have:
596.7-105.975
490.725 which is your answer
Hope this helps :)