Answer:
See below ~
Step-by-step explanation:
Question 6(e) :
⇒ x² ≤ 16
<em>Take square root on each side :</em>
⇒ √x² ≤ √16
⇒ x ≤ 4 and x ≥ -4
⇒ -4 ≤ x ≤ 4
Answer:
Step-by-step explanation:
Assuming this integral:
![\int_{-\infty}^0 5 e^{60x} dx](https://tex.z-dn.net/?f=%20%5Cint_%7B-%5Cinfty%7D%5E0%205%20e%5E%7B60x%7D%20dx)
We can do this as the first step:
![5 \int_{-\infty}^0 e^{60x} dx](https://tex.z-dn.net/?f=%205%20%5Cint_%7B-%5Cinfty%7D%5E0%20e%5E%7B60x%7D%20dx)
Now we can solve the integral and we got:
![5 \frac{e^{60x}}{60} \Big|_{-\infty}^0](https://tex.z-dn.net/?f=%205%20%5Cfrac%7Be%5E%7B60x%7D%7D%7B60%7D%20%5CBig%7C_%7B-%5Cinfty%7D%5E0%20)
![\int_{-\infty}^0 5 e^{60x} dx = \frac{e^{60x}}{12}\Big|_{-\infty}^0 = \frac{1}{12} [e^{60*0} -e^{-\infty}]](https://tex.z-dn.net/?f=%20%5Cint_%7B-%5Cinfty%7D%5E0%205%20e%5E%7B60x%7D%20dx%20%3D%20%5Cfrac%7Be%5E%7B60x%7D%7D%7B12%7D%5CBig%7C_%7B-%5Cinfty%7D%5E0%20%3D%20%5Cfrac%7B1%7D%7B12%7D%20%5Be%5E%7B60%2A0%7D%20-e%5E%7B-%5Cinfty%7D%5D)
So then we see that the integral on this case converges amd the values is 1/12 on this case.
Answer:
B
Step-by-step explanation:
please mark as brainlist answer
We must look at each equation and pick out which property matches with the choices
For the equation:
5(8+3)=5*8+5*3
The property is
Distributive Property
For the equation:
4x+(5x+3)=9x+3
The property is
Commutative property of Addition
For the equation:
a+b=b+a
The property is
Associative Property of Addition
Check the picture below, so pretty much reaches its maximum height at the vertex, now let's take a peek at the equation above hmmmm
![~~~~~~\textit{vertical parabola vertex form} \\\\ y=a(x- h)^2+ k\qquad \begin{cases} \stackrel{vertex}{(h,k)}\\\\ \stackrel{"a"~is~negative}{op ens~\cap}\qquad \stackrel{"a"~is~positive}{op ens~\cup} \end{cases} \\\\[-0.35em] ~\dotfill\\\\ h(t)=-16(t ~~ - ~~ \stackrel{h}{5})^2~~ + ~~\stackrel{k}{116}~\hfill \underset{maximum~height}{\stackrel{vertex}{(5~~,~~\underset{\uparrow }{116})}}](https://tex.z-dn.net/?f=~~~~~~%5Ctextit%7Bvertical%20parabola%20vertex%20form%7D%20%5C%5C%5C%5C%20y%3Da%28x-%20h%29%5E2%2B%20k%5Cqquad%20%5Cbegin%7Bcases%7D%20%5Cstackrel%7Bvertex%7D%7B%28h%2Ck%29%7D%5C%5C%5C%5C%20%5Cstackrel%7B%22a%22~is~negative%7D%7Bop%20ens~%5Ccap%7D%5Cqquad%20%5Cstackrel%7B%22a%22~is~positive%7D%7Bop%20ens~%5Ccup%7D%20%5Cend%7Bcases%7D%20%5C%5C%5C%5C%5B-0.35em%5D%20~%5Cdotfill%5C%5C%5C%5C%20h%28t%29%3D-16%28t%20~~%20-%20~~%20%5Cstackrel%7Bh%7D%7B5%7D%29%5E2~~%20%2B%20~~%5Cstackrel%7Bk%7D%7B116%7D~%5Chfill%20%5Cunderset%7Bmaximum~height%7D%7B%5Cstackrel%7Bvertex%7D%7B%285~~%2C~~%5Cunderset%7B%5Cuparrow%20%7D%7B116%7D%29%7D%7D)