Answer:
<I= 15degrees
Step-by-step explanation:
Using the cosine rule formulae;
j² = i²+k²-2i cos <J
j² = 37²+57² - 2(37)(57)cos <141
j² = 1369+ 3249- 4218cos <141
j² = 4618- 4218cos <141
j² = 4618-(-3,278)
j²= 7,896
j = √7,896
j = 88.86inches
Next is to get <I
i² = j²+k²-2jk cos <I
37² = 88.86²+57² - 2(88.86)(57)cos <I
1369 = 7,896.0996+ 3249- 10,130.04cos <I
1369 = 11,145.0996 - 10,130.04cos <I
1369 - 11,145.0996 = - 10,130.04cos <I
-9,776.0996=- 10,130.04cos <I
cos <I =9,776.0996 /10,130.04
cos<I = 0.96506
<I = 15.19
<I= 15degrees
Answer:
x = 10
Step-by-step explanation:
3x - 5 = 2x + 5
3x - 5 + 5 = 2x + 5 + 5
3x = 2x + 10
3x - 2x = 2x - 2x + 10
1x = 10
x = 10
Answer:
20m
Step-by-step explanation:
The rooms are 4m x 5m.
To find the area, multiply length by width: 4*5=20
Let u = 5x+1. Then du = 5·dx, and your integral is
Answer:
![\int_{-\infty}^0 5 e^{60x} dx = \frac{1}{12}[e^0 -0]= \frac{1}{12}](https://tex.z-dn.net/?f=%20%5Cint_%7B-%5Cinfty%7D%5E0%205%20e%5E%7B60x%7D%20dx%20%3D%20%5Cfrac%7B1%7D%7B12%7D%5Be%5E0%20-0%5D%3D%20%5Cfrac%7B1%7D%7B12%7D)
Step-by-step explanation:
Assuming this integral:
We can do this as the first step:
Now we can solve the integral and we got:
![\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.
