Answer:
B
Step-by-step explanation:
Answer:
1000
Step-by-step explanation:
100 times 10 = 1000
Answer:
Dennis paid $82 and Connie paid $46.
Step-by-step explanation:
We can set up an equation by putting in variables, c representing how much Connie paid. Since we know that Dennis paid $36 more, we will also factor that in the equation.
c + c + 36 = 128
Where c + 36 represents the amount Dennis paid, and 128 represents the total amount paid as given in the question. We can start by adding like terms. 2c + 36 = 128
Now, we can subtract 36 from each side,
2c + 36 - 36 = 128 - 36
2c = 92
Divide each side by two,
2c/2 = 92/2
c = 46
Now, to make sure this is correct, let's substitute our c for 46 in our equation:
46 + 46 + 36 = 128
92 + 36 = 128
128 = 128
Therefore, our equation is correct, and Dennis paid $82 while Connie paid $46.
Option B:
![I=1.0\times\ 10^{0} \ \text {watts}/ \text m^2}](https://tex.z-dn.net/?f=I%3D1.0%5Ctimes%5C%2010%5E%7B0%7D%20%5C%20%5Ctext%20%7Bwatts%7D%2F%20%5Ctext%20m%5E2%7D)
Solution:
Given sound level = 120 decibel
To find the intensity of a fire alarm:
![$\beta=10\log\left(\frac{I}{I_0} \right)](https://tex.z-dn.net/?f=%24%5Cbeta%3D10%5Clog%5Cleft%28%5Cfrac%7BI%7D%7BI_0%7D%20%5Cright%29)
where ![I_0=1\times10^{-12}\ \text {watts}/ \text m^2}](https://tex.z-dn.net/?f=I_0%3D1%5Ctimes10%5E%7B-12%7D%5C%20%5Ctext%20%7Bwatts%7D%2F%20%5Ctext%20m%5E2%7D)
Step 1: First divide the decibel level by 10.
120 ÷ 10 = 12
Step 2: Use that value in the exponent of the ratio with base 10.
![10^{12}](https://tex.z-dn.net/?f=10%5E%7B12%7D)
Step 3: Use that power of twelve to find the intensity in Watts per square meter.
![$10^{12}=\left(\frac{I}{I_0} \right)](https://tex.z-dn.net/?f=%2410%5E%7B12%7D%3D%5Cleft%28%5Cfrac%7BI%7D%7BI_0%7D%20%5Cright%29)
![$10^{12}=\left(\frac{I}{1\times10^{-12}\ \text {watts}/ \text m^2} \right)](https://tex.z-dn.net/?f=%2410%5E%7B12%7D%3D%5Cleft%28%5Cfrac%7BI%7D%7B1%5Ctimes10%5E%7B-12%7D%5C%20%5Ctext%20%7Bwatts%7D%2F%20%5Ctext%20m%5E2%7D%20%5Cright%29)
Now, do the cross multiplication,
![I=10^{12}\times1\times\ 10^{-12} \ \text {watts}/ \text m^2}](https://tex.z-dn.net/?f=I%3D10%5E%7B12%7D%5Ctimes1%5Ctimes%5C%2010%5E%7B-12%7D%20%5C%20%5Ctext%20%7Bwatts%7D%2F%20%5Ctext%20m%5E2%7D)
![I=1\times\ 10^{12-12} \ \text {watts}/ \text m^2}](https://tex.z-dn.net/?f=I%3D1%5Ctimes%5C%2010%5E%7B12-12%7D%20%5C%20%5Ctext%20%7Bwatts%7D%2F%20%5Ctext%20m%5E2%7D)
![I=1\times\ 10^{0} \ \text {watts}/ \text m^2}](https://tex.z-dn.net/?f=I%3D1%5Ctimes%5C%2010%5E%7B0%7D%20%5C%20%5Ctext%20%7Bwatts%7D%2F%20%5Ctext%20m%5E2%7D)
![I=1.0\times\ 10^{0} \ \text {watts}/ \text m^2}](https://tex.z-dn.net/?f=I%3D1.0%5Ctimes%5C%2010%5E%7B0%7D%20%5C%20%5Ctext%20%7Bwatts%7D%2F%20%5Ctext%20m%5E2%7D)
Option B is the correct answer.
Hence
.
Answer:
A) x = 8![\sqrt{2}](https://tex.z-dn.net/?f=%5Csqrt%7B2%7D)
Step-by-step explanation:
in a 45-45-90 triangle, the legs to hypotenuse ratio is 1 : ![\sqrt{2}](https://tex.z-dn.net/?f=%5Csqrt%7B2%7D)
so in this problem the leg is 8 and the hypotenuse is 8![\sqrt{2}](https://tex.z-dn.net/?f=%5Csqrt%7B2%7D)