Answer:
3 sin(41t) - 3 sin(t)
Step-by-step explanation:
The general formula to convert the product of the form cos(a)sin(b) into sum is:
cos(a) sin(b) = 0.5 [ sin(a+b) - sin (a-b) ]
The given product is:
6 cos(21t) sin(20t) = 6 [ cos(21t) sin(20t) ]
Comparing the given product with general product mentioned above, we get:
a = 21t and b = 20t
Using these values in the formula we get:
6 cos(21t) sin(20t) = 6 x 0.5 [ sin(21t+20t) - sin(21t-20t)]
= 3 [sin(41t) - sin(t)]
= 3 sin(41t) - 3 sin(t)
Therefore, second option gives the correct answer
Listen .8 Is pronounced eight tenths or in fraction eight over ten then simplified to 4 over 5
Answer: Hours by Tina practiced this month is 3 times the hours she practiced last month such that 15 x 3 =45 hours.
Step-by-step explanation:
Given : Duration of Tina practiced piano last month= 15 hours
Duration of Tina practiced piano this month= 45 hours
We can see 45 is a multiple of 15 such that 
Therefore, Hours by Tina practiced this month is 3 times the hours she practiced last month such that 15 x 3= 45 hours.
Answer:
The value of <em>c</em> is
.
Step-by-step explanation:
The perfect square of the difference between two numbers is:

The expression provided is:

The expression is a perfect square of the difference between two numbers.
One of the number is <em>x</em> and the other is √<em>c</em>.
Use the above relation to compute the value of <em>c</em> as follows:
![x^{2}-15x+c=(x-\sqrt{c})^{2}\\\\x^{2}-15x+c=x^{2}-2\cdot x\cdot\sqrt{c}+c\\\\15x=2\cdot x\cdot\sqrt{c}\\\\15=2\cdot\sqrt{c}\\\\\sqrt{c}=\frac{15}{2}\\\\c=[\frac{15}{2}]^{2}\\\\c=\frac{225}{4}](https://tex.z-dn.net/?f=x%5E%7B2%7D-15x%2Bc%3D%28x-%5Csqrt%7Bc%7D%29%5E%7B2%7D%5C%5C%5C%5Cx%5E%7B2%7D-15x%2Bc%3Dx%5E%7B2%7D-2%5Ccdot%20x%5Ccdot%5Csqrt%7Bc%7D%2Bc%5C%5C%5C%5C15x%3D2%5Ccdot%20x%5Ccdot%5Csqrt%7Bc%7D%5C%5C%5C%5C15%3D2%5Ccdot%5Csqrt%7Bc%7D%5C%5C%5C%5C%5Csqrt%7Bc%7D%3D%5Cfrac%7B15%7D%7B2%7D%5C%5C%5C%5Cc%3D%5B%5Cfrac%7B15%7D%7B2%7D%5D%5E%7B2%7D%5C%5C%5C%5Cc%3D%5Cfrac%7B225%7D%7B4%7D)
Thus, the value of <em>c</em> is
.
Answer:
x=2
Step-by-step explanation:
have a nice day