Answer:
2 * cos(11t/2) * sin(3t/2)

Explanation:
To answer this question, we will simply use the formula relating the difference between the sines as follows:
sin A - sin B = 2 * cos[(A+B)/2] * sin [(A-B)/2]

Now, we have:
A = 7t
B = 4t

Substitute with the givens in the formula as follows:
sin 7t - sin 4t = 2 * cos[(7+4)/2] * sin [(7-4)/2]
sin 7t - sin 4t = 2 * cos[11t/2] * sin [3t/2]

Hope this helps :)

6 0

4 years ago

Find the value of R so that the line that passes through each pair of points has the given slope: (8, -2 ), (r, -6), m=-4

kondor19780726 [428]

$\bf \begin{array}{lllll}
&x_1&y_1&x_2&y_2\\
% (a,b)
&({{ 8}}\quad ,&{{ -2}})\quad 
% (c,d)
&({{ r}}\quad ,&{{ -6}})
\end{array}
\\\\\\
% slope = m
slope = {{ m}}= \cfrac{rise}{run} \implies 
\cfrac{{{ y_2}}-{{ y_1}}}{{{ x_2}}-{{ x_1}}}\implies \cfrac{-6-(-2)}{r-8}=-4
\\\\\\
\cfrac{-6+2}{r-8}=-4\implies -4=-4(r-8)\implies \cfrac{-4}{-4}=r-8\\\\\\ 1+8=r$

8 0

3 years ago

How long of a ladder will he need?

anzhelika [568]

This is a Pythagorean theorem problem. the ladder is 12 from the building and needs to teach 14 ft up. the length of the ladder it's the hypotenuse
12²+14²=c²
144+196=c²
340=c²
c=√340 or about 18.5 ft

3 0

3 years ago