Answer:
x = π/6, π/2, 5π/6, 3π/2
Step-by-step explanation:
cos x = sin(2x)
Use double angle formula.
cos x = 2 sin x cos x
Move everything to one side and factor.
cos x − 2 sin x cos x = 0
cos x (1 − 2 sin x) = 0
Set each factor to 0 and solve.
cos x = 0
x = π/2, 3π/2
1 − 2 sin x = 0
sin x = 1/2
x = π/6, 5π/6
The total solution is:
x = π/6, π/2, 5π/6, 3π/2
Answer:
(7, - 3 )
Step-by-step explanation:
Under a clockwise rotation about the origin of 270°
a point (x, y ) → (- y, x )
Thus
(- 3, - 7 ) → (7, - 3 )
Hey there!
The answer to your question is a = s - b - C/2
<u>To solve for "a", we must get "a" on it's own side of the equal sign.</u> We can first subtract "s" from both sides:
<em>0 = a + b + C/2 - s</em>
Then, we can subtract a from both sides:
<em>-a = b + C/2 - s</em>
Finally, we divide both sides by -1, so a is by itself.
<em>a = -b - C/2 + s</em>
And we can rearrange it to the standard form:
a = s - b - C/2
Good luck, and hope it helped! Have a great day!
Answer:
The exponential function to model the duck population is:
f(n)=415*(1.32)^n, where:
x is the duck population
n is the number of years
Step-by-step explanation:
In order to calculate the duck population you can use the formula to calculate future value:
FV=PV*(1+r)^n
FV=future value
PV=present value
r=rate
n=number of periods of time
In this case, the present value is the initial population of 415 and the rate is 32%. You can replace these values on the formula and the exponential function to model the duck population would be:
f(n)=415*(1+0.32)^n
f(n)=415*(1.32)^n, where:
x is the duck population
n is the number of years
Answer:
About 41.5%
Step-by-step explanation:
<em>Given:</em>
<em>A bowl has 8 green grapes and 15 red grapes. Henry randomly chooses a grape, eats it, and then chooses another grape. </em>
<em>To Find:</em>
<em>What is the probability that both grapes are red?</em>
<em>Answer choices:</em>
<em>about 39.7% </em>
<em>about 41.5%</em>
<em> about 42.5% </em>
<em>about 44.5%</em>
<em>Solution:</em>
<em>Since, there are 8 green grapes and 15 red grapes, the total number of grapes is 23 . </em>
<em>As the red grapes are 15.. </em>
<em>Thus, </em>
<em>The probability of choosing a red grape the first time is 15/23.</em>
<em>Because out of the total 23 grapes only 15 were red grape.</em>
<em> The probability of choosing the red grape the second time will be 14/22. Because the number of red grapes has already decreased by one and so is the total number of grapes after first choice</em>
<em>Hence, the probability of choosing or eating two red grapes will be :</em>
<em>15/23×14/22 </em>
<em>=105/253 </em>
<em>=0.415</em>
<em>= 41.5% </em>
<em>Therefore, the probability that both grapes are red is about 41.5%</em>
<u><em>Kavinsky</em></u>
