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Neko [114]
3 years ago
6

Find an equation of the tangent line to the graph of the function f(x) = 2sinx at the point where x = pi/3.

Mathematics
1 answer:
BigorU [14]3 years ago
3 0
The equation of the tangent line of f(x) is given by y = f'(x)x + c
f(x) = 2sin x
f'(x) = 2cos x

At x = pi/3
f'(pi/3) = 2 cos(pi/3) = 1
f(pi/3) = 2 sin(pi/3) = √3
√3 = 1(π/3) + c
c = √3 - π/3

Therefore, required equation is
y = x + √3 - π/3
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Choose the set of equivalent fractions that correctly uses the LCD for these fractions 3/4 and 1/6
valina [46]

Answer: 9/12, 2/12

Step-by-step explanation:

Start by writing multiples of 6 and 4

4: 4, 8, 12

6: 6, 12, 18

Did you see the multiple that both numbers have? Yup, it's 12. So that has to be your denominator for both fractions. This is because you have to have the <u>LEAST</u> COMMON Denominator (LCD). So both numbers have 12 in common as one of their multiples and, it's the least common one because there are no numbers that come before it that are common for both numbers. Now, you just have to change the denominators of both fractions into 12. To do that to 3/4, just multiply the top and bottom by 3 to get 9/12. To do that to 1/6, just multiply the top and bottom by 2 to get 2/12.  Hope this helps!

NOTE: REMEBER THAT WHATEVER YOU DO TO THE TOP OF A FRACTION, YOU HAVE TO DO IT TO THE BOTTOM TOO (AND VICE VERSA)

6 0
3 years ago
millicent earned $435 last year in interest. If $3000 was invested at a certain rate of return and $4500 was invested in a fund
tatiyna

Answer:

7% and 5%

Step-by-step explanation:

The computation of the two rates of interest is shown below;

The interest  rate for $3,000 be x%

And, for $4,500 the interest rate is (x -2%)

The total interest earned is

= x% of $4,500 + (x - 2)% of $4,500

So, the two rates of interest is

x% of $4,500 + (x - 2)% of $4,500 = $435

30x + 45(x - 2) = $435

30x + 45x - 90 = $43

75x = $25

x = 7%

x - 2 = 7 - 2

= 5%

8 0
3 years ago
Staci is attending a music festival. The ticket to the festival costs $87.96. Staci plans to purchase $30.00 t-shirt from the ev
prohojiy [21]
First, we have to calculate the remaining amount of money after the cost of the ticket. It is 200 - 87.96 = 112.04 Dividing this number to 30, we can find the maximum number of t-shirts she can buy. It is less 4 and more than 3. So that, the final answer is 3. 
4 0
3 years ago
A tumor in a rat responds to a new radiation treatment by shrinking 5% with each treatment. How many treatments before the tumor
Nuetrik [128]
A quarter of its original size would be 25% of 100%, right? Therefore, the tumor would have to shrink 75%. If each treatment, the tumor shrinks 5% that would mean it takes 15 treatments to shrink 75 percent. 

If this helped, please thank, rate, and give brainliest answer!
8 0
3 years ago
Which expression simplifies...
Zina [86]

Answer:

  see below

Step-by-step explanation:

If suffices to look at the last term. It must simplify to 4/(3w²), so the exponents of z must match in numerator and denominator, and the ratio of constants must reduce to 4/3.

The exponents of z have the right values in choices B and D, but the ratio of constants only matches in choice D. Looking at the rest of choice D, we see that we can factor 6w²z² from both numerator and denominator, then factor 2 from the remaining numerator to make it match the desired form.

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3 0
3 years ago
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