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atroni [7]
3 years ago
6

In circle A as shown below, segment DC is tangent to circle A at D. Also, DC = 4 and BC = 2

Mathematics
1 answer:
algol [13]3 years ago
4 0

Answer:6

Step-by-step explanation:

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Keegan is priting and selling his original design on t-shirts. He has concluded that for x shirts, in thousands sold his total p
Damm [24]

Complete question is;

Keegan is printing and selling his original design on t-shirts. He has concluded that for x shirts, in thousands sold his total profits will be p(x) = -x³ + 4x² + x dollars, in thousands will be earned. How many t-shirts (rounded to the nearest whole number) should he print in order to make maximum profits? What will his profits rounded to the nearest whole dollar be if he prints that number of shirts?

Answer:

Number of t-shirts to make maximum profit = 2790 shirts

Maximum profit = $12,209

Step-by-step explanation:

From the question, we are given that the profit function is;

p(x) = -x³ + 4x² + x

For the maximum value of the profit function,

(dp/dx) = 0 and (d²p/dx²) < 0

Since, p(x) = -x³ + 4x² + x

Then,

(dp/dx) = -3x² + 8x + 1

at maximum point (dp/dx) = 0, thus;

-3x² + 8x + 1 = 0

Solving this using quadratic formula, the roots are;

x = -0.12 or 2.79

Also, (d²p/dx²) = -6x + 8

Now, let's put the roots of x into -6x + 8 and check for maximum value conditon;

at x = -0.12

(d²p/dx²) = -6(0.12) + 8 = 7.28 > 0

At x = 2.79

(d²p/dx²) = -6(2.79) + 8 = -8.74 < 0

Maximum has to be d²p/dx² < 0

So, the one that meets the condition is -8.74 < 0 at x = 2.79

Thus, the maximum of the profit function exists when the number of shirts, x = 2.79 (in thousands) = 2790

Now, the maximum profits that corresponds to this number of t-shirts of 2.79(in thousands) is obtained by putting 2.79 for x in the profit function;

So,

p(2.79) = -(2.79)³ + 4(2.79²) + 2.79

p(x) = -21.7176 + 31.1364 + 2.79

p(x) = 12.2088 (in thousand dollars) ≈ $12,209

6 0
3 years ago
Two angles are supplementary. One angle is 16° less than three times the other. Find the measures of the angles
Ivan

Answer:

Step-by-step explanation:

x and y are supplementary angles, so their sum is 180°.

x+y = 180°

x is 16° less than three times y

x = 3y - 16°

(3y-16°) + y = 180°

4y = 196°

y = 49°

x = 3y-16° = 131°

7 0
3 years ago
How do you do this? Because I don’t get it
olganol [36]
Multiply by -1 each time to get the answer in the output
6 0
2 years ago
Read 2 more answers
The owners of an amusement park selected a random sample of 200 days and recorded the number of park patrons with annual passes
Nitella [24]

Answer:

b. The method used to calculate the confidence interval has a 90% chance of producing an interval that captures the population mean number of annual pass holders in the park on any given day.

Step-by-step explanation:

The confidence interval calculated from the sample at a particular confidence level, gives a certain percentage of confidence based on the confidence level that the true mean of the population exists within the confidence interval Calculated.

For the scenario above, we can say that there is a 90% chance that the population mean number of annual pass holders in the park on a given day is within the interval (35, 51)

3 0
3 years ago
Laws of Sine just need a way to solve this, I got kicked out of my last tutor and lost the work and can't get it back
Stels [109]

The measurement of angle A = 52 ° .

In question we need to find angle A ,

To find angle A using Law of Sines :

Law of Sine : ( a / sin A ) = ( b / sin B ) = ( c / sin C ) where a , b and c are the sides opposite to angle A , B and C resp. of a triangle .

Applying Law of Sines ,

25 / sin A = 28 / sin 62

sin A = ( 25 * sin 62 ) / 28

sin A = 0.7883

Therefore , angle A = 52 ° .

Hence , the measurement of angle A = 52 ° .

To learn more on Law of Sines follow link :

brainly.com/question/2807639

#SPJ9

4 0
11 months ago
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