Mustafa is staring at a pizza spinning on a wheel in a glass case.
The pizza is cut into four even slices. The distance P(t) (in cm) between the center of the tastiest looking
slice and the door of the glass case as a function of time t (in seconds) can be modeled by a sinusoidal
function of the form a cos(b. t) + d.
Att = 0, the center of the tastiest looking slice is farthest from the door, at a distance of 30 cm away,
After 2 seconds, it is closest to the door, at a distance of 10 cm.
Find P(t).
t should be in radians.
P(t)

Answer:

Step-by-step explanation:

You can break it down into steps if you'd like.

-5 ( 3h - 8) = -15h + 40

So,

7h - 5 ( 3h -8 ) = -72

7h - 15h + 40 = -72

Now you can combine the like terms

-8h + 40 = -72

Add 8h to both sides

40 = -72 + 8h

Add 72 to both sides

40 + 72 = 8h

112 = 8h

Divide both sides by 8 to find h.

h = 112/8 = 14

Answer:

The dimensions of the aquarium that minimize the cost of the materials:

[tex]x=y=\sqrt[3]{\frac{2V}{5}}\\z=\sqrt[3]{\frac{25V}{4}}[/tex]

Step-by-step explanation:

Let x, y and z be the dimensions of aquarium .

Surface area of an aquarium = xy+2yz+2xz

Volume of aquarium V=[tex]Length \times Breadth \times Height=xyz[/tex]  ----A

We are given that slate costs five times as much (per unit area) as glass

So, Cost function : C=5xy+2yz+2xz

Now we will use langrage multiplier to find the dimensions of the aquarium that minimize the cost of the materials.

[tex]\nabla C =\lambda \nabla V[/tex]

[tex](\frac{\partial C}{\partial x},\frac{\partial C}{\partial y},\frac{\partial C}{\partial z})= \lambda (\frac{\partial V}{\partial x},\frac{\partial V}{\partial y},\frac{\partial V}{\partial z})[/tex]

[tex](5y+2z,5x+2z,2y+2x)=\lambda(yz,xz,xy)[/tex]

So,

[tex]5y+2z=\lambda yz[/tex]   ----1

[tex]5x+2z=\lambda xz[/tex] -----2

[tex]2y+2x=\lambda xy[/tex]  ----3

Multiply 1 ,2 and 3 by x,y and z respectively.

[tex]5xy+2xz=\lambda xyz[/tex]   ----4

[tex]5xy+2yz=\lambda xyz[/tex] -----5

[tex]2yz+2xz=\lambda xyz[/tex]   ----6

Now equate 4 and 5

5xy+2xz=5xy+2yz

x=y

Substitute y=x in 5 and 6 and equate them

[tex]5x(x)+2(x)z=2(x)z+2xz\\5x^2=2xz\\5x=2z\\\frac{5}{2}x=z[/tex]

Substitute the values in A

[tex]V = xyz = x \times x \times \frac{5}{2}xV=\frac{5}{2}x^3\\\sqrt[3]{\frac{2}{5}V}=x\\x=y=\sqrt[3]{\frac{2}{5}V}\\z=\frac{5}{2}x=\frac{5}{2}(\sqrt[3]{\frac{2}{5}})=\sqrt[3]{\frac{25V}{4}}[/tex]

Hence,

The dimensions of the aquarium that minimize the cost of the materials:

[tex]x=y=\sqrt[3]{\frac{2V}{5}}\\z=\sqrt[3]{\frac{25V}{4}}[/tex]

Answer:  c

Step-by-step explanation:

c is the answer

Answer:

45

Step-by-step explanation:

corresponding angles are congruent

3 and 7 are corresponding

Answer:

25.50=3.75h+0.50d

Step-by-step explanation:

Answer:

About 1200

Step-by-step explanation:

I would round them to the nearest 10 so 27 would become 30 and 42 would be 40.

Then you would multiply to get the answer of about 1200.

Hope that helps and have a great day!

Answer:

Its B because 500 tickets is the maximum amount

Step-by-step explanation:

Answer:

0.75

Step-by-step explanation:

Answer: 35/16

Step-by-step explanation:

Answer:

35/16

Step-by-step explanation:

49x15=735

Denominator will stay the same because both are same (24)

Then you simplify  735/24

Which will give you 35/16

Answer:

x = -3 ±3sqrt(3)

Step-by-step explanation:

3(x+3)^2-81=0

Add 81 to each side

3(x+3)^2=81

Divide each side by 3

3/3(x+3)^2=81/3

(x+3)^2=27

Take the square root of each side

sqrt ((x+3)^2)=±sqrt(27)

x+3 =±sqrt(9*3)

x+3 =±sqrt(9)*sqrt(3)

x+3 =±3sqrt(3)

Subtract 3 from each side

x = -3 ±3sqrt(3)

Answer:

1+1 is 2 and 2+3 is 5

Step-by-step explanation:

Answer: 6

Step-by-step explanation: Since there are three different ways to get from A to B, that creates three variants of each way to get from B to C.

Say the roads are numbered. From A to B, you can use roads 1, 2, or 3. From B to C, you can use roads 4 or 5. The different combinations are 1-4, 1-5, 2-4, 2-5, 3-4, and 3-5.

Answer:

The last one is 8

Step-by-step explanation:

I'm unsure of the question.

Answer:

5

Step-by-step explanation:

Step-by-step explanation:

m-7/3 = m+2

= m-7 = 3(m+2)

= m-7 = 3m+6

= -7-6 = 3m-m

= 2m = -13

= m = -13/2

Answer:

∫ cosec²(7-5x) dx =[-cot(7-5x)]/-5 +c

=(1/5)cot(7-5x)+c

note: d/dx(cotx)=- cosecx

Answer:

18.75 cups of flour

Step-by-step explanation:

The answer is 18.75 cups of flour as you have to multiply 5 by 3 3/4. The result will be 18.75. Hope it helps!

You need 18 3/4 cups of flour, to make 5 batches of the recipe.

An element of a whole is a fraction. The number is represented mathematically as a quotient, where the numerator and denominator are split. Both are integers in a simple fraction. A fraction appears in the numerator or denominator of a complex fraction. The numerator of a proper fraction is less than the denominator.

If one batch of the recipe calls for 3 3/4 cups of flour, then 5 batches of the recipe will require:

5 × 3 3/4 cups

To multiply a whole number by a mixed number, we first convert the mixed number to an improper fraction:

3 3/4 = (4 × 3 + 3) / 4 = 15/4

Now we can multiply:

5 × 15/4 = (5 × 15) / 4 = 75/4

To convert this fraction to a mixed number, we divide the numerator by the denominator and write the remainder as a fraction:

75 ÷ 4 = 18 remainder 3

So, 75/4 is equal to 18 3/4.

Therefore, 5 batches of the recipe will require:

18 3/4 cups of flour.

To learn more about fractions;

https://brainly.com/question/10354322

#SPJ2

Answer:

1

Step-by-step explanation:

y2-y1

/

x2-x1

6 - 9

/

1-4

= -3/-3

which simplifies to 1

Answer:

Around 2.63

Step-by-step explanation:

144 x 2.63 = 378.72

I would put 2.60, but you do you

Answer:

1

Step-by-step explanation:

5/7 *14/10 = 14/7 * 5/10 = 2 * 1/2 =1

Hope I understood the question correctly.

Answer:

I think it's 92.88

Step-by-step explanation:

add up 20 and 9 to get a total of 29%

then multiply .29 and 72 to get 20.88

then add 20.88 and 72 to get the total cost including tips and tax

Answer:

14          30

-----  =  ------

5

cross multiple 30(5)=150

divide 150/14= 10.7142857

idk if they want you to round but

11 or

10.7

Answer:

9

Step-by-step explanation:

2x3=6

3x3=9

Answer:

6 1/4

Step-by-step explanation:

#CarryOnLearning

Answer:

1.) False

The product [tex]\bold{\frac{5}{2}}[/tex]([tex]\bold{\frac{4}{25}}[/tex]) will give the unit price of one kilogram of rice.

2.) False

Emily paid less than $1.50 per kilogram of rice.

3.) True

If Emily has $1.00 \:to\: spend\: on\: rice, she\: can\: get [tex]\frac{4}{10}[/tex]$ of a kilogram of rice.

#CarryOnLearning

Answer:

Question 1

The correct option is  A

Question two

 The correct option is B

Question three

   [tex]SE= 0.5[/tex]  

Question four

   [tex]z = - 3 [/tex]

Question five

The correct option is A

Step-by-step explanation:

   The population mean is  [tex]\mu =  50 \ grams[/tex]

   The sample size is  n = 16

   The population size is N  = 4000

   The sample mean is  [tex]\= x  =  48.5 \grams[/tex]

   The standard deviation is [tex]s  =  2 \ gram(s)[/tex]

Considering the first question

 The correct option is  A

z test because the SD of the population is known and the weights follow the normal curve

Considering  the second question

The correct option is  B

Yes, because with only 20 observations the sample SD is not a great estimate of the true population SD.

Considering  the third question  

   Generally the standard error is mathematically represented as

         [tex]SE= \frac{s }{\sqrt{n} }[/tex]

=>      [tex]SE= \frac{2 }{\sqrt{16} }[/tex]

=>       [tex]SE= 0.5[/tex]    

The null hypothesis is  [tex]H_o :  \mu  =  50[/tex]

The alternative  hypothesis is  [tex]H_a :  \mu  <  50[/tex]

Generally the test statistics is mathematically represented as

      [tex]z = \frac{ \= x  - \mu  }{ SE }[/tex]

=>    [tex]z = \frac{ 48.5 - 50 }{ 0.5}[/tex]

=>   [tex]z = - 3 [/tex]

Generally the p-value is mathematically represented as

     [tex]p-value  = P(Z <  z )[/tex]

=>  [tex]p-value  = P(Z <  - 3  )[/tex]

From the z-table the

    [tex]P(Z <  - 3  ) =0.0013499[/tex]

=>  [tex]p-value  = 0.0013499[/tex]

From the obtained values we see that

  [tex]p-value  <  \alpha[/tex]

So we reject the null hypotheses

The conclusion

it's very unlikely that the factory is making the candy bars 50 grams as they claim

Testing the hypothesis, we have that:

At the null hypothesis, we test if the factory is doing what it is supposed to, that is, the mean is of 50 grams, hence:

[tex]H_0: \mu = 50[/tex]

At the alternative hypothesis, we test if the factory is cheating the customer, that is, the mean is of less than 50 grams, hence:

[tex]H_1: \mu < 50[/tex]

We have the standard deviation for the population, thus, the z-distribution is used. The test statistic is given by:

[tex]z = \frac{\overline{x} - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]

The parameters are:

For this problem, the values of the parameters are: [tex]\overline{x} = 48.5, \mu = 50, \sigma = 2, n = 16[/tex]

Hence, the standard error is:

[tex]S_e = \frac{2}{\sqrt{16}} = 0.5[/tex]

The value of the test statistic is:

[tex]z = \frac{\overline{x} - \mu}{S_e}[/tex]

[tex]z = \frac{48.5 - 50}{0.5}[/tex]

[tex]z = -3[/tex]

The critical value for a left-tailed test, as we are testing if the mean is less than a value, with a significance level of 0.05, is of [tex]z^{\ast} = -1.645[/tex]

Since the test statistic is less than the critical value for the left-tailed test, we can reject the null hypothesis.

A similar problem is given at https://brainly.com/question/14983950