Calc find the maximum of f(x, y) = y2 + xy â x2 on the square 0 ⤠x ⤠6, 0 ⤠y ⤠6.

In the function sin⁻¹(9x + 1), the 'outside' function is sin⁻¹(x). This is because it is the function performing an operation on the 'inside' function, which is 9x + 1.

For the function sin−1(9x + 1), the 'inside' function is indeed 9x + 1. The 'outside' function is sin⁻¹(x), also known as the inverse sine or arcsine function. In composite functions, the 'inside' function is the function that is being acted on, while the 'outside' function is the function carrying out the action on the inside function. So here, the action of sine inverse or arcsine is being performed on the 'inside' function 9x + 1.

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Answer:

(y-6)

Step-by-step explanation:

[tex]y^2 - 10y + 24[/tex]

We need to find out two factors whose product is 24 and sum is -10

-6  times -4 = 24

-6  +    -4 = -10

So two factors are -6  and -4

We write the factors inside the parenthesis

(y-6) (y-4)

Factor (y-4) is already given

So another factor is (y-6)

Final Answer:

y - 6

Explanation:

To find another factor of the quadratic expression (y^2 – 10y + 24) given that (y – 4) is one factor, we need to perform factorization. Let's find the factors of the constant term, 24, which when added together give us the coefficient of the middle term, which is –10.
The factors of 24 are: 1, 2, 3, 4, 6, 8, 12, and 24.
We are looking for two factors of 24 that add up to –10, and since one of the given factors is (y – 4), we are specifically looking for factors that would give us ((y - 4)) when multiplied by a binomial of the form (y - n), where (n) represents the other factor.
Now, notice that the factors 6 and 4 add up to 10, and when multiplying two binomial factors, we actually find such that when expanded they give us the original quadratic expression. In this case, (6 times 4 = 24), and (-6 + (-4) = -10), which are our constant and coefficient of \(y\), respectively.
Therefore, we can write the quadratic expression as the product of two binomial expressions: ((y - 6)(y - 4))
Since we are already given that \(y - 4\) is a factor, the other factor must be (y - 6).

Answer:

8

Step-by-step explanation:

volume of glass 2 = pi*r^2*h/3= 3.14 *2.5^2*6/3 = 39.25 cubic cm

60-39.25 = 20.75 cu cm was in 1st cup

volume of cylinder = pi *r^2 *h

20.75 = 3.14 *2^2 *h

20.75 = 3.14*4*h

20.75 = 12.56*h

h = 20.75 /12.56 = 1.652 round to 1.7

Answer:

The height of glass 1 is 1.7 cm.    

Step-by-step explanation:

We are given the following information in the question:

The total amount of water that Samuel poured into the glasses is 60 cubic centimeters.

Volume of glass 2 = Volume of cone =

[tex]\displaystyle\frac{1}{3}\pi r^2h\\\\\text{Putting value of r and h}\\\\= \frac{1}{3}\times 3.14\times \frac{5}{2}\times \frac{5}{2}\times 6 = 39.25\text{ cubic cm}[/tex]

Volume of glass 1 =

[tex]\text{ Total Volume } - \text{Volume of glass 2}\\= 60 - 39.25\\= 20.75\text{ cubic cm}[/tex]

Volume of glass 1 = Volume of cylinder =

[tex]20.75 = \pi r^2h\\\text{where r is the radius of cylinder and h is the height of cylinder}\\\\\text{Putting the values of r}\\\\  20.75 = 3.14\times \displaystyle\frac{4}{2}\times \frac{4}{2}\times h\\\\h = \frac{20.75}{3.14\times 2\times 2} 1.656 \approx 1.7[/tex]

Thus, the height of glass 1 is 1.7 cm.

Answer:

x = 8.4

Explanation:

The solution is, the value is 100 x 100 =10000.

In mathematics, multiplication is a method of finding the product of two or more numbers. It is one of the basic arithmetic operations, that we use in everyday life.

here, we have,

given that,

100 x 100

i.e. we have to multiply 100 with 100

so, we get,

100 x 100

=10000

Hence, The solution is, the value is 100 x 100 =10000

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Answer:

3^3

Step-by-step explanation:

Answer:

  True

Step-by-step explanation:

In simplest terms, if the triangle is ΔABC with ∠B≅∠C, then you can show ΔABC ≅ ΔACB using the ASA congruence theorem. (BC≅CB by the symmetric property). Then AB ≅ AC by CPCTC (corresponding parts of congruent triangles are congruent).

To remove the area of 20'x22' from the total space of 2240 square feet, multiply the dimensions to get the area to deduct, which is 440 square feet. Then subtract this from the total area to find the remaining space, which is 1800 square feet.

To deduct an area of 20 feet by 22 feet from a total space of 2240 square feet, you first need to calculate the area of the space you are removing. To find the area of a rectangle, you multiply its length by its width.

Area to deduct = Length × Width = 20' × 22' = 440 square feet.

Next, subtract the area to deduct from the total space:

Remaining space = Total space - Area to deduct = 2240 sq ft - 440 sq ft = 1800 square feet.

Therefore, you are left with 1800 square feet of space after deducting the area of 20'x22' from the original total space of 2240 square feet.

Answer:

a

Step-by-step explanation:

Answer:

A. 3.31227766..., irrational

Step-by-step explanation:

We have been given two numbers. We are asked to find sum of given numbers and classify the type of number after addition.

[tex]\frac{3}{20}+\sqrt{10}[/tex]

[tex]0.15+3.1622776601683793[/tex]

[tex]3.3122776601683793[/tex]

We can see that [tex]\frac{3}{20}[/tex] is a rational number, while [tex]\sqrt{10}[/tex] is an irrational number as its digits are repeating infinitely after decimal.

We know that sum of a rational and irrational number is irrational, therefore the sum of given numbers is irrational and option A is the correct choice.

Answer:

The ratio would be 2:5

Explanation:

The ratio of drops of blue dye to total drops of dye is got by dividing drops of blue dye  (12) by total drops, which is the sum of blue and yellow drops (12+18):

[tex]\displaystyle\frac{12}{12+18}=\frac{12}{30}[/tex]

Once we simplify the fraction by dividing both top and bottom by 6, we would get:

[tex]\displaystyle\frac{2}{5}[/tex]

Therefore, the ratio of drops of blue dye to total drops of dye is:  2:5

The simplified ratio of blue dye to total dye used by Julian is 2:5. This means that for every 2 drops of blue dye, there are 5 total drops of dye.

The question is asking for the ratio of blue dye to the total amount of dye. Julian used 12 drops of blue dye and 18 drops of yellow dye, making the total number of dye drops 30 (12 blue + 18 yellow). Therefore, the ratio of blue dye to total dye is 12 to 30. However, this ratio can be simplified by dividing each figure by their greatest common divisor (gcd) which is 6. So, the simplified ratio is 2:5.

This means for every 2 drops of blue dye, there are 5 total drops of dye. It's a useful way of comparing quantities in mathematics or in everyday life circumstances like this one, where Julian is mixing dyes.

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Answer:

Markup percent = 117.50%

Step-by-step explanation:

Markup percent = (sales price - unit cost)/unit cos  *100

Given: Unit cost = $16.55, sales price = $35.99

Now plug in these given values in the above formula, we get

Markup percent = (35.99 - 16.55)/16.55 *100

= (19.44/16.55)*100

= 117.50%

Hope this will helpful.

Thank you.

Answer:

Option: B is the correct answer.

  B. The function has more than one x-intercept.

Step-by-step explanation:

We are given a table of  values as follows:

            x                    y

           -3                    4

            0                    -3

             1                     2

             5                    0

             11                    7  

As we know that a function is a continuous function this means that the graph first decreases from 4 to -3 ( since at x=-3 we have y=4 and at x=0 we have y= -3) and then it increases from -3 to 7 ( since at x=0 we have y= -3 and at x=11 we have y=7)

Hence, the function will intersect the x-axis two times between x= -3 and x=11.

           Hence, the function has more than one x-intercept.

Answer: The function had more than in intercept,

Step-by-step explanation: