Find a Cartesian equation for the curve.
r = 3 sec(θ)

Identify the curve.
▢ ellipse
▢ line
▢ hyperbola
▢ limaçon
▢ circle

Answer:

f(8) = 51

Step-by-step explanation:

f(x) = 6x + 3

Let x = 8

f(8) = 6(8) + 3

     = 48+3

     = 51

Answer:

51

Step-by-step explanation:

f ( x ) = 6x + 3

To find the value of f ( 8 ), replace x with 8.

f ( 8 ) = 6 × 8 + 3

f ( 8 ) = 48 + 3

f ( 8 ) = 51

The new point that will be formed when the point (-4,5) is rotated 270 degrees counterclockwise is; (5, 4)

There are different types of transformations namely dilation, rotation, reflection e.t.c

Now, when we rotate a point 270 degrees counterclockwise about the origin our point A(x,y) becomes A'(y,-x). This means that we switch x and y and make x negative.

Now, we are told that the point (-4,5) is rotated 270 degrees counterclockwise. Thus, following the transformation rule as described above gives us;

(-4,5) → (5, 4)

Thus, we conclude that the new coordinate we will obtain in this process is (5, 4)

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The value of  [tex]3\frac{3}{5}[/tex] ×[tex](-8\frac{1}{3})[/tex] is after simplification is C)-30

What is mixed fraction?

A mixed number combines an integer (whole number) with a fraction. It is also sometimes referred to as a mixed fraction (part of a whole number). When a number contains both an integer (whole number) and a correct fraction, it is known as a mixed number or mixed fraction (a fraction whose numerator is less than its denominator).

Here the given expression is ,

=> [tex]3\frac{3}{5}[/tex] ×[tex](-8\frac{1}{3})[/tex]

Now we need to convert them into improper fraction then,

=> [tex]\frac{15+3}{5}[/tex] × [tex]\frac{-(24+1)}{3}[/tex]

=> [tex]\frac{18}{5}[/tex] × [tex]\frac{-25}{3}[/tex]

=> 6 × -5 = -30

Hence the correct option is C)-30.

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The angle B in triangle ABC is 60° i.e. C.

What is a triangle?

In Geometry, triangles are the type of polygons, which have three sides and three vertices. This is a two-dimensional figure with three straight sides. A triangle is considered a 3-sided polygon. The sum of all the three angles of a triangle is equal to 180°. The triangle is contained in a single plane. Based on its sides and angle measurement, the triangle has six types.

Based on the sides of a triangle, a triangle is classified into 3 types, namely:

Scalene Triangle – All the sides are of different measures.

Isosceles Triangle – Two sides of a triangle are of the same measure and the remaining side has a different measure.

Equilateral Triangle – All the 3 sides of a triangle are of the same measure.

Based on the angles of a triangle, a triangle is classified into 3 types, namely:

Acute Angle Triangle – All the angles of a triangle is less than 90°.

Obtuse Angle Triangle – One of the angles of a triangle is greater than 90°.

Right Angle Triangle – One of the angles of a triangle is equal to 90°.

Now

∠NAB+∠CAB=180°  (Supplementary angles)

∠CAB=180-∠NAB

=180-100

∠CAB=80°

As

∠A+∠B+∠C=180° (sum of all angles of a triangle =180°)

∠B=180-80-40

∠B=60°

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Numbers divisible by 2 and 5:

Check:

[tex]10\div2=5\\10\div5=2[/tex]  

[tex]20\div2=10\\20\div5=4[/tex]

[tex]30\div2=15\\30\div5=6[/tex]

The given series is convergent and the sum(S) is 5.555.

Consider 10 - 8 + 6.4 - 5.12 + ...

A geometric progression will converge if the common ratio of the series is between -1 and 1.

Here is the common ratio,

r = -8/10

⇒ r = -0.8

Which is -1 < -0.8 < 1.

Hence, the given series is convergent.

Sum of series = S = a/(1 - r)

Here, first term(a) = 10,

common ratio(r) = -0.8,

S = a/(1 - r)

⇒ S = 10/(1 - (-0.8))

⇒ S = 10/(1 + 0.8)

⇒ S = 10/1.8

⇒ S = 5.555

Therefore, the given series is convergent and the sum( S)is 5.555.

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The value of the integral can be calculated by using the simple rules of definite integral and double integral.

The first integral is a bit tricky, as the limits of integration are not in the standard order (with respect to x and y). However, we can change the order of integration by switching the limits of integration, so that we can use Fubini's theorem.

The double integral can be solved by converting the rectangular region R into polar coordinates.

The double integral is ∫∫R 5xsin(x+y)dA, R=[0,pi/3]×[0,pi/6]. This can be further solved as

= ∫(0,pi/3) ∫(0,pi/6) 5rrsin(rcos(θ)+rsin(θ))dθ dr

= ∫(0,pi/3) ∫(0,pi/6) 5r^2sin(r(cos(θ)+sin(θ)))dθ dr

= ∫(0,pi/3) 5r^2(-cos(r*(cos(θ)+sin(θ))) | (0,pi/6))dr

= ∫(0,pi/3) 5r^2(-cos(r*(√(2)/2)))dr

= -5/2∫(0,pi/3) r^2cos(r*(√(2)/2))dr

The integral above is not in a closed form but can be evaluated using numerical integration techniques.

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Complete Question:

Calculate the iterated integral. integral_0^3 integral_0^1 5xy Square root x^2 + y^2 dy dx = Calculate the double integral. double integral R 5x sin (x + y) dA, R = [0, pi/3] times [0, pi/6] The value of integral is

The quotient of the division is x^3 - 3x^2 - 10x + 64

From the question, we have the following parameters that can be used in our computation:

quotient of (x^4-6x^3-19x^2+24x) divided by (x+3)

Using the long division method of quotient, we have

x + 3 | x^4 -6x^3 -19x^2 +24x

The division steps are as follows

            x^3 - 3x^2 - 10x + 64

x + 3 | x^4 -6x^3 -19x^2 +24x

         x^4 + 3x^3

------------------------------------------------

              -3x^3  -19x^2 +24x

              -3x^3 - 9x^2

------------------------------------------------

                          -10x^2 + 24x

                          -10x^2 - 30x

------------------------------------------------

                                           64x

                                           64x + 192

----------------------------------------------------

                                            -192

Hence, the quotient is x^3 - 3x^2 - 10x + 64

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Answer:

  B, C

Step-by-step explanation:

You want to graph the inequalities y≤1/4x+3 and y≥-x+2 and identify points that are solutions to the system.

The graph is attached. It matches selection B of the graphs you are shown. The points that lie in the solution area are B(2, 1) and C(3, 3).

Answer: 4/7

Step-by-step explanation:

pretty simple, 1/7 and 3/7 both has a denominator of "7", so the seven stays the same. (While writing this I made a chart to see where I put everything)

Write:

 1/7 = (denominator 7)

+ 3/7 = (denominator 7)

Now we start doing the math, what goes into 7? 7x1 so 1 x 3 = 3

know we go up to the numerator, 7x1=7, so 1 x 1 = 1

add 3 + 1 and that adds up to 4

so your answer is 4/7, hope it helps

The area of trapezoid is 16 m².

Given in the figure,

Height of trapezoid = 4 m

Length of 1st parallel base = 2 m

Length of 2nd parallel base = 6 m

We know that,

Area of trapezoid = 1/2 * sum of bases * height

∴

Area of trapezoid = 1/2 * (2+6) * 4

                             = 8 * 2 = 16 m²

Therefore, the area of trapezoid is 16 m².

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Radius, diameter, center, and circumference--all are parts of a circle .Every point in the plane that is a certain distance away from a certain point forms a circle (center).

Every point in the plane that is a certain distance away from a certain point forms a circle (center). It is, thus, a curve formed by points moving in the plane at a fixed distance from a point. A circle is a closed two-dimensional object where every pair of points in the plane are equally spaced out from the "center." A line that goes through the circle creates a specular symmetry line. At every angle, it is also rotationally symmetric about the center.

Area of circle =  

[tex]\pi r^2\\r = 10\\A = 3.14 X 10 X 10\\A = 314 unit sq\\[/tex]

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On solving the provided question, we can say that area of circle = [tex]\pi r^2 =[/tex] 3.14*.3.4*3.4 = 1.28112 cm sq.

Every point in the plane that is a certain distance away from a certain point forms a circle (center). It is, thus, a curve formed by points moving in the plane at a fixed distance from a point. At every angle, it is also rotationally symmetric about the center. A circle is a closed two-dimensional object where every pair of points in the plane are equally spaced out from the "center." A line that goes through the circle creates a specular symmetry line. At every angle, it is also rotationally symmetric about the center.

here,

in the circle

the given radius is as = 3.4

area of circle = [tex]\pi r^2 =[/tex] 3.14*.3.4*3.4 = 1.28112 cm sq.

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Answer:

7 students.

Step-by-step explanation:

A trick for this is to find 10% of the students in the Environmental Club and then divide by 2.

10% of 140 is simple; just remove the 0 and you got 14.

Next, divide 14/2 to get 5%

14/2 = 7

7 students are apart of the Environmental Club

The solutions are -

S3 = (1/3) - (1/4) + (1/4) - (1/5) + (1/5) - (1/6)

S4 = (1/3) - (1/4) + (1/4) - (1/5) + (1/5) - (1/6) + (1/6) - (1/7)

S5 = (1/3) - (1/4) + (1/4) - (1/5) + (1/5) - (1/6) + (1/6) - (1/7) + (1/7) - (1/8)

The sum of the series is 1/3.

To find S3, we need to find the sum of the first 3 terms of the series:

S3 = (1/3) - (1/4) + (1/4) - (1/5) + (1/5) - (1/6)

To find S4, we need to find the sum of the first 4 terms of the series:

S4 = (1/3) - (1/4) + (1/4) - (1/5) + (1/5) - (1/6) + (1/6) - (1/7)

To find S5, we need to find the sum of the first 5 terms of the series:

S5 = (1/3) - (1/4) + (1/4) - (1/5) + (1/5) - (1/6) + (1/6) - (1/7) + (1/7) - (1/8)

To find the sum of the telescoping series, we can use the property of the telescoping series where the terms will cancel out. In this case, we can see that the first term of each group of two terms cancels out with the second term of the next group of two terms.

S = (1/3) - (1/8)

The series starts at n=2 and ends at infinity, so the sum of the series is the difference between 1/3 and the limit of 1/n as n approaches infinity, which is zero.

S= (1/3) -0 = 1/3

So the sum of the series is 1/3.

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The complete question is -

Calculate S3, S4, and S5 and then find the sum for the telescoping series: S=∑n=2∞(1/n+1)−(1/n+2). where Sk is the partial sum using the first k values of n.

The equation of the line in slope intercept form is y = 1 / 2 x - 3 / 2.

The equation of a line can be represented in slope intercept form as follows:

y = mx + b

where

Let's find the slope of the line using the coordinates.

Therefore, using (-1, -2) and (-5, -4)

Hence, the slope of a line is the change in the dependent variable with respect to the change in the independent variable.

Therefore,

m = -4 + 2 / -5 + 1

m = - 2 / -4

m = 1 / 2

Therefore, let's find the y-intercept using (-1, -2)

y = 1 / 2 x + b

-2 = 1 / 2 (-1) + b

-2 + 1 / 2 = b

- 3 / 2 = b

Therefore, the equation of the line is y = 1 / 2 x - 3 / 2.

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The value of a is 3√3/2 and value of b is 3/2. The solution has obtained using the trigonometry formulas.

What is trigonometry?

The study of the right-angle triangle's sides, angles, and connection is the main focus of the field of mathematics known as "trigonometry." Therefore, it helps to find the unknown or missing angles or sides of a right triangle using the trigonometric formulas, functions, or trigonometric identities. The angles in trigonometry can either be expressed in degrees or radians. The most used trigonometric angles for computations include 0, 30, 45, 60, and 90 degrees.

In the figure, we are given that one angle measures 30° and the other measures 90° and the hypotenuse is 3.

So, using trigonometry, we know that

Cos theta = adjacent side/hypotenuse

And, Cos 30° is √3/2

So,

⇒√3/2 = a/3

⇒a= 3√3/2

Sin theta = opposite side/hypotenuse

And, Sin 30° is 1/2

So,

⇒1/2 = b/3

⇒b= 3/2

Hence, the value of a is 3√3/2 and value of b is 3/2.

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Answer:

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An IV is infusing at 77mcgtt/min. rate of flow equal in mL/h is 77 mL/h

1gtt/min equals 3.00 mL/h

If you simply need to figure out the infusion rate, or the mL per hour to infuse, take the total volume in mL, divided by the total time in hours that the medication is ordered to be infused over, to equal the rate in mL per hour.

1 drop per minute to milliliters per hour = 3.00 mL/h

2 drops per minute to milliliters per hour = 6.00 mL/h

Change hours to minutes. Change milliliters to drops.

1 ml : 60mcgtt

1hr :60min

77mcgtt/min =77*60/60 ml/h

                  =77ml/h

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The correct graph of the solution to the compound inequality as given in the task content is;

As evident from the task content, it follows that the correct graph of the solution to the compound inequality is to be determined.

Since the given compound inequality is; -13 > -5x + 2 > -28.

To solve the inequality, subtract 2 from all sections of the compound inequality;

-15 > -5x > -30

Divide through the inequality by -5 while flipping the inequality signs so that we have;

3 < x < 6

Therefore, the correct graph for the compound inequality in discuss is as represented in the attached image.

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The domain and the range of this function in interval notation include the following;

Domain = [-6, ∞].

Range = [-∞, 0].

In Mathematics, the horizontal extent of a graph represents all domain values and they are read and written from smaller to larger numerical values, and from the left of a graph to the right.

Furthermore, the vertical extent of a graph represents all range values and they are always read and written from smaller to larger numerical values, and from the bottom of the graph to the top.

By critically observing the graph shown in the image attached below, we can reasonably and logically deduce the following:

Domain = -6 < x < ∞ or [-6, ∞].

Range = -∞ < y < 0 or [-∞, 0].

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The answer is : [tex]X= (A^{-1} C -B^{-1})D[/tex]

According to the question,

AX [tex](D^{-1} + X^{-1} B^{-1} )[/tex] =C

⇒X[tex](D^{-1} + X^{-1} B^{-1} )[/tex]= [tex]A^{-1} C[/tex]

⇒[tex]XD^{-1} + XX^{-1} B^{-1}[/tex] = [tex]A^{-1} C[/tex]

⇒ [tex]XD^{-1} +B^{-1}[/tex] = [tex]A^{-1} C[/tex]

⇒ [tex]XD^{-1} = A^{-1} C -B^{-1}[/tex]

⇒  [tex]X= (A^{-1} C -B^{-1})D[/tex]

So, the answer is : [tex]X= (A^{-1} C -B^{-1})D[/tex]

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The formula for the area of a trapezoid is (a+b)*h/2, where a and b are the lengths of the bases and h is the height.

To estimate the total area between the curve and the x-axis using trapezoids, we can divide the region between the curve and the x-axis into a number of trapezoids, and calculate the area of each trapezoid. The sum of the areas of all the trapezoids will estimate the total area.

For example, consider the curve y = x^2 and the x-axis between x = 1 and x = 2. We can divide this region into 3 trapezoids with bases at x = 1, x = 1.5, x = 2, and heights of 0.25, 0.5625, and 1 respectively.

The area of the first trapezoid is (1 + 1.5) * 0.25 / 2 = 0.1875

The area of the second trapezoid is (1.5 + 2) * 0.5625 / 2 = 0.40625

The area of the third trapezoid is (2 + 2) * 1 / 2 = 1

The sum of the areas of all the trapezoids is 0.1875 + 0.40625 + 1 = 1.60625. This estimates the total area between the curve y = x^2 and the x-axis between x = 1 and x = 2.

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The exact value of cos (-pi/3) can be found using the unit circle or the angle addition formula.

Using the unit circle, we know that the x-coordinate of the point on the unit circle that corresponds to an angle of -pi/3 is cos(-pi/3) and y-coordinate is sin(-pi/3).

On the unit circle, the angle of -pi/3 is the same as the angle of 2pi/3 (since the unit circle has a period of 2pi), therefore the x-coordinate of the point on the unit circle that corresponds to an angle of -pi/3 is -1/2.

Alternatively, using the angle addition formula:

cos (-pi/3) = cos(pi - pi/3) = cos(pi) * cos (pi/3) - sin(pi) * sin(pi/3) = -1/2

So, the exact value of cos (-pi/3) is -1/2.

These approximate percentages are defined by the Empirical Rule, for a normally distributed variable:

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The answer is 2¾. You can also buy calculators that do this for you automatically.

Answer:

Step-by-step explanation:

2 3/4

If Loretta accidentally recorded a deposit of $47.88 as a debit in her register, her check register will differ from the bank statement by $0.

A deposit amount is debited to the check register as an asset, increasing the amount the account holder has in the bank.

It is the bank's responsibility to credit the deposit since it is a liability to them, not an asset.

Under accounting principles, assets are debited while liabilities are credited.  Loretta's debit entry in her register does not constitute an accounting error under the generally-accepted accounting principles.

Thus, Loretta has not committed an accounting error by recording a deposit of $47.88 as a debit in her register, and her register will not differ from the bank statement for this reason.

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The center of the ellipse is (2, -8), The endpoints of the major axis are 10 units from the center, The endpoints of the minor axis are 9 units from the center, To graph the ellipse, connects (2, 2), (11, -8), (2, -18) and (-7, -8) with  smooth curve.

An ellipse in mathematics is a plane curve that has two focal points and is such that the sum of the two distances from any point on the curve to the focal points is a constant. It generalizes a circle, a special kind of ellipse in which the two focal points coincide.

Glven:

The equation of ellipse is,

[tex]\frac{(x-2)^2}{81}+\frac{(x+8)^2}{100}=1[/tex]

SInce, the general form of ellipse is,

[tex]\frac{(x-h)^2}{a^2}+\frac{(y-k)^2}{b^2}=1[/tex]

where,

(h, k) is the center of ellipse

a is the minor axis

b is the major axis.

Here

(h, k) = (2, -8) is the center of the ellipse.

9 is the minor axis and 10 is the major axis of the ellipse.

Also the graph of ellipse connects (2, 2), (11, -8), (2, -18) and (-7, -8) with  smooth curve.

Hence,  the center of the ellipse is (2, -8).

The endpoints of the major axis are 10 units from the center.

The endpoints of the minor axis are 9 units from the center.

To graph the ellipse, connects (2, 2), (11, -8), (2, -18) and (-7, -8) with  smooth curve.

The graph of the ellipse visit.

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Answer:

x=8

Step-by-step explanation:

Answer:

3x+y+4-(y + 6) = 14 + x

x=8