Let R be the region in the first quadrant bounded by the graph of y = Vx - 1. the x-axis, and the vertical line * = 10. Which of the following integrals gives the volume of the solid generated by revolving R about the y-axis?

Answer:

solution,

CD=3x-12

AB=14

BD=6

AC=21

Angle bisector theorem ,

\( \frac{ab}{bd} = \frac{ac}{cd} \\ \: or \: \frac{14}{6} = \frac{21}{3x - 12} \\ or \: 14(3x - 12) = 21 \times 6( \: cross \: multiplication) \\ or \: 42x - 168 = 126\)

Adding 168 on both sides

\(or \: 42x - 168 + 168 = 126 + 168 \\ or \: 42x = 294\)

dividing 42 on both side

\( \frac{42x}{42} = \frac{294}{42} \\ \)

\(x = 7\)

Hope this helps..

Good luck on your assignment..

The stated figure's necessary area is (D) 96 m².

The size of a patch is determined by its surface area.

A surface region or plane area is the area of an open surface or the boundary of a three-dimensional object, whereas a plane region or area refers to the area of a form or planar lamina.

So, b * h is the parallelogram's area.

base: 10 m

six meters high

Triangle Area have to be: 1/2 (or .5) * b * h

base: 12 m

height: 6 m

0.5 * 12 * 6 = 36 m

Add the following values:

60 + 36 = 96 m²

Therefore, the stated figure's necessary area is (D) 96 m².

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Complete question:

The area of the figure is about:

(A) 36m²

(B) 60m²

(C) 72m²

(D) 96m²

The manufacturer can take corrective actions to maintain the quality of the dustless chalk and ensure it meets the desired density standards.

It seems part of your message got cut off. However, I can still provide some general information about quality control programs and how they can be used to monitor chalk density.

In quality control programs, the manufacturer uses statistical methods to monitor and ensure the consistency and quality of the products they produce.

One common technique used is Statistical Process Control (SPC). SPC involves taking samples from the production process at regular intervals and analyzing them to identify any variations or abnormalities.

To monitor chalk density, the manufacturer can take 24 different subgroups of chalk samples, each subgroup consisting of "n" samples. The sample standard deviation calculated for each subgroup can be used to estimate the variation in chalk density within each subgroup.

The manufacturer can then use control charts to track the process over time. Control charts display the sample means and control limits, which are calculated based on the sample standard deviations.

By comparing the sample means with the control limits, the manufacturer can identify when the process is out of control or when there are significant variations in chalk density.

If the process goes out of control or if there are consistent deviations in chalk density.

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Explanation:

The GCF of the coefficients 8 and 6 is 2, which forms the coefficient for the answer.

Focusing on the variable terms, we can see that c^3 is found in both expressions. It might help to rewrite the c^4 as c^3*c

Since c^3 is in both, this means c^3 is the remaining part of the answer.

Combining everything gets us to the GCF 2c^3

If we had something like 8c^3+6c^4, then it would factor to 2c^3(4+3c) after pulling out the GCF. I'm using the distributive property.

Answer:

2c³

Step-by-step explanation:

factors of 6:  1, 2, 3, 6

factors of 8:  1, 2, 4, 8

Greatest factor is 2

GCF if c³ and c⁴ is the smaller exponent, so c³

If Jina used three times as many pounds of Type B coffee as Type A, then the amount of Type A coffee used is 27 pounds.

Let the number of pounds of type A coffee used in the blend be denoted by "x",

The shop used 3times as many pounds of type-B coffee,

So, the number of pounds of type B coffee used in the blend is = 3x.

The total cost of the blend is given as $503.55, and

We know that the cost of "type A" coffee is $5.75 per pound, and the cost of "type B" coffee is $4.3 per pound.

So, we can write the following equation,

⇒ 5.75x + 4.3(3x) = 503.55

Simplifying and solving for x, we get:

⇒ 5.75x + 12.9x = 503.55

⇒ 18.65x = 503.55

⇒ x = 27

Therefore, Jina used 27 pounds of type A coffee in the blend.

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Answer:

49 / 9π + 16

Step-by-step explanation:

So 110 / 360 = 11 / 36

The circumference of the circle is 16π

11 / 36 * 16 = 44 / 9π

44 / 9π + 8 + 8 is the answer since you gotta add the sides.

This might be wrong so check my steps.

Answer:

1. petting zoo

2. carousel

3. games

Step-by-step explanation:

i think it's the right order not 100% though

The sequence of transformations used to show the congruence of polygons JKLMN and PQRST is to reflect PQRST across the y-axis and then translate the result down 10 units.

We are given two polygons. Both the polygons are congruent, and to prove it, we can use the concept of transformations. The first transformation we need to perform is to reflect the polygon PQRST across the y-axis. The next transformation that needs to be performed is to translate the result down by 10 units. We find that the polygon PQRST now coincides with the polygon JKLMN. Hence, it is proved that the polygons are congruent to each other.

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We have the next cost given function:

The average cost function is given by:

Replace:

Simplify the expression:

Derivate A(x)

Set A'(x)=0

Solve for x:

Therefore, the average cost per unit will be minimized at 100 units of production level.

Answer:

=84.4m

Step-by-step explanation:

252÷7.2=35

7.2×2=14.4

35×2=70

14.4+70=84.4

=84.4m

The correct option is B.

Rank

The RANK function in a Microsoft Excel spreadsheet enables users to order the various pieces of data by their numerical values. By entering an absolute value for the range of cells the user wants to rank, they can also use the rank function. If an absolute value is not specified, the program's auto-formula may cause the rank of the various cells to alter.

A spreadsheet is a computer program used for organizing, organizing, analyzing, and storing tabular data. Spreadsheets were created as electronic alternatives to paper accounting worksheets. Data typed into table cells serves as the program's input.

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To find a basis for the orthogonal complement of subspace W in R^4, where W is spanned by vectors w1, w2, and w3, we can use the Gram-Schmidt process.

This process involves finding a set of orthogonal vectors that span the orthogonal complement of W.

Steps:

Start with the vectors that span the subspace W: w1 = (2, 1, 3, 3), w2 = (1, 2, 3, 0), and w3 = (3, 1, 4, 5).

Apply the Gram-Schmidt process: Take the first vector, w1, as the first vector in the orthogonal complement basis. Normalize w1 by dividing it by its magnitude to obtain a unit vector u1 = w1 / ||w1||.

Calculate the projection: Project the remaining vectors, w2 and w3, onto u1 and subtract the projections from the original vectors. The resulting vectors will be orthogonal to u1.

Normalize the orthogonal vectors: Normalize the resulting orthogonal vectors obtained in the previous step by dividing them by their magnitudes to obtain unit vectors u2 and u3.

The set {u1, u2, u3} is a basis for the orthogonal complement of W. These vectors are orthogonal to each other and also orthogonal to the vectors in W.

By following these steps, you can obtain a basis for the orthogonal complement of the subspace W spanned by the given vectors in R^4. The resulting basis will consist of vectors {u1, u2, u3} that are orthogonal to W.

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Answer:

x = 5, x = -5

Step-by-step explanation:

First, you can notice both terms of the equation are divisible by 2, so you can factor it out to get:

2(x^2 - 25) = 0

You can recognize the expression x^2 - 25 as the special product for the difference of squares, so it would be factored into (x + 5)(x - 5). When we plug it in we get:

2(x + 5)(x - 5) = 0

Now, we can use the zero-product property to get two equations:

x + 5 = 0

-and-

x - 5 = 0

Solving them both we get:

x = 5, x = -5

Answer:

The slope of the line through the points is -5/7

Step-by-step explanation:

Here, we want to calculate the value of the slope through the lines

Mathematically;

m = y2-y1/(x2-x1)

Where (x1,y1) = (-4,2)

and (x2,y2) = (3,-3)

Substituting these values, we have;

m = (-3-2)/(3-(-4)) = -5/7 = -5/7

The slope of the line through (-4, 2) and (3, -3) is; -5/7

According to the question;

The slope, m of the line is given mathematically as;

Therefore, in this case;

Slope, m = -5/7

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Answer:

D

Step-by-step explanation:

when x=0, y=2

The probability that a randomly selected pupil will have an IQ above 136 is approximately 0.0082, or 0.82%.

To find the probability that a randomly selected pupil will have an IQ above 136, we need to calculate the standard score (z-score) corresponding to an IQ of 136 and then use the standard normal distribution.

First, we calculate the z-score using the formula:

z = (X - μ) / σ

where X is the IQ score, μ is the mean, and σ is the standard deviation.

In this case, X = 136, μ = 100, and σ = √225 = 15.

z = (136 - 100) / 15

z = 2.4

Next, we find the probability corresponding to the z-score using a standard normal distribution table or a calculator. The probability of having an IQ above 136 is the complement of the probability of having an IQ below 136.

P(Z > 2.4) ≈ 1 - P(Z < 2.4)

Using a standard normal distribution table or calculator, we find that P(Z < 2.4) is approximately 0.9918.

Therefore, P(Z > 2.4) ≈ 1 - 0.9918 = 0.0082.

So, the probability that a randomly selected pupil will have an IQ above 136 is approximately 0.0082, or 0.82%.

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Particular solution with the determined constants is:
y(t) = 4*cos(7t) - (5/7)*sin(7t)

To solve the given initial-value problem y'' + 49y = 0 with initial conditions y(0) = 4 and y'(0) = -5, follow these steps:

Step 1: Identify the type of problem.
This is a second-order linear homogeneous differential equation with constant coefficients.

Step 2: Write down the characteristic equation.
The characteristic equation for this problem is \(r^2\) + 49 = 0.

Step 3: Solve the characteristic equation.
\(r^2\) = -49
r = ±√(-49) = ±7i

Since the roots are complex conjugates, the general solution of the differential equation is in the form:
y(t) = C1*cos(7t) + C2*sin(7t)

Step 4: Apply the initial conditions to find the constants.
Apply the initial condition y(0) = 4:
4 = C1*cos(0) + C2*sin(0)
4 = C1
So, C1 = 4

Next, find the first derivative of y(t):
y'(t) = -7*C1*sin(7t) + 7*C2*cos(7t)

Apply the initial condition y'(0) = -5:
-5 = -7*4*sin(0) + 7*C2*cos(0)
-5 = 7*C2
So, C2 = -5/7

Step 5: Write the particular solution.
The particular solution with the determined constants is:
y(t) = 4*cos(7t) - (5/7)*sin(7t)

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Step-by-step explanation:

Let the number be \(\overline{abc}=100a+10b+c\).

\(100a+10b+c=34a+34b+34c \\ \\ 66a-24b-33c=0 \\ \\ 22a-8b-11c=0\)

Taking the equation mod \(11\) yields \(-8b \equiv \pmod{11}\), meaning \(b=0\).

So, \(22a-11c=0 \implies c=2a\).

So, the only possibilites are \((a,c)=(1,2), (2,4),(3,6), (4,8)\).

Therefore, there are \(4\) such numbers.

Answer:

Step-by-step explanation:

If the same line holds the hypotenuse of two right triangles, both of the triangles are similar.

This is because they have same ratio of corresponding sides.

Yes .

Let's check your graph

In ∆ADE and ∆ABC

Hence both triangles are similar

The content dimension of a message deals with the what of a message, while the relational dimension of a message deals with the how of a message is the correct answer.

Content dimensions is a generic concept to have multiple variants of a content node. It involves the information being explicitly discussed. The content repository supports any number of dimensions. The content dimension is the meaning of the actual message itself.

"Relational dimension of communication is a concept in which we have similar weight and impact as that of the message. This concept deals with the quality or nature of the relationships and networks."

Hence we can conclude that the content dimension of a message deals with the what of a message, while the relational dimension of a message deals with the how of a message is the correct answer.

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Answer:

y = 0.25x

Step-by-step explanation:

remember the formula for the slope

\(\frac{y_{2} - y_{1} }{x_{2} - x_{1} }\)

so substitute in two pairs to find the slope

for this problem, let's use the first two give

( -4,  -1 )

( 0, 0 )

\(x_{1}\) = -4

\(y_{1}\) = -1

\(x_{2}\) = 0

\(y_{2}\) = 0

so now substitute

( 0 - - 1) / ( 0 - - 4)

= 1/4

now the equation of a line is

y = mx + b

where (m) is the slope, and (b) is the y-intercept, but since this line passes through the origin (0, 0) there will be no y-intercept so the equation of the line is

y = 1/4 x

or

y = 0.25x

Answer:

4 whole cube × 5 whole square

Step-by-step explanation:

Hope the answer above helps you...

The length of ST in the triangle STU, we can use the sine rule. Given that the measure of angle ZU is 90°, angle ZT is 26°, and US is 13 feet, we can calculate the length of ST to the nearest tenth of a foot. Therefore, the length of ST in the triangle STU is approximately 5.45 feet.

In triangle STU, we have angle ZU as a right angle, which means triangle STU is a right triangle. The sine rule can be used to relate the lengths of the sides and the measures of the angles in a triangle. The sine rule states that in any triangle, the ratio of a side length to the sine of its opposite angle is constant.

Using the sine rule, we can write:

ST / sin ZT = US / sin ZU

Given that sin ZU = 1 (since ZU is a right angle), and US = 13 feet, we can substitute these values into the equation:

ST / sin 26° = 13 / 1

To find the length of ST, we can solve for it:

ST = sin 26° * 13

Evaluating the right-hand side of the equation, we find:

ST ≈ 5.45 feet (rounded to the nearest tenth of a foot)

Therefore, the length of ST in the triangle STU is approximately 5.45 feet.

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D is correct :)

The bunnies are multiplying by 5 each time. The exponent will have the growth be 5 times the product before.

Hope this helps :)

Answer:

the 4th answer is correct

Step-by-step explanation:

although technically, we don't have enough information, it's the only one that it could be.

Answer:

\(\frac{6}{35}\)

Step-by-step explanation:

To find the ' middle ' add the 2 fractions and divide by 2 ( average )

\(\frac{1}{5}\) + \(\frac{1}{7}\) ( change denominators to 35 , the LCM of 5 and 7 )

= \(\frac{7}{35}\) + \(\frac{5}{35}\)

= \(\frac{12}{35}\)

midway = \(\frac{12}{35}\) ÷ 2 = \(\frac{6}{35}\)

The fraction is exactly midway between 1/5 and 1/7  is  \(\frac{6}{35}\) .

Sometimes you need to find the point that is exactly midway between two other points. For instance, you might need to find a line that bisects (divides into two equal halves) a given line segment. This middle point is called the "midpoint".

According to the question

The fraction is exactly midway between 1/5 and 1/7

Now ,

To find midway between 1/5 and 1/7

Step1 : Add fraction 1/5 and 1/7

= \(\frac{1}{5} +\frac{1}{7}\)

= \(\frac{12}{35}\)

Step2 : Divide the sum by 2 or multiply by 1/2

= \(\frac{12}{35}\) * \(\frac{1}{2}\)

= \(\frac{6}{35}\)

Hence, the fraction is exactly midway between 1/5 and 1/7  is  \(\frac{6}{35}\) .

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Answer:

D

Step-by-step explanation:

Somehting bknbye3uehnfhnjun Español uno, como sulfhídrica

Final Price is $10.40

Step-by-step explanation:

In this question we are using the percentage formula which is y/100 times x = z

so we do 20/100 x 13 = 2.60

Now we subtract 2.6 from 13 because $2.60 was the discount price

so we get $10.40