limit x->oo (sqrt(x^2-9x+1)-x)=?

I solved it up until -9x+1/((√x^2-9x+1)+x) but I don't know what to do after this.

Answer:

The maximum distance between supports for the beam to support a weight of 1600 lb is also 4.5 feet.

Step-by-step explanation:

We are given that weight P is inversely proportional to the distance D between the supports of the beam, and for this certain type of wooden beam, we have:

P = 7200/D

To find the distance between supports needed to carry 1600 lb, we can substitute P = 1600 in the above equation and solve for D:

1600 = 7200/D

D = 7200/1600

D = 4.5 feet

So the distance between supports needed to carry 1600 lb is 4.5 feet.

To find the maximum distance between supports for the beam to support a weight of 1600 lb, we can use the same equation and solve for P = 1600:

1600 = 7200/D

D = 7200/1600

D = 4.5 feet

Therefore, the maximum distance between supports for the beam to support a weight of 1600 lb is also 4.5 feet.

Answer:

∠FBC = 150°

Step-by-step explanation:

The straight line's angle is 180°. Minus angle ∠EF (30°) from 180 to get the measurement  of angle ∠FBC

The measure of the angle NSR is equal to 113 degrees

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

The circle

Using the angle of intersecting chords theorem, we have following equation

NSR = 1/2(Sum of major and minor arcs NS)

So, we have

NSR = 1/2 * (176 + 50)

Evaluate

NSR = 113

Hence, the angle is 113 degrees

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Answer:

For the Triangle it is 3 and for the quadrilateral,(trapezoid) it is 10.5

Step-by-step explanation:

for the triangle do bxh/2. and for the trapezoid divide it into a square and triangle.

The formula for population variance uses the division of (sum of squared deviations) by the total number of elements in the population, while the formula for sample variance uses the division of (sum of squared deviations) by the sample size minus one.

The formula for population variance uses the division of (sum of squared deviations) by the total number of elements in the population, while the formula for sample variance uses the division of (sum of squared deviations) by the sample size minus one.

The formula for population variance is given by:

σ² = (1/N) * ∑(X - μ)²,

where N is the total number of elements in the population, X is an individual value in the population, and μ is the mean of the population.

s²= (1/(n-1)) * ∑(X - m)²,

where n is the sample size and m is the mean of the sample.

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Given the figure of a right-angle triangle and the indicated angle θ

As shown, the hypotenuse = 7

And the opposite side = 4

We will use the Pythagorean theroem to find the adjacent side:

Now, we will find cot θ, sec θ, and cos θ as follows:

So, the answer will be:

Answer:

4.5 feet of snow = 27 inches H2o. Please read the explanation for better details

Step-by-step explanation:

if 0.5 feet of snow melts into 2 inches of water, then that means that 6 inches of snow melts into 2 inches of water. This means that for every 2 inches of snow you melt, it will become 1 inch of water. If 4.5 ft = 54 inches, you simply divide by 2, getting your answer of 27 inches of snow. Hope this helps! :)

Therefore, out of the 24 students that Blake interviewed, 9 of them participate in sports.

An equation is a mathematical statement that indicates that two expressions are equal. It typically consists of variables, constants, and mathematical operations such as addition, subtraction, multiplication, and division. The expressions on both sides of the equation are separated by an equal sign "=" which means that the two expressions have the same value.

Here,

According to the table, Blake interviewed a total of 24 students. To find out how many of these students participate in sports, we need to add up the number of students who collect sports cards and participate in sports, as well as the number of students who do not collect sports cards and participate in sports. So:

Total students who participate in sports = Number of students who collect sports cards and participate in sports + Number of students who do not collect sports cards and participate in sports

Total students who participate in sports = 6 + 3

Total students who participate in sports = 9

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Given:

P = Set of all triangles,

Q = Set of scalene triangles,

R = Set of isosceles triangles and

S = Set of equilateral triangles.

To find:

Which of the following statements are true or false?

Solution:

We know that,

Scalene triangles : All sides are different.

Isosceles triangles : Two sides are equal.

equilateral triangles : All sides are equal.

Set of all triangles contains all scalene triangles. So, set of scalene triangles Q is a subset of Set of all triangles P.

\(Q\subset P\)

So, (a) is true.

All isosceles triangles are not equilateral triangles. So, set of isosceles triangles R is not a subset of set of equilateral triangles S.

\(R\nsubseteq S\)

So, (b) is false.

Set of all isosceles triangles contains all equilateral triangles. So, set of equilateral triangles S is a subset of set of isosceles triangles R .

\(S\subset R\)

So, (c) is true.

Answer:

60

step-by-step explanation:

Answer: 60

Step-by-step explanation: Basically just multiply the whole number by 2 :)

Whenever you see something times 0.5, just know that its going to be that number times 2 (like another half of that number if you understand)

Why? Because 0.5 is basically like a one half (1/2) and you flip the stuff. since 0.5 is a half, here's a tip. Whenever you're dividing with decimals, use the formula KCF (keep, change, flip) (what my teacher taught me before)          

Here's a drawing to better explain:

Answer:

19 would be the naswer

Step-by-step explanation:

Answer:

Step-by-step explanation:

b

mode= most

Answer:

B is the answer from this one

Step-by-step explanation:

I did this today aswell and got 100%

For the fractions, the calculation of 3/5 of 2/3 of 3/4 of 560 is equal to 168.

To calculate 3/5 of 2/3 of 3/4 of 560, break it down step by step:

Step 1: Calculate 3/4 of 560:

3/4 × 560 = (3 × 560) / 4 = 1680 / 4 = 420

Step 2: Calculate 2/3 of the result from Step 1:

2/3 × 420 = (2 × 420) / 3 = 840 / 3 = 280

Step 3: Calculate 3/5 of the result from Step 2:

3/5 × 280 = (3 × 280) / 5 = 840 / 5 = 168

Therefore, 3/5 of 2/3 of 3/4 of 560 is equal to 168.

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The expression that is equivalent to the given expression where the expression is given as (18)2⋅(19)2 is (18 * 19)^2

The expression is given as

(18)2⋅(19)2

Rewrite the above expression properly

So, we have

(18)^2 * (19)^2

The factors in the above expression have the same exponent.

So, the expression can be rewritten as

(18 * 19)^2

Hence, the expression that is equivalent to the given expression where the expression is given as (18)2⋅(19)2 is (18 * 19)^2

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The solution to the system of equations is (x, y) = (-261/47, 44/47) as an ordered pair.

To solve the given system of equations:

Equation 1: 8x + 9y = -36

Equation 2: x + 7y = 1

We can use the method of substitution or elimination to find the values of x and y. Let's use the method of substitution:

From Equation 2, we can solve for x:

x = 1 - 7y

Substituting this value of x into Equation 1:

8(1 - 7y) + 9y = -36

8 - 56y + 9y = -36

-47y = -44

y = 44/47

Substituting the value of y back into Equation 2 to find x:

x + 7(44/47) = 1

x + 308/47 = 1

x = 1 - 308/47

x = (47 - 308)/47

x = -261/47

Therefore, as an ordered pair, the solution to the system of equations is (x, y) = (-261/47, 44/47).

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Answer:

The probability of spending between 4 and 7 days in recovery

P(4≤x≤7) = 0.5445

Step-by-step explanation:

Step(i):-

Given mean of the Population μ = 5.3 days

Given standard deviation of the population 'σ' = 2 days

Let 'X' be the random variable in normal distribution

Let    x₁ = 4

\(Z_{1} = \frac{x_{1}-mean }{S.D} = \frac{4-5.3}{2} = -0.65\)

Let    x₂ = 7

\(Z_{2} = \frac{x_{2}-mean }{S.D} = \frac{7-5.3}{2} = 0.85\)

Step(ii):-

The probability of spending between 4 and 7 days in recovery

P(4≤x≤7) = P(-0.65≤Z≤0.85)

             =  P(Z≤0.85) - P(Z≤-0.65)

            = 0.5 + A( 0.85) - ( 0.5 - A(-0.65)

            = 0.5 + A( 0.85) -  0.5 +A(0.65)   ( ∵A(-0.65) = A(0.65)

           =   A(0.85) + A(0.65)

          = 0.3023 + 0.2422

         = 0.5445

Final answer:-

The probability of spending between 4 and 7 days in recovery

P(4≤x≤7) = 0.5445

Answer:

\(x∈( - ∞;8]\)

Step-by-step explanation:

\(x + 9 - 3 \leqslant 14\)

Collect like-terms:

\(x \leqslant 14 - 9 + 3\)

\(x \leqslant 8\)

\(x∈( - ∞;8]\)

The volume of the given figure is 1176 cubic cm.

The value of the figure is calculated by multiplying all three side areas. Volume is a measure of the amount of space that an object or a substance occupies. It is typically expressed in cubic units such as cubic meters (m³), cubic centimetres (cm³), or cubic feet (ft³).

The volume of the figure is calculated as,

Volume = 2 ( 15 x 6 + 20 x 6 + 20 x 18 )

Volume = 1176 Cubic cm

Hence, the volume of the figure will be equal to 1176 Cubic cm.

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Step-by-step explanation:

OK, 'Brainless'....  the triangle side length rule states that any two sides of a triangle must sum to greater than the remaining side length...

42 + 20 > x        then  12 , 20, 22, 32, 42, 50     will work here

42+x > 20            all of the possibles work here

20 + x > 42         32, 42, 50, 62 and 70 work here

   so   32 and 42 are in all of the lists ....that is your answer

Answer:i dont know

Step-by-step explanation:

The total volume of the dill spears is approximately 160 cm³.

To find the total volume of the dill spears, we'll need to determine the volume of the pickling liquid and subtract it from the total volume of the jar.

Given information:

Base area of the jar = 45 cm²

Height of the jar = 13 cm

Pickle juice drained = 160 cm³

First, let's calculate the volume of the jar:

The volume of a cylinder can be found using the formula V = πr²h, where r is the radius of the base and h is the height of the cylinder.

The base area of the jar is given as 45 cm², which means πr² = 45.

So, we can find the radius (r) of the base using the formula r = √(45/π).

Let's calculate the value of r:

r = √(45/π) ≈ 3.79 cm

Now we can find the volume of the jar:

V_jar = πr²h

= π(3.79)²(13)

≈ 1818.73 cm³

Next, let's calculate the volume of the pickling liquid:

Given that 160 cm³ of pickle juice was drained, the volume of the pickling liquid is equal to the volume of the jar minus the volume of the drained pickle juice.

V_pickling_liquid = V_jar - 160

≈ 1818.73 cm³ - 160 cm³

≈ 1658.73 cm³

Finally, to find the total volume of the dill spears, we need to subtract the volume of the pickling liquid from the volume of the jar:

Total volume of dill spears = V_jar - V_pickling_liquid

≈ 1818.73 cm³ - 1658.73 cm³

≈ 160 cm³

Therefore, the total volume of the dill spears is approximately 160 cm³.

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Answer:

-14x² - x + 4

Step-by-step explanation:

(-10x² + 5x - 3) - (4x² + 6x - 7)

= (-10x² + 5x - 3) - (+4x²) - (+6x) - (-7)

= (-10x² + 5x - 3) -4x² -6x +7

= -10x²-4x² +5x-6x -3+7

= -14x²  - x + 4

The area of the sector is 37.7 ft.

A sector is a region of a circle that is bounded by two radii and the arc of the circle that lies between the endpoints of those radii.

The formula for the area of a sector is given by

Where θ is the central angle in degrees, and r is the radius of the circle

Here we have

A circle has a radius of 4 ft.  

The central angle of sector formed = 270°

Using the formula, Area of sector = (θ/360°) × π r²

Area of the given sector = [ 270/360] × 3.14 × (4)²

= [0.75 ] × [50.24]

= 37.68 ft

= 37.7 ft

Therefore,

The area of the sector is 37.7 ft.

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Answer:

{2,3,5,6,8}

Step-by-step explanation:

U={1,2,3,4,5,6,7,8}

A{3,4,5,6}

B{1,4,8}

C{2,3,4,5,6}

We are to find

{A' n B} U {A' n C'}

={3,5,6,8}. U. {2}

= {2,3,5,6,8}

From the above explanation, the option B statement is not correct.

From the given options we need to identify which statement is not correct.

An obtuse angle is any angle greater than 90° and less than 180°.

From option A:

100° angle is an obtuse angle, because which is greater than 90° and less than 180°.

From option B:

175° angle is a reflex angle because it is greater than 180° and less than 360°.

From option C:

Less than 90° lies in I quadrant, more than 90° and less than 180° lies in II quadrant and more than 180° and less than 270° lies in III quadrant.

From option D:

An 85° angle is an acute angle because it is greater than 0° and less than 90°.

From the above explanation, the option B statement is not correct.

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The graph of the line y = 2x - 2 intersects the y-axis at the point (0, -2).

Given that we have the following equation

y = 2x - 2

The equation of a straight line in the standard form is y = mx + c, where m is the slope of the line, and c is the y-intercept. The y-intercept is the point at which the line intersects the y-axis.

The equation of the line is y = 2x - 2. To find where the line intersects the y-axis, we need to set x = 0 and solve for y.

So, when x = 0, we get:

y = 2(0) - 2

y = -2

Therefore, the line intersects the y-axis at the point (0, -2).

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