Make a the subject of the formula:
10a + 9b = 3c

The maximum strut load is 70.87 kN. The maximum strut load can be calculated using the following equation: Maximum strut load = 2 * unit weight * gravity * depth * sin(friction angle) * cos(friction angle)

In this case, the unit weight is 20 kN/m3, the gravity is 9.81 m/s^2, the depth is 7.5 m, and the friction angle is 36°. Plugging these values into the equation, we get the following:

Maximum strut load = 2 * 20 * 9.81 * 7.5 * sin(36°) * cos(36°) = 70.87 kN

Therefore, the maximum strut load is 70.87 kN.

The maximum strut load occurs at the first row of struts, which is installed at a depth of 0.5 m below ground surface. The strut load decreases with depth, and the maximum strut load is reached at the first row of struts.

The strut load is caused by the weight of the soil above the struts. The soil above the struts exerts a lateral force, which is resisted by the struts. The maximum strut load occurs when the lateral force is at its maximum.

The maximum strut load is an important design consideration for braced cuts. The strut load must be able to be safely carried by the struts. If the strut load is too high, the struts may buckle or fail.

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Answer:

To do this you have to multiply 3.14 times the diameter, so 14 x 3.14 = 43.96 which is the diameter you cn round it!

Step-by-step explanation:

Answer:

36 x⁸y⁶

 √2/2

Step-by-step explanation:

Factor 1296 into its prime factors

           1296 = 24 • 34 

To simplify a square root, we extract factors which are squares, i.e., factors that are raised to an even exponent.

Factors which will be extracted are :

           1296 = 24 • 34 

No factors remain inside the root !!

To complete this part of the simplification we take the squre root of the factors which are to be extracted. We do this by dividing their exponents by 2 :

           36 = 22 • 32 

At the end of this step the partly simplified SQRT looks like this:

         36 √(x¹⁶y¹²)

STEP2:Simplify the Variable part of the SQRT

Rules for simplifing variables which may be raised to a power:

   (1) variables with no exponent stay inside the radical

(2) variables raised to power 1 or (-1) stay inside the radical

   (3) variables raised to an even exponent: Half the exponent taken out, nothing remains inside the radical. examples:

      √(x⁸)=x⁴

     √(x^-6)=x^-3

 Applying these rules to our case we find out that

      SQRT(x¹⁶y¹²) = x⁸y⁶

Combine both simplifications

      sqrt (1296x¹⁶y¹²) =  36 x⁸y⁶

Simplified Root : 36 x⁸y⁶ 

number 2)

3√2/3√4=

=3√2/3×2

=3√2/6

=3√2/6 ×3/3

=1√2/2

=√2/2

Answer: 18 pieces

Step-by-step explanation:

If she took 10 pieces and then each child received 2 pieces and she has four children then

10+2+2+2+2=

10+8=

18

Answer:

554433221100

is in form

and have to divide by 11

554433221100/11

50403020100 is the answer.

Answer: 9 numbers

Step-by-step explanation:

Answer:

6.75 miles per half hour

Step-by-step explanation:

Answer:

Step-by-step explanation:

A boat traveled 27 miles in 2 hours. At this rate, how many miles will the boat travel in  1/2 hour?

in 2 hours there are 4 half hours

27 : 4 = 6.75 miles

Answer:

Its D my friend

Step-by-step explanation:

Answer:

(D) yes, because (StartFraction b Over a + c EndFraction)(a + c) = b

Step-by-step explanation:

Triangle A B C with centroid G is shown on an x and y-axis. Lines are drawn from each point through the centroid to the opposite side to form line segments A F, B D, and C E. Point A is at (0, 0), point D is at (c, 0), point C is at (2 c, 0), point B is at (2 a, 2 b), point F is at (a + c, b),and point E is at (a, b).The equation of line Line A Gis y = (StartFraction b Over a + c EndFraction)x. The midpoint of BC is (a + c, b). Does the midpoint of BC lie on Line A G? Why or why not?

(A) no, because (StartFraction b Over a + c EndFraction)b does not equal a + c

(B) no, because (StartFraction b Over a + c EndFraction)(a + c) does not equal b

(C) yes, because (StartFraction b Over a + c EndFraction)b = a + c

(D) yes, because (StartFraction b Over a + c EndFraction)(a + c) = b

The factor that does NOT control the stability of a slope is the angle of repose for intact bedrock. The angle of repose refers to the steepest angle at which a pile of loose material remains stable without sliding. It is mainly applicable to loose materials like soil and granular substances, not intact bedrock.

Bedrock stability depends on factors such as its strength, fracturing, and geological properties, rather than the angle of repose. Factors that control the stability of a slope include whether the slope is rock or soil. Rock slopes tend to be more stable than soil slopes due to the cohesive nature of intact rock.

The amount of water in the soil also affects slope stability, as excessive water can increase pore pressure and reduce the shear strength of the soil, leading to slope failure. Additionally, the orientation of fractures, cleavage, and bedding in the rock can influence slope stability by creating planes of weakness or strength.

To summarize, while the angle of repose is a significant factor in slope stability, it is not applicable to intact bedrock. The stability of a slope is influenced by the type of material (rock or soil), the presence of water, and the orientation of fractures and bedding.

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Answer:

There are no coefficients.

Step-by-step explanation:

Answer:

28716

Step-by-step explanation:

plz mark branliest

The linear approximation of f(x) = e^x at a = 1 is L(x) = e(x - 1) + e.

To find the linear approximation of f(x) = e^x at a = 1, we can use the formula:

L(x) = f(a) + f'(a) * (x - a)

where f(a) is the value of the function at a, f'(a) is the derivative of the function evaluated at a.

First, we find f(a) by substituting a = 1 into f(x):

f(1) = e^1 = e

Next, we find f'(x) by taking the derivative of f(x):

f'(x) = e^x

Then, we evaluate f'(1) to get:

f'(1) = e^1 = e

Now, we have all the information we need to find the linear approximation:

L(x) = e + e * (x - 1)

Simplifying this expression gives:

L(x) = e(x - 1) + e

Therefore, the linear approximation of f(x) = e^x at a = 1 is L(x) = e(x - 1) + e.

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a...... The limit of √x-6 as x approaches 6 is 0.

b...... lim √x-6 does not exist

a. Evaluate lim √x-6.
Answer: The limit of √x-6 as x approaches 6 is 0.
b. Explain why lim √x-6 does not exist.
Answer: lim √x-6 does not exist because the value of √x-6 is undefined for any x value less than 6. Since the limit is taken as x approaches 6, the value of √x-6 would become undefined and the limit does not exist.

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Answer:

$4.18 dollars per pound

Step-by-step explanation:

We can find the price in dollars per pound by dividing the cost by the number of pounds:

14.63/3.5 = 4.18

This means the price in dollars per pound is $4.18

The amount of interest John will get after 12 years given his savings and interest rate is 1,680 Euros

Simple interest is a type of interest rate paid only on principal. It is called by multiplying principal by interest rate by time.

Simple interest = principal × rate × time

= 14,000 × 0.01 × 12

= 1,680 Euros

In conclusion, given John's savings and interest rate, he'll earn 1,680 Euros as interest after 12 years.

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Christ spent a total amount of $ 14.50 on the shirt.

Here we use the linear equation concept to solve the problem.

Since we do not know the amount that Christ has assume that with a variable and form a linear equation using the data given.

Now solve the resultant equation for the value of the variable and find the amount spent by Christ on the shirt as given below

Here we have

Christy spent 2/5 of her money on a shirt.

She has $21.75 left

Let 'x' be the amount that Christy has

From the data,

Christy spent 2/5 of her money on a shirt.  

Amount spent by Christy = 2/5 of x = 2x/5

Remaining amount = x - 2x/5

From the data,

Chrisy is left with $ 21.75

=> x - 2x/5 = 21.75

=> 3x/5 = 21.75

=> 3x = 108.75

=> x = 36.25

Amount the that she spent 2x/5 = 2 (36.25)/5 = 14.50

Therefore,

Christ spent a total amount of $ 14.50 on the shirt.

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Answer:

The range of f(x) is  { 6 , 7 , 8 }

Step-by-step explanation:

Given a function y=f(x), the domain of f(x) is the set of values that x can take and the range of f(x) is the set of values that f gets when x is in the domain.

We have the function:

f(x)=1/2x+5

And the domain is

(2,4,6)

Compute the range by assigning each value of x:

For x=2:

f(2) = (1/2)2 + 5 = 1 + 5 = 6

For x=4:

f(2) = (1/2)4 + 5 = 2 + 5 = 7

For x=6:

f(2) = (1/2)6 + 5 = 3 + 5 = 6=8

The range of f(x) is:  { 6 , 7 , 8 }

Answer:

Rupees 39,000 are

378.63 Pound sterling

After the correct formula for a reactant in an equation has been written, The solution is balanced by adjusting the subscripts.

It is necessary to change the subscripts in order to balance an equation once the proper formula for a reactant has been written. Make sure there are the same amount of atoms of each element on the reactant and product sides of the equation in order to balance an equation. The chemical formula itself shouldn't be changed in order to achieve this balance, and it might or might not show up on the product side of the equation. However, changing the subscripts is essential. Moreover, provided that they are balanced, the formula's figures may be placed on either side of the equation.

Therefore, after the correct formula for a reactant in an equation has been written, The solution is balanced by adjusting the subscripts.

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To find out the number of grandchildren, we calculate the number of items in each basket (16 + 20 + 24 = 60), divide the total number of items by the number of items in each basket (60 ÷ 60 = 1), and conclude that Jan has 1 grandchild.

To find out how many grandchildren Jan has, we need to determine the number of baskets she can make with the given items.

1. Calculate the number of items in each basket by adding up the number of DVDs, video games, and gift cards:

16 + 20 + 24 = 60.
2. Divide the total number of items by the number of items in each basket to find the number of baskets:

60 ÷ 60 = 1.
3. Since each basket represents one grandchild, Jan has 1 grandchild.

To find out the number of grandchildren, we calculate the number of items in each basket (16 + 20 + 24 = 60), divide the total number of items by the number of items in each basket (60 ÷ 60 = 1), and conclude that Jan has 1 grandchild.

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The value of the piecewise function for f(3) is 4

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

f(x) = 2x if x < 1

f(x) = 1/2x + 5/2 if x >= 1

The function f(3) implies that we make use of the function

f(x) = 1/2x + 5/2

This is because it is valid for x >= 1

substitute the known values in the above equation, so, we have the following representation

f(3) = 1/2 * 3 + 5/2

Evaluate

f(3) = 4

Hence, the piecewise function for f(3) is 4

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Answer:

7.a) 5

7.b) 1/2

8. 1

Step-by-step explanation:

7.

a)

Read the points on the graph (0, 0) and (1, 5).

slope = (5 - 0)/(1 - 0) = 5/1 = 5

b)

read the points on the graph (0, 0) and (4, 2).

slope = (2 - 0)/(4 - 0) = 2/4 = 1/2

8.

Points (1, 4) and (5, 8)

slope = (8 - 4)/(5 - 1) = 4/4 = 1

Answer:

III (third) quadrant

Step-by-step explanation:

Answer: Choice B

Quadrant II, because the slope is positive and the y intercept is negative.

===============================================================

Explanation:

The y intercept is -6 which places the graph below the x axis when x = 0. The graph will go uphill as we move to the right (since the slope is positive), so we cut through quadrant 4 and move to quadrant 1 at some point. Going in reverse of this, we go through quadrant 3.

Only quadrant 2 is never passed through or touched at all.

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

Here's another way to see why this is. Notice that x < 0 is the case for quadrant 2 since we're to the left of the vertical y axis. If x is negative, then so is (2/3)x. Recall that negative times positive = negative.

Adding on -6 to any negative value just gets us in even more negative territory. So ultimately, y is always negative when x < 0.

But if x < 0 leads to y < 0, then we're in Q3 and not Q2. In short, x < 0 will never get us to Q2 no matter what negative x value we pick.

The graph below hopefully visually summarizes and confirms what we discussed so far.

Answer:

200+(50x) x = months

Step-by-step explanation:

the start up is 200, every month x han has to pay 50

total cost = 200+(50x)

Therefore , the solution of the given problem of ordered pair comes out to be the ordered pair (1, 1/2).

"Ordered pairs" are two separate variables that are arranged in a way that suggests a specific sequence. The coordinates for x and y in an order pair are represented, respectively, by the main and second components. The sample following uses close parentheses to indicate the ordered combination.

Here, The formulae are as follows:

=>y = -z + 2      ...(1)

=> y = -2x² + z + 1  ...(2)

Equation (1) can be substituted for equation (2) to find the value of z:

=> Z = x² + 1/2 - z + 2 = -2x² + z + 1

=> 2z = 2x² + 1

We can now enter this value of z into equation (1) and find the value of y:

=> y = -z + 2

=> y = -(x² + 1/2) + 2

=> y = -x² + 3/2

As a result, the equation system can be expressed as:

=> z = x² + 1/2

=> y = -x² + 3/2

When x=0:

=> z = 0² + 1/2 = 1/2

=> y = -0² + 3/2 = 3/2

Therefore, there is no answer for the ordered pair (0, 3/2).

When x=1:

=> z = 1² + 1/2 = 3/2

=> y = -1² + 3/2 = 1/2

The answer is the ordered pair (1, 1/2).

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The probability that Alice's number is greater than Bob's number given that Alice's number is divisible by 5 is 1/7.

To solve this problem, we first need to determine the total number of possible outcomes. Since Alice and Bob choose a number each, there are 15 options for Alice's first choice and 14 options remaining for Bob's first choice. Therefore, the total number of possible outcomes is 15 x 14.

The probability of Alice's number being greater than Bob's number given that Alice's number is divisible by 5 is then given by the ratio of the number of favorable outcomes (30) to the total number of possible outcomes (15 x 14):

Probability = favorable outcomes / total outcomes

Probability = 30 / (15 x 14)

Probability = 30 / 210

Probability = 1 / 7

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The angle in degrees south of east, is a line connecting your starting point to your final position is 144.46°.

The displacement vector represents the displaced distance along with the direction of displacement. The initial point of the displacement is represented by a tail of a vector arrow whereas, the final point is represented by the arrowhead. Assume i walk 17.5 m straight west and then 24.0 m straight north. Let vectors A and B denotes the displacement. The total displacement, R is determined by adding both vector and direction is θ. So, \( \vec R = \vec A + \vec B\)

\( \vec R = −17.5 \hat{i} + 24 \hat j\)

The magnitude of the displacement vector is denoted by,

\(| \vec R |= \sqrt{{ (- 17.5)}^{2} + {24}^{2} } = \sqrt{882.25} = 29.70 \\ \)

The angle of displacement is given by,

\(θ={tan}^{- 1} ( \frac{24}{ - 17.5}) \)

From the above diagram, the displacement is at − 54.46° , which is in the west-north direction in the compass. Let the south of east angle be φ. Now, the angle south of east is φ = 180° - 90° - θ Hence required angle is 90° + 54.46° = 144.46°.

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Complete question:

Suppose you walk 17.5 m straight west and then 24.0 m straight north. At what angle, in degrees south of east, is a line connecting your starting point to your final.

1. We can calculate the slope (m): m = 498.7

2. We have the equation of the trend line: y = 498.7x - 1009.75

3.  The forecasted sales for year 5 is approximately 1483.75.

4.  The forecasted sales for year 6 is approximately 1982.45.

To use the Linear Trend Equation for forecasting sales in year 5 and 6, we need to calculate the equation of the trend line first. The formula for a linear trend line is:

y = mx + b

Where:

y = dependent variable (sales)

x = independent variable (year)

m = slope of the line

b = y-intercept

To find the slope (m) and y-intercept (b), we can use the least squares method or the method of linear regression. However, since we only have four data points, we'll use a simplified version of the linear regression formula:

m = [(nΣxy) - (ΣxΣy)] / [(nΣx^2) - (Σx)^2]

b = (Σy - mΣx) / n

Let's calculate the values:

n = number of data points = 4

Σx = sum of years = 1 + 2 + 3 + 4 = 10

Σy = sum of sales = 230 + 235 + 239 + 243 = 947

Σxy = sum of (year * sales) = (1 * 230) + (2 * 235) + (3 * 239) + (4 * 243) = 4861

Σx^2 = sum of (year^2) = (1^2) + (2^2) + (3^2) + (4^2) = 30

Now we can calculate the slope (m):

m = [(nΣxy) - (ΣxΣy)] / [(nΣx^2) - (Σx)^2]

= [(4 * 4861) - (10 * 947)] / [(4 * 30) - (10^2)]

= [19444 - 9470] / [120 - 100]

= 9974 / 20

= 498.7

Next, let's calculate the y-intercept (b):

b = (Σy - mΣx) / n

= (947 - (498.7 * 10)) / 4

= (947 - 4987) / 4

= -4039 / 4

= -1009.75

Now we have the equation of the trend line:

y = 498.7x - 1009.75

To forecast sales in year 5, substitute x = 5 into the equation:

y = 498.7 * 5 - 1009.75

= 2493.5 - 1009.75

= 1483.75

Therefore, the forecasted sales for year 5 is approximately 1483.75.

To forecast sales in year 6, substitute x = 6 into the equation:

y = 498.7 * 6 - 1009.75

= 2992.2 - 1009.75

= 1982.45

Therefore, the forecasted sales for year 6 is approximately 1982.45.

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Answer and Step-by-step explanation:

Scale factor of 4

x, y: (3, 10)

Translate 3 units right, up 10 units.

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