Write the equation of the line that passes through the points (-2,-8) and (9,8).
Put your answer in fully simplified point-slope form, unless it is a vertical or
horizontal line.

The weight of the truck,  When a loaded truck pulls onto it, the boat sinks an additional 5.00cm into the river is  11,788 N.

To discover the weight of the truck, we ought to utilize the concept of buoyancy.

When the truck pulls onto the vessel, it uproots a sum of water that breaks even with its claimed weight. The weight of this uprooted water makes an upward buoyant constraint on the pontoon.

The watercraft sinks an extra 5.00 cm, which suggests that the buoyant constraint breaks even with the weight of the truck furthermore the weight of the uprooted water, and this adds up to the weight causing the boat to sink assist.

Let's accept that the thickness of water is 1000 kg/m³ (this can be ordinary esteem for new water). The volume of water uprooted by the pontoon is rise to its length times its width times the profundity it sinks into the water:

V = (6.00 m)(4.00 m)(0.05 m) = 1.20 m³

The weight of this uprooted water is:

Wwater = Vρg = (1.20 m³)(1000 kg/m³)(9.81 m/s²) ≈ 11,788 N

where ρ is the thickness of water and g is the speeding up due to gravity.

Since the buoyant drive is broken even with the weight of the truck furthermore the weight of the uprooted water, we have:

Wtruck + Wwater = Fbuoyant

where Wtruck is the weight of the truck and Fbuoyant is the buoyant drive. Ready to improve this condition to illuminate for the weight of the truck:

Wtruck = Fbuoyant - WWater

The buoyant drive is broken even with the weight of the water uprooted by the watercraft, which we calculated prior to being around 11,788 N. In this manner:

Wtruck = 11,788 N - 0

 Wtruck ≈ 11,788 N

So, the weight of the truck is around 11,788 N. 

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The full question is

A small ferryboat is 4.00m wide and 6.00m long. When a loaded truck pulls onto it, the boat sinks an additional 5.00cm into the river. What is the weight of the truck?

Answer:

Solution

verified

Verified by Toppr

Correct option is A)

We first calculate slant height L of the pyramid with base s=10 cm and height 12 cm:

L 2 =H 2 +( 2s )

2

=12

2

+(

2

10

)

2

=12

2

+5

2

=144+25=169

⇒L=

169

=13

The perimeter of the base is P=4s, since it is a square, therefore,

P=4×10=40 cm

The general formula for the lateral surface area of a regular pyramid is LSA=

2

1

Pl where P represents the perimeter of the base and l is the slant height.

Since the perimeter of the pyramid is P=40 cm and the slant height is l=13 cm, therefore, the lateral surface area is:

LSA=

2

1

Pl=

2

1

×40×13=260 cm

2

Now, the area of the base B=s

2

with s=10 cm is:

B=s

2

=10

2

=100 cm

2

The general formula for the total surface area of a regular pyramid is TSA=

2

1

Pl+B where P represents the perimeter of the base, l is the slant height and B is the area of the base.

Since LSA=

2

1

Pl=260 cm

2

and area of the base is B=100 cm

2

, therefore, the total surface area is:

TSA=

2

1

Pl+B=260+100=360 cm

2

Hence, total surface area of the pyramid is 360 cm

2

.

Answer:

1/2

Step-by-step explanation:

When you find the sine of an angle, it is the opposite side / hypotenuse. This means that the hypotenuse of this triangle is 2 and the side opposite to 60° is √3. This means that the side adjacent to 60° is 1 (Pythagorean Theorem). When you find the cosine of an angle, it is the adjacent side / hypotenuse, which in this case will be 1 / 2. Hope this helps!

Answer:

1/2.

Step-by-step explanation:

Sine = opposite side / hypotenuse.

The side opposite 60 degrees has length√3 and the hypotenuse = 2.

By Pythagoras the side adjacent to the angle 60 = √( 2^2 - 3)

= 1 unit.

So cos 60 = adjacent / hypotenuse = 1/2.

Answer:

the first number is 200

the second number is 10

Step-by-step explanation:

Answer:

its e

Step-by-step explanation:

because e is is referring to savvy

The solution to the following equations are:

x + 8 = 6

subtract 8 from both sides

x = 6 - 8

x = -2

x - 1 = -4

Add 1 to both sides

x = -4 + 1

x = -3

10 + x = 5

subtract 10 from both sides

x = 5 - 10

x = -5

x + 4 = -14

subtract 4 from both sides

x = -14 - 4

x = -18

x - 3 = -9

Add 3 to both sides

x = -9 + 3

x = -6

-4 + x = -8

Add 4 to both sides

x = -8 + 4

x = -4

-5 = 10x

divide both sides by 10

x = -5/10

x = -0.5

-4x = -60

divide both sides by -4

x = -60/-4

x = 15

3x = -24

divide both sides by 3

x = -24/3

x = -8

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The decay factor of the equation given in the task content is; 0.87.

According to the task content; the equation given is; y = 453(0.87)^4.

By comparison with exponential decay functions, it follows that the decay factor from the equation given is; 0.87 which insinuates that the factor of change after each decay is 0.87.

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Answer:

Radical expressions are utilized in financial industries to calculate formulas for depreciation, home inflation and interest. Electrical engineers also use radical expressions for measurements and calculations. Biologists compare animal surface areas with radical exponents for size comparisons in scientific research

a. Asking for the "slope of a secant line" is the same as asking for an average rate of change. The secant line represents the average rate of change between two points on a curve or function.

b. Asking for the "slope of a tangent line" is the same as asking for an instantaneous rate of change. The tangent line represents the rate of change of a function at a specific point.

c. Asking for the "value of the derivative f'(a)" is not the same as asking for an average rate of change or an instantaneous rate of change.

d. Asking for the "value of the derivative f'(a)" is the same as asking for the slope of a tangent line.

a.When we ask for the slope of a secant line, we are interested in the average rate of change of a function over an interval. The secant line connects two points on the curve, and its slope represents the average rate at which the function's output changes with respect to the input over that interval.

b. When we ask for the slope of a tangent line, we are interested in the instantaneous rate of change of a function at a specific point. The tangent line touches the curve at that point, and its slope represents the rate at which the function's output changes with respect to the input at that precise point.

c. When we ask for the value of the derivative f'(a), we are specifically interested in the rate of change of the function f at a specific point a. The derivative represents the instantaneous rate of change of the function at that point, but it is not the same as asking for an average rate of change over an interval or a tangent line's slope.

d.When we ask for the value of the derivative f'(a), we are essentially asking for the slope of the tangent line to the curve of the function at the point a. The derivative provides the slope of the tangent line, representing the instantaneous rate of change of the function at that point.

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Cash paid for insurance during 2014 was $15,100.The following formula can be used to determine the cash spent on insurance in 2014:

Insurance expense in 2014 minus an increase in prepaid insurance = Cash paid for insurance.

The difference between the prepaid insurance balance at December 31, 2014, and December 31, 2013, can be used to compute the rise in prepaid insurance:

Prepaid insurance at December 31, 2014 minus Prepaid insurance at December 31, 2013 equals $1,500 minus $2,400, or -$900.

The fact that the prepaid insurance balance fell between 2013 and 2014 indicates that the business used more insurance coverage than it had purchased for the year. As a result, the 2014 insurance premiums paid in cash are:

Insurance expense for 2014 minus the increase in prepaid insurance is $14,200 - (-$900) = $15,100 in cash paid for insurance.

The correct response is (C) $15,100.

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In statistics the sampling method is collecting data based on sample of people who represent a population, whereas the census method involves studying each and every member of the population.

What is statistics?

The gathering, characterization, analysis, and drawing of inferences from quantitative data are all tasks that fall under the purview of statistics, a subfield of applied mathematics. Probability theory, linear algebra, and differential and integral calculus play major roles in the mathematical theories underlying statistics.

The differences between census and sampling method is -

The investigator gathers data using the census method, which asks questions about every component of the population.

The investigator gathers data using the sampling method by selecting a sample of the objects that represent the entire population.

The Census Method of Collecting Data is appropriate when the area under inquiry is rather small. The sampling method is preferred when the investigation region is large.

The Census Method requires more time to gather data. The sampling method requires less time to gather data.

Generally speaking, the Census Method is more accurate than the Sampling Method. This accuracy can be attributed to the Census Method's inclusion of a study of every component of the population. The sampling approach has a lower level of accuracy because it examines a smaller sample of the population. However, since there are fewer elements in the sampling method, errors are simple to find and eliminate. Consequently, if that's the case, the sampling method gives more accuracy than census method.

Therefore, the differences for census and sampling method are pointed out.

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What is the difference between census method and sampling method in statistics?

Answer:

-7/1

Step-by-step explanation:

Answer:

A. n^18

Step-by-step explanation:

√(n^36)

n^(36 × 1/2)

n^(18)

Answer:

\(n^1^8\)

Step-by-step explanation:

So writing \(\sqrt{n^3^6}\) in a the other form I’d easy.

The 36 in the other form is the numerator and the 2square outside the radical is the denominator,

And if the n inside the radical is just a normal variable or digit.

So 36/2 is 18 so the answer is n^18.

Answer:

norway

Step-by-step explanation:

Answer:

the measure of angle 1 is 130 and the measure of angle 7 is 50.

Step-by-step explanation:

4x-30=2x+50

x=40

plug x into angle 1

plug x into angle 5

angle seven is supplementary to 5

the measure of angle 5 is 130.

180-130=50

Angle 7= 50

The correct answer is f°\(f^(-1)\)(x) = x, indicating that the composition of the function f with its inverse function \(f^(-1)\)results in the identity function.

To find the inverse function \(f^(-1)\)(x), we swap the roles of x and y in the equation f(x) = x/(x-2) and solve for y.

Given f(x) = x/(x-2), let's solve for x in terms of y:

y = x/(x-2)

Multiply both sides by (x-2):

y(x-2) = x

Distribute on the left side:

yx - 2y = x

Move all terms involving x to one side:

yx - x = 2y

Factor out x on the left side:

x(y - 1) = 2y

Divide both sides by (y - 1):

x = 2y / (y - 1)

Therefore, the inverse function f^(-1)(x) is:

\(f^(-1)(x) = 2x / (x - 1)\)

Now, let's find f°f^(-1)(x) by composing the functions f and \(f^(-1):\)

\(f^(-1)(x) = 2x / (x - 1)\)

Substituting \(f^(-1)\)(x) into f(x), we have:

\(f(f^(-1)(x)) = f(2x / (x - 1))\)

Replacing x in f(x) with 2x / (x - 1), we get:

\(f(f^(-1)(x)) = (2x / (x - 1)) / ((2x / (x - 1)) - 2)\)

Simplifying further:

\(f(f^(-1)(x)) = (2x / (x - 1)) / ((2x - 2(x - 1)) / (x - 1))\)

\(f(f^(-1)(x)) = (2x / (x - 1)) / (2(x - 1) / (x - 1))\)

\(f(f^(-1)(x)) = 2x / 2\)

\(f(f^(-1)(x)) = x\)

Therefore, f°f^(-1)(x) = x, indicating that the composition of the function f with its inverse function f^(-1) results in the identity function.

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The number of miles they would have driven if they hadn't taken a shortcut is 31.3 miles

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

Distance travelled = 35.2 miles

Shortcut = 3.9 miles

Using the above as a guide, we have the following:

Distance after taking shortcut = Distance travelled - Shortcut

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

Distance after taking shortcut = 35.2 - 3.9

Evaluate

Distance after taking shortcut = 31.3

Hence. the distance after taking shortcut is 31.3 miles

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Answer:

A sample is a subset of the population.

Answer:

3/7 × 28 = 12 apples are rotten

Hope it helps

Answer:

12

Step-by-step explanation:

3/7*28/1=12

Las frecuencias son magnitudes que nos permiten representar valores de un fenómeno específico.

La frecuencia rotativa es un término que se refiere a la cantidad de ciclos completados en un período de tiempo por un elemento que gira en su propio eje. La magnitud con la que se puede asociar la frecuencia rotativa depende de distintos factores, no obstante los más comunes suelen ser: segundos, minutos y horas. Algunos ejemplos de frecuencia rotativa es:

La rueda de mi bicicleta tiene una frecuencia rotativa de 50 giros por minuto.

La frecuencia porcentual es un término que se refiere a la cantidad de elementos que tienen características similares por lo que pueden clasificarse en una categoría o clase similar. Por ejemplo, la frecuencia porcentual de personas con uniforme en mi escuela es del 90%.

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Triangulation is the method of finding the location of an object based on the measurements made from the two other locations. The above statement is true statement.

Triangulation is the division of a face or plane polygon into a series of triangles, usually with the limitation that each side of a triangle is fully shared by two adjacent triangles. In geometry, triangulation is the division of planar objects into triangles, or more broadly, the division of high-dimensional geometric objects into simplifications. Triangulation of a 3D volume involves subdivision into packed tetrahedra that directly measure distances to points. It is a method for finding the location of the object.

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Answer:

20, the answer is 20 members

Answer:

3) On a test of 25 questions, a student 4) Alisa earned $30 raking leaves. She ... 80% horror. 6Sn-sdo 1800 ... How many tickets were a) What percent of her weight did sold? ... b) Atlantic Auditorium has 850 seats. b) At the next visit, we were happy to see ... members of the art club voted in the more students joined. election.

Step-by-step explanation:

Answer:

Step-by-step explanation:

Raul's steps are incorrect. The correct steps to evaluate the expression 3-(-5)-7 would be:

3-(-5)-7 = 3+5-7 (Using the order of operations, first we have to evaluate the parentheses, since the negation sign is inside it)

= 8-7 (After evaluating the parentheses)

= 1 (Subtracting 7 from 8)

So, the expression 3-(-5)-7 = 1

Answer:

cars= 32 , trucks= 55

Step-by-step explanation:

add all the cars up then the trucks

Call me your daddy right now

Answer:

Correct answer should be x= -6

Step-by-step explanation:

prove me wrong

Answer:

12.8d - 40

Step-by-step explanation:

Distributive property: Multiply the outside number with each of the numbers in the paranthesis.

FOLLOW - PEMDAS

Another way:

(4 • 3.2d) - (4 • 10)

(12.8d) - (40)

12.8d - 40

Answer:

43%

Step-by-step explanation:

There are 39 girls. 21 of them like biology. 11 out of 34 who like chemistry are girls.

No. of girls who prefer biology = 21

There are (100-39) boys. 16 of them like physics. (34-11) of them like chemistry.

No. of boys who prefer biology = 100-39-16-34+11

                                                    = 22

Percentage of students who prefer biology = \(\frac{21+22}{100}\) × 100%

                                                                        = \(\frac{43}{100}\) × 100%

                                                                        = 43%

Answer:

The two bowling alleys cost the same when there are 10 people in the group.

Step-by-step explanation:

Bustlin' Bowling first:

$35 base price and then $2 for each person. You can model that with b = 35 + 2x where b is the price and x is the guest number.

Grand Entertainment next:

$20 base price and then $3.50 for each person. You can model that with g = 20 + 3.5x where g is the price and x is the guest number.

So the question asks for the number of people (or what's x) that makes the cost of both bowling places equal.

In variables, it's asking when b = g, what is x?

Starting with b = g, we can replace those with the actual equations. If b = 35 + 2x and g = 20 + 3.5x, then b = g is the same as 35 + 2x = 20 + 3.5x.

I think you know how to solve that (because the trickiest part is usually translating the words into a solvable equation) but in case you don't, here's how:

35 + 2x = 20 + 3.5x

Subtract 2x from both sides.

35 = 20 + 3.5x - 2x

35 = 20 + 1.5x

Subtract 20 from both sides.

35 - 20 = 1.5x

15 = 1.5x

Divide both sides by 1.5.

15/1.5 = 1.5x/1.5

10 = x

Sooo, the answer is 10 people.

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Given parametric equations are x(t) = Ln(t) and y(t) = (Ln(t))^2. We have to graph the given parametric equations using ln restrictions without a calculator or desmos.

Here, we are going to find the value of t, which helps us to graph the given parametric equation using ln restrictions.Step-by-step explanation to find the value of t are:We have,

x(t) = Ln(t) ⇒ t = e^x(t) ....(1)y(t) = (Ln(t))^2⇒ t = e^(y(t)/2) ...

.(2)From (1) and (2),

we get e^x(t) = e^(y(t)/2)e^(2x(t)) = y(t) ...

(*)We know that the domain of ln x is (0, ∞). Let's determine the range of x(t) and y(t):From equation (1), if t → 0, then x(t) → - ∞From equation (1), if t → ∞, then x(t) → ∞From equation (2), if t → 0, then y(t) → 0From equation (2), if t → ∞, then y(t) → ∞Now,

we can graph the given parametric equations using the following steps: Assign values to t such as

t = 0.1, 0.2, 0.3, 0.4, 0.5, 0.6, .7, 0.8, 0.9, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 20, 30, 40, 50, 60, 70, 80, 90, 100

Step 2: Calculate x(t) and y(t) corresponding to t values.Step 3: Plot the points obtained in step 2.Step 4: Join all the points obtained in step 3 using a smooth curve.The graph of the given parametric equation is shown below.

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