the scale factor of two similar solids is 2:5. the volume of the smaller solid a is 200. which equation could you use to find the volume of the larger solid b

Using calculus,

For the parabola

.

.

Take the derivative of both sides

.

This is where the formula come from, you don't need to know where this came from.

The equation of the line

.

In this problem, we know that the coefficient of y is equal to 4p

So

.

.

.

.

.

For proof, let's graph this function

.

Now let's plug in the knowns to find the tangent line

If my work does not pop up, the answer is y=-x-3

The required equation of the tangent to the parabola at the given point y = -x - 3.

Functions are the relationship between sets of values. e g y=f(x), for every value of x there is its exists in a set of y. x is the independent variable while Y is the dependent variable.

Here,
Given expression,
x² = 12y

Comparing the above expression with the given expression,
P = 3

Now, we have p = 3 and (x₀, y₀) = (-6, 3)

So,
The equation of the tangent is given as,
y = -6/(2×3)x - 3
y = -x - 3

Thus, the required equation of the tangent to the parabola at the given point y = -x - 3.

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It is possible to choose a and b such that the value of function(x) at any given point is equal to the limit of f(x) as x approaches any value. This guarantees that f is continuous throughout.

A function's limit as x approaches any value must match the value of f(x) at that moment in order for the function to be continuous everywhere. In order to ensure that this need is satisfied, the values of a and b that make up f(x), whether it be a linear equation, polynomial, or another sort of equation, must be chosen. Since the behaviour of the function varies smoothly as x approaches any value, this ensures that the function is continuous throughout. In other words, a and b values must be selected in a way that the function is continuous, i.e., defined and devoid of breaks or discontinuities.

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The complete question is

Find the values of a and b that make f continuous everywhere that f is continuous throughout.

Answer:

Step-by-step explanation:

One quarter = 1/4

1/4 of a number is 6.

We have to find that number by taking

6 times 4 = 24

So, we know that number is 24

What is one-third of the number?

1/3 of 24 = 8

So, the answer is 8.

The old will Mr Lim be in 6 years time is 46 years old.

To make solving this problem easier, we need to consider the ages of Mr Lim and his son. For example by multiplying the number x.

Let:

Mr Lim's age = a

His son's age = b

So that,

The ratio of ages in the current year:

Mr Lim's age to his son's age = 5x : 2x

a : b = 5x : 2x

The ratio of ages in the four years ago:

Mr Lim's age to his son's age = 3x : x

(a - 4) : (b - 4) = 3x : x

[tex]\frac{a-4}{b -4} =\frac{3x}{x}[/tex]

[tex]\frac{5x-4}{2x -4} =\frac{3x}{x}[/tex]

[tex]\frac{5x-4}{2x -4} =\frac{3}{1}[/tex]

5x - 4 = 6x - 12

5x - 6x = -12 + 4

-x = -8

x = 8

So that we know the age of Pak Lim's and the age of his son's this year.

Mr Lim's age = 5x

                     = 5 × 8

                     = 40 years old

His son's age = 2x

                     = 2 × 8

                     = 16 years old

After that, we find Mr Lim's age 6 years from now by adding 6 years to this year's age.

Mr Lim's age be in 6 years time = 40 + 6

                                                    = 46 years old

So, the old will Mr Lim be in 6 years time is 46 years old.

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The sample should be milled to a radius that is approximately 7.19 times its original radius in order to increase its work function by 2%.

The work function of a material is related to its surface area, and milling a sample into smaller nano-spheres increases its surface area. The increase in work function can be approximated by the following equation:

ΔW = kTln(A/A₀)

where ΔW is the change in work function, k is Boltzmann's constant, T is the temperature in Kelvin, A is the new surface area of the milled sample, and A₀ is the original surface area of the sample.

To find the size to which the sample should be milled to increase its work function by 2%, we need to rearrange the equation to isolate the new surface area:

A/A₀ = e^(ΔW/kT)

Plugging in the known values, we get:

A/A₀ = e^(0.02 * 5.1 eV / (8.62 * 10⁻⁵ eV/K * 300 K))

= 51.64

The new surface area is 5064% larger than the original surface area.

Since the sample is being milled into nano-spheres, the new surface area is proportional to the square of the radius. Let's call the original radius of the sample "r₀". Then the new radius is:

r = √(A/A₀) * r₀ = √(51.64) * r₀ = 7.19 * r₀

--The question is incomplete, answering to the question below--

"g a gold (au) macro scale sample has a work function of 5.1 ev. to what size should the sample be milled to increase its work function by 2 %? assume that the sample is milled into nano-spheres and give the size in terms of radius. What is the relation between the new radium and original radius?"

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Answer:

[tex]x = \frac{5(6 + y)}{6} [/tex]

Step-by-step explanation:

[tex]1. \: 6x = 30 + 5y \\ 2. \: x = \frac{30 + 5y}{6} \\ 3. \: x = \frac{5(6 + y)}{6} [/tex]

There's your answer

The right answer is option A, which reads "four times one-third" multiplied by the number of one-third cup servings in four cups.

You can multiply, reduce, add, or take this away in mathematics. An expression is put together as follows: Verb, numeric value, and math operator A mathematical formulation is composed of numbers, variables, and procedures (such as addition, subtraction, multiplication or division etc.) Opposing phrases and phrases is possible. An exponential function is any mathematical declaration that has variables, integers, or an mathematical operation. As an instance, the phrase 4m + 5 consists of both the terms 4m and 5, as well as the supplied equation's variable m, each of which is divided by the mathematical sign +.

given

the expression = "  number of one-third cup servings in 4 cups "

= four times one-third

= 4*1/3

The right answer is option A, which reads "four times one-third" multiplied by the number of one-third cup servings in four cups.

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Answer:

The grandfather is 72 years old and the granddaughter is 8 years old now.

Step-by-step explanation:

To calculate this, first calculate the grandfather's age in 8 years:

72 + 8 = 80.

Then, use the given information to calculate the granddaughter's age in 8 years: 8 + 8 = 16.

Finally, use the given information to calculate the grandfather's age now: 5 x 16 = 80, so 80/5 = 16, and 16 x 9 = 72.

The long will it take him to reach his goal is 48w.

To make it easier to solve the problem above, we change the sentence into a mathematical sentence.

Steven goal weight is 195 pounds. He currently weighs 339 pounds.

So that we know the amount of weight reduced:

= 339 - 195

= 144 pounds

He plans to lose three pounds each week. The long will it take him to reach his goal:

= 144 : 3

= 48 weeks

= 48w

So, the long will it take him to reach his goal is 48w.

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Answer:

If csc = 29/21, then the reciprocal of this is equal to the sine of the angle. So,

sin = 21/29.

Since cosine is less than 0, then the angle must be in the second or third quadrant, which means that the sine of the angle must be positive. So,

sin = 21/29, and cos = -√(1 - sin^2) = -√(1 - (21/29)^2)

Next, we can find the tangent by taking the ratio of sine to cosine:

tan = sin / cos = 21/29 / -√(1 - (21/29)^2) = -21/√(841 - 441)

Finally, we can find the cotangent by taking the reciprocal of the tangent:

cot = 1 / tan = -√(841 - 441) / 21

So, the remaining trigonometric functions are:

sin = 21/29

cos = -√(1 - (21/29)^2)

tan = -21/√(841 - 441)

cot = -√(841 - 441) / 21

Answer & Explanation:

sin Θ = opp/hyp

cos Θ = adj/hyp

tan Θ = opp/adj

csc Θ = hyp/opp

sec Θ = hyp/adj

cot Θ = adj/opp

1.

sin Θ = opp/hyp = (8√2)/18 = (4√2)/9

cos Θ = adj/hyp = 14/18 = 7/9

tan Θ = opp/adj = (8√2)/14 =  (4√2)/7

csc Θ = hyp/opp = 18/(8√2) = (9√2)/(4√2√2) = (9√2)/8

sec Θ = hyp/adj = 18/14 = 9/7

cot Θ = adj/opp = 14/(8√2) = (7√2)/(4√2√2) = (7√2)/8

The length is the unknown side increases while keeping the known side lengths fixed, the measurement of angle Z will increase. So, the triangle will not fit the given conditions anymore.

The properties of the triangle are: The sum of all the angles of a triangle (of all types) is equal to 180°. The sum of the length of the two sides of a triangle is greater than the length of the third side. In the same way, the difference between the two sides of a triangle is less than the length of the third side.

Given,  two sides and the angle opposite one of the sides. Under Sides, enter 9 for a and 6 for b. Under Angles, enter 30 for B.

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Complete question:

Depending on a given set of conditions and the properties of triangles, any of these four outcomes is possible when constructing triangles:

No triangles fit the condition.

One unique triangle fits the condition.

Two triangles fit the condition.

Infinitely many triangles fit the condition.

Complete the steps below to find the number of triangles that can be constructed based on the following conditions: one side measures 7 centimeters, another side measures 9 centimeters, and the angle between them measures 74°.

Part A

What does the dotted line in the diagram represent?

Part B

Now think about changing the triangle. What happens to angle Z if the unknown side length increases while keeping the known side lengths (XZ and ZY) the same? Will the triangle still fit the given conditions?

Part C

What happens to angle Z if the unknown side length decreases while keeping the known side lengths (XZ and YZ) the same? Will the triangle still fit the given conditions?

Part D

Based on your conclusions in parts B and C, can the length of the unknown side be changed in any way without changing the given conditions for the triangle?

Part E

You know the given conditions for the triangle are fixed. You also know the unknown side length is fixed. What does this tell you about the two angles adjacent to the unknown side?

Part F

From your conclusions in part E, how many triangles can be constructed based on the given conditions?

art G

Let c be the unknown side of the triangle. Use this triangle calculator to solve for c. Under Sides, enter 7 for side a and 9 for side b. Under Angles, enter 74 for angle C. Click Calculate once you have entered the information. What is the length of side c?

Part H

Now try to construct a triangle using a different set of measurements. This time, you’ll enter three angle measurements. Return to the Calculator tab, and click the Clear button to begin a new calculation.

Under Angles, enter 45 for A, 40 for B, and 95 for C. Then click Calculate. What happened? What message did the tool deliver? Explain the message in terms of the properties of a triangle and the given angles.

Part I

Click Clear in the tool to begin a new calculation. This time, you’ll check for valid triangles given two sides and the angle opposite one of the sides.

Under Sides, enter 9 for a and 6 for b. Under Angles, enter 30 for B. Then click Calculate. What happened? What message did the tool deliver? Click “Show other solution” in the tool and explain the message in terms of the angle measurements and the given information.

Answer:

10/6 or 1 4/6

Step-by-step explanation:

Just add the numerators together 10/6. If you need a simplified version it would be 1 4/6.

Step-by-step explanation:

Since 4104 students are employed sophomores, juniors, or seniors, the total number of unemployed students is 11,989 - 4104 = 7885.

And since 745 students are employed freshman, the number of unemployed freshman is 7885 - 745 = 7140.

So, the total number of freshman is 745 + 7140 = 7885.

The Venn diagram would look like this:

[ Freshmen ] [ Sophomores, Juniors, Seniors ]

[ 7885 ] __________ [ 4104 ]

| 745 |

__________

[ 7140 ]

So, there are 7885 freshman.

Answer: 75.6, 14.4

Step-by-step explanation:

Note 2 angles are complementary if they adds up to 90 degrees. Lets set x to be the first angle.

x - (x - 61.2) = 90

Then we can know:

2x = 90 + 61.2;

2x = 151.2;

x = 75.6

Now we know the first angle is 75.6, we know the second angle is 75.6 - 61.2 = 14.4. Hope you find this helpful!

By evaluating a proportional relation, we can see that if 10 fiction books are sold, then 13 non-fiction books are sold.

Here we know that 3 fiction books are sold for every 4 non-fiction books sold.

Then if x fiction books are sold, the number of non-fiction books sold are given by the proportional relation:

y = (4/3)*x

Here we know that 10 fiction books are sold, so x = 10, replacing that we will get:

y = (4/3)*10 = 40/3 = 13.33

So 13 non-fiction books are sold.

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Answer: 200 dollars more

Step-by-step explanation: I did 30% of 500 which is 150 that Noel has.

70% of 500 which is 350. 350-150 is 200

Frank has saved 200$ more than Noel

Answer: 200 dollars

The first step that we should do is divide 500 into 10 separate parts. Each part is 10 percent of the price. 500 divided by 10 is 50.

This means that Frank saved 50 x 7 and Noel saved 50 x 3.

50 x 7 is 350 and 50 x 3 is 150.

Frank saved 350 , while Noel saved 150.To check if we are correct we can add 350 and 150, which is 500 that brings us back to our original answer. Next we must subtract Franks total from Noel to figure out the difference.

350-150 is 200.

This means that Frank saved 200 more dollars than Noel.

I hope this helped & Good Luck <3 !!!

Answer:

Step-by-step explanation:

The factored form of a polynomial function with roots r1 and r2 can be found by multiplying two linear factors (x - r1) and (x - r2).

Here are the steps to find the factored form of the polynomial function with roots 3i and 2:

Write the first linear factor: (x - 3i)

Write the second linear factor: (x - 2)

Multiply the two linear factors: (x - 3i)(x - 2)

Expand the product to find the polynomial function:

x^2 - (3i + 2)x + (3i * 2) = x^2 - 2x - 6i

And there you have it, the factored form of the polynomial function with roots 3i and 2 is x^2 - 2x - 6i.

Answer:

Step-by-step explanation:

i have no clue to be honest

There is only one point missing on the scatter plot graph.

And the point is (10, 2.6).

Coordinates are a collection of numbers that aid in displaying a point's precise location on the coordinate plane.

The data for the gasoline purchases are given in the table.

From the diagram:

The missing point on the scatter plot graph is,

(10, 2.6)

Hence, the point is (10, 2.6).

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In general, the employees at Store 1 got more sleep, with an average of 8.5 hours of sleep per employee, compared to Store 2's average of 7.5 hours.

The dot plots for the two stores show that Store 1 had employees who got between 5 and 10 hours of sleep, whereas Store 2 had employees who got between 4 and 8 hours of sleep. The median for Store 1 was 8.5 hours of sleep, and the median for Store 2 was 7.5 hours of sleep. This indicates that, in general, the employees at Store 1 got more sleep than the employees at Store 2. The dot plots also show that there were more employees at Store 1 with 8 hours of sleep than Store 2, and fewer employees at Store 1 with 6 hours of sleep than Store 2. This suggests that Store 1 had more employees getting 8 hours of sleep, and fewer employees getting 6 hours of sleep, than Store 2. This can be further seen by the fact that the average amount of sleep for employees at Store 1 was 8.5 hours, while the average amount of sleep for employees at Store 2 was 7.5 hours. Therefore, in general, the employees at Store 1 got more sleep than the employees at Store 2, with an average of 8.5 hours of sleep per employee, compared to Store 2's average of 7.5 hours.

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The complete question is

The following dot plots show the number of hours of sleep employees got before a major sale at two stores. Each dot represents a different employee. Complete the comparison of the typical hours of sleep. In general, the employees at got more sleep, with of sleep per employee compared to Store 2's.

In a histogram, the width of the bars represents the range of values that fall into each specific category or bin. The spacing between the bars has no meaning in terms of the data being represented.

The ordering of the bars is based on the range of values within each bin, with the bars typically ordered from left to right in ascending order of value.

This is different from a bar graph, where the width and spacing of the bars can have meaning in terms of the comparison of the values being represented. For example, if the width of the bars in a bar graph represents the value of a data point, then a wider bar would indicate a higher value.

The spacing between the bars in a bar graph can also be used to show the relative difference between values. In a bar graph, the ordering of the bars may or may not have meaning, depending on the specific context and the purpose of the graph.

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Answer: T = 0.25x + 50, where x represents the number of chirps in 1 minute.

Step-by-step explanation:

Answer:

6W + W = 770
==> 7W = 770

W = 110 and L = 660 in case you are looking for the solution

Step-by-step explanation:

Let L -= length and W the width of the rectangular field

six times as long as it is wide translates to:
L = 6W

Perimeter of field = 2(L + W)

Given perimeter = 770 feet
2(L + W) = 770
L + W = 770/2 = 385

Since L = 6W, substitute for L in the above equation:
6W + W = 770

7W = 770

W = 770/7 = 110 feet

L = 6W = 6(110) = 660 feet

the width = 55 feet and the length = 330 feet

so basically we take the width as x and the length as 6x then since the perimeter of a rectangle = 2*width + 2*length we will form the equation 6x + 6x + x + x = 770
then we'll solve this equation
14x = 770
x = 55
then multiply x by 6 to get the length which is 330

Answer:

Step-by-step explanation:

The monthly payment on a loan and the total interest that will be paid during the term of the loan can be found using an amortization formula.

Here are the steps to find the monthly payment and total interest for the given loan conditions:

Convert the interest rate to a decimal: 7.5% = 0.075

Divide the interest rate by the number of periods (months) per year: 0.075 / 12 = 0.00625

Find the number of payment periods: 8 years * 12 months/year = 96

Calculate the monthly payment using the amortization formula:

Payment = Loan Amount * (Interest Rate / (1 - (1 + Interest Rate)^(-Number of Payments)))

Payment = $6,200 * (0.00625 / (1 - (1 + 0.00625)^(-96)))

Payment = $79.88

So, the monthly payment on the loan is $79.88.

Calculate the total interest paid over the term of the loan:

Total Interest = (Monthly Payment * Number of Payments) - Loan Amount

Total Interest = ($79.88 * 96) - $6,200

Total Interest = $7,538.88

So, the total interest that will be paid during the term of the loan is $7,538.88.

Answer:

The equation that makes the most sense to solve with the Zero Product Property is x^2+9x+6=0.

Step-by-step explanation:

The required simplified expression of the given expression is [tex]{\frac{2}{x^5y^4}}$[/tex].

The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.

Here
When simplifying the expression 4x²y⁴/2x⁷y⁸, we can divide the numerator and denominator by the greatest common factor of each, which is x²y⁴. Doing so gives us:

[tex]$\frac{4x^2y^4}{2x^7y^8} = \frac{4}{2x^5y^4} = \frac{2}{x^5y^4} = \boxed{\frac{2}{x^5y^4}}$[/tex]

Thus, the required simplified expression of the given expression is [tex]{\frac{2}{x^5y^4}}$[/tex].

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Answer:

[tex]5b + 7p = 79[/tex]

[tex]7b + 5p = 77[/tex]

Answer:12/5

Step-by-step explanation:

tan(x)=opposite/adjacent

tan(x)=12/5

Answer:

2.4

Step-by-step explanation:

This is a right-angled triangle:

where:
Side XY = hypotenuse

              = 13 units

With respect to Angle X:

Side YZ = opposite side

             = 12 units

Side XZ = adjacent side

              = 5 units

Trigonometric function:

Tan∅= [tex]\frac{opposite}{adjacent}[/tex]

 ∴TanX = [tex]\frac{SideYZ}{SideXZ}[/tex]

             = [tex]\frac{12}{5}[/tex]

             = 2.4