i need help oi would help me alot sorry i am putting it like this brainly is weird

I Need Help Oi Would Help Me Alot Sorry I Am Putting It Like This Brainly Is Weird

Answers

Answer 1

Answer:

ok so i dont care lol

Step-by-step explanation:

Answer 2

Answer:

The first one (1/6 divided by 1/2)

Step-by-step explanation:

Since Alice is splitting 1/6 of the box of cereal into 1/2, you need to divide.


Related Questions

Use the diagram below. If m∠3 = 60°, find m∠4.

Use the diagram below. If m3 = 60, find m4.

Answers

The answer is 44 degree.

Answer:

120

Step-by-step explanation:

Can the sides of a triangle have lengths 2, 2, and 6?

Answers

Answer:

Yes if it is an Isosceles Triangle

Step-by-step explanation:

write an equation for a parabola with a vertex of (-1, -10) and a focus of (-1, -9)

Answers

Answer:

(x + 1)² = 4(y + 10)

Step-by-step explanation:

Equation of parabola:

(x - h)² = 4a(y - k)

with vertex(h, k) and focus (h, k + a)

vertex(h, k) = (-1, -10)

h = -1 and k = -10

focus (h, k + a) = (-1, -9)

⇒ k + a = -9

⇒ -10 + a = -9

⇒ a = 10 - 9

a = 1

Equation of parabola:

(x - h)² = 4a(y - k):

(x - (-1))² = 4(1)(y - (-1))

= (x + 1)² = 4(y + 10)


Know how to read a list of data and answer questions like how
many more did…, what percentage of did…., what percentage of
responses did….., what proportion of customers is …

Answers

Reading a list of data and answering questions related to comparisons, percentages, and proportions involves analyzing the given information and calculating relevant metrics based on the data.

To determine "how many more" or the difference between two values, you subtract one value from the other. For example, if you are comparing the sales of two products, you can subtract the sales of one product from the other to find the difference in sales.

To calculate "what percentage of" a specific value, you divide the specific value by the total and multiply it by 100. This will give you the percentage. For instance, if you want to find the percentage of customers who rated a product positively out of the total number of customers, you divide the number of positive ratings by the total number of customers and multiply it by 100.

To determine "what proportion of" a group falls into a specific category, you divide the number of individuals in that category by the total number of individuals in the group. This will give you the proportion. For example, if you want to find the proportion of customers who prefer a certain brand out of the total number of customers surveyed, you divide the number of customers preferring that brand by the total number of customers.

By applying these calculations to the given data, you can provide accurate answers to questions regarding comparisons, percentages, and proportions.

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Raven purchases a new cell phone for $800 that depreciates annually. the value of her cell phone per year, x, can be modeled by the exponential function f(x) = 800(0.82)x. what is the range of this exponential function in terms of the context of the problem? [0, [infinity]) â„ (800, [infinity]) (0, 800]

Answers

The range for this function is (0,800].

What is a geometric progression?

It is a sequence of terms in which the succeeding term is can be found out by multiplying with a constant non zero value.

here the first term is 800 as it is the initial price. We can see that the common ratio is less than 1 which is 0.82, hence its a decreasing progression.

so the maximum value in range is 800

as x tends to infinity the equation tends to 0

hence the funtion apporaches 0

so the range will be (0,800]

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Using geometric progression, the range for this function is (0,800].

What is geometric progression?

A mathematical sequence known as a geometric progression (GP) is one in which each following phrase is generated by multiplying each preceding term by a fixed integer, or "common ratio."

This progression is sometimes referred to as a pattern-following geometric sequence of numbers.

Here the first term is 800 as it is the initial price. We can see that the common ratio is less than 1 which is 0.82.

Hence it's a decreasing progression.

So, the maximum value in the range is 800.

As x tends to infinity the equation tends to 0.

Hence, the function approaches 0

So the range will be (0,800].

Therefore, using a geometric progression, the range for this function is (0,800].

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simplify log(2)*log(5)*log 2(32)

MANY POINTS

Answers

log(2) * log(5) * log2(32) ≈ 1.052245.

We can simplify this expression by using the fact that log a(b^c) = c*log a(b) and the values of log(2) and log(5) which are approximately 0.301 and 0.699 respectively.

We have:

log(2) * log(5) * log2(32)

= log(2) * log(5) * 5

= 0.301 * 0.699 * 5

= 1.052245

Therefore, log(2) * log(5) * log2(32) ≈ 1.052245.

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A gardener has two different strengths of weedkiller: a 6% solution and a 15% solution, some of each solution needs to be mixed together to make 30 litres of a 10% solution. How much of each kind of solution is required?

Answers

Answer:

Approximately 16.67 liters concentration of the 6% solution and approximately 13.33 liters of the 15% solution are required to make 30 liters of a 10% solution.

Step-by-step explanation:

Let's denote the amount of the 6% solution as x liters and the amount of the 15% solution as y liters. We need to find the values of x and y that satisfy the conditions.

Since we want to make 30 liters of a 10% solution, we can set up the following equations:

Equation 1: x + y = 30 (total volume equation)

Equation 2: (0.06x + 0.15y) / 30 = 0.10 (concentration equation)

From Equation 1, we have x = 30 - y. Substituting this into Equation 2, we get:

(0.06(30 - y) + 0.15y) / 30 = 0.10

Simplifying the equation gives:

(1.8 - 0.06y + 0.15y) / 30 = 0.10

1.8 + 0.09y = 3

0.09y = 1.2

y ≈ 13.33

Substituting y back into Equation 1, we find:

x + 13.33 = 30

x ≈ 16.67

Therefore, approximately 16.67 liters of the 6% solution and approximately 13.33 liters of the 15% solution are required to make 30 liters of a 10% solution.

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1. Cameron ran 3 miles in 24 minutes. Identify the equivalent ratio that represents Cameron's run. *

Answers

The equivalent ratio that represents Cameron's run is 1 : 8

Equivalent Ration:

In mathematics, the definition of equivalence ratio says: The equality of two ratios is also called a ratio. Front and follow have different values, but reducing them to their simplest form gives the same value.

For example, to find out if 2:3 and 16:24 are equivalent ratios, we need to reduce both ratios to their simplest form. The HCF of 2 and 3 is 1, so 2:3 is already in the simplest form. The HCF for 16 and 24 is 8. Divide these two numbers by 8 to get the reduced form. This means (16÷8):(24÷8) = 2:3. It's clear that 2:3 and 16:24 are the same value, equivalent ratios.

Based on the question :

Cameron ran 3 miles in 24 minutes.

Now,

Therefore we can say that :

Cameron ran 1 miles in 8 minutes;

Therefore, the equivalent ration is 1 : 8.

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does the following table represent a valid discrete probability distribution? x 1 2 3 4 5 p(x=x) 0.11 0.06 0.25 0.41 0.51 question 10 options: yes no

Answers

No, the given table does not represent a valid discrete probability distribution. A valid discrete probability distribution must satisfy two conditions:

The probabilities assigned to each outcome should be between 0 and 1 (inclusive): In the given table, the probabilities range from 0.06 to 0.51. These values fall within the valid range of 0 to 1, satisfying the condition.

The sum of all probabilities should be equal to 1: To check this, we add up the probabilities given in the table: 0.11 + 0.06 + 0.25 + 0.41 + 0.51 = 1.34. The sum of the probabilities exceeds 1, violating the condition.

Since the sum of the probabilities is greater than 1, the given table does not satisfy the second condition for a valid probability distribution. The probabilities assigned to the outcomes are not properly normalized to ensure that the total probability is 1.

In order to represent a valid discrete probability distribution, the probabilities assigned to each outcome should be scaled down by dividing each probability by the sum of all probabilities. This normalization process ensures that the total probability across all outcomes adds up to 1.

Therefore, the correct answer is "No," as the given table does not represent a valid discrete probability distribution due to the violation of the sum of probabilities being equal to 1.

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2x-5y=20
What is y and what is x

Answers

Answer:

x=10 and y=4

Im not sure if this is correct but I looked it up and it said it was right

Answer:

x = 5/2y + 10y = 2/5x - 4

(if you're looking for intercepts then: x = 10, y = -4)

Step-by-step explanation:

\(\sf{2x - 5y = 20\)

\(\sf{Finding~x:\)

\(2x - 5y = 20\)

     \(+ 5y = + 5y\)

↪ 2x = 5y + 20

\(\frac{2x}{2} = \frac{5y}{2} + \frac{20}{2}\)

x = 5/2y + 10

\(\sf{Finding~y:}\)

\(2x - 5y = 20\)

\(-2x~ = ~~~~-2x\)

↪ -5y = -2x + 20

\(\frac{-5y}{-5} = \frac{-2x}{-5} + \frac{20}{-5}\)

y = 2/5x - 4

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

Hope this helps!

Can someone help me out with my math homework my grades are baddddd

Can someone help me out with my math homework my grades are baddddd

Answers

Answers:

Area of figure 2 = 150 square cmWX = 25/6 cm (exact)WX = 4.167 (approximate)

It's not clear which version of WX your teacher wants, so I provided both of them.

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

Explanation:

Focus on the perimeters. The jump from 36 to 30 means the linear scale factor is 30/36 = 5/6

This means,

WX/YZ = 5/6

WX/5 = 5/6

6WX = 5*5

6WX = 25

WX = 25/6 which is exact

WX = 4.167 approximately

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

The linear scale factor is 5/6, so the area scale factor is (5/6)^2 = 25/36.

The area of figure 1 is 216 cm^2, making the area of figure 2 to be 216*(25/36) = 150 cm^2

9/4n = 1.5/7 Please Explain

Answers

Answer:

9/4n= 1.5/7

right now to find this equation it is a proportion so you cross multiply and you gonna get 63=6n and divide 6 on both sides and u get 10.5.

Check 9/4n= 9/42 and to simply u will get 1.5/7

Step-by-step explanation:

f: x 5 – 3x. (a) Find f(–1). (b) Find f –1(x).

Answers

Answer:

\(f(-1) = 8\)

\(f^{-1}(x) = \frac{5}{3} - \frac{x}{3}\)

Step-by-step explanation:

Given

\(f(x) = 5 - 3x\)

Required

\(f(-1)\) and \(f^{-1}(x)\)

Solving for f(-1)

Substitute -1 for x in \(f(x) = 5 - 3x\)

\(f(-1) = 5 - 3(-1)\)

\(f(-1) = 5 + 3\)

\(f(-1) = 8\)

Solving for \(f^{-1}(x)\)

Let y = f(x)

\(y = 5 - 3x\)

Interchange the position of x and y

\(x = 5 - 3y\)

Make y the subject of formula (add 3y to both sides)

\(3y + x = 5 - 3y + 3y\)

\(3y + x = 5\)

Subtract x from both sides

\(3y + x - x = 5 - x\)

\(3y = 5 - x\)

Divide through by 3

\(\frac{3y}{3} = \frac{5}{3} - \frac{x}{3}\)

\(y = \frac{5}{3} - \frac{x}{3}\)

Replace y with \(f^{-1}(x)\)

\(f^{-1}(x) = \frac{5}{3} - \frac{x}{3}\)

What is the area of the following trapezoid? 14 mm 10 mm 28 mm 210 mm 2 280 mm 2 O 420 mm 2 O 140 mm 2​

Answers

Answer:

210 mm2

Step-by-step explanation:

you add both the bases and then height ;)

Is f = 3 a solution to the inequality below?

23 ≥ 11+f

Yes or no?

Also please explain

Answers

Answer: Yes

Step-by-step explanation:

f=3

11+3= 14

23 > 14

es correcto decir que 23 es mas grande que 11+f

A particle moves along a line so that its velocity at time t is v(t) = t^2 - t - 6 (measured in meters per second). (a) Find the displacement of the particle during 1 lessthanorequalto t lessthanorequalto 9. (b) Find the distance traveled during this time period. SOLUTION By this equation, the displacement is s(9) - s(1) = integral_1^9 v(t) dt = integral_1^9 (t^2 - t - 6) dt = [t^3/7 - t^2/2 - 6t]_1^9 = 154.67 This means that the particle moved approximately 154.67 meters to the right. Note that v(t) = t^2 - t - 6 = (t - 3)(t + 2) and so v(t) lessthanorequalto 0 on the interval [1, 3] and v(t) greaterthanorequalto V 0 on [3, 9]. Thus, from this equation, the distance traveled is integral_1^9 |v(t)| dt = integral_1^3 [-v(t)] dt + integral_3^9 v(t) dt = integral_1^3 (-t^2 + t + 6) dt + integral_3^9 (t^2 - t - 6) dt = [______]_1^3 + [______]_3^9 = ______

Answers

The displacement of the particle during 1 ≤ t ≤ 9 is approximately 154.67 meters to the right, while the total distance traveled is 305.33 meters.

To find the distance traveled during 1 ≤ t ≤ 9, we split the integral into two parts based on when the velocity is positive and negative. We have:

∫1^3 |v(t)| dt = ∫1^3 -(t^2 - t - 6) dt = [-t^3/3 + t^2/2 + 6t]1^3 = 6

∫3^9 |v(t)| dt = ∫3^9 (t^2 - t - 6) dt = [t^3/3 - t^2/2 - 6t]3^9 = 299.33

Therefore, the total distance traveled is 6 + 299.33 = 305.33 meters.
Hence the displacement of the particle during 1 ≤ t ≤ 9 is approximately 154.67 meters to the right, while the total distance traveled is 305.33 meters.

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Laura has a strip of ribbon 1 m long. How many one thirds strips can be cut from it

Answers

From the given information provided, Laura can cut 3 one-thirds strips from the 1 meter long ribbon.

If Laura has a strip of ribbon 1 meter long, we need to find out how many one-thirds strips can be cut from it.

To do this, we need to divide the length of the ribbon by the length of each one-third strip:

Number of one-thirds strips = Length of ribbon / Length of one-third strip

The length of each one-third strip is 1/3 meters, since one-third of a meter is required to make each strip.

So we can substitute these values into the formula:

Number of one-thirds strips = 1 meter / (1/3 meter)

Number of one-thirds strips = 1 meter x (3/1)

Number of one-thirds strips = 3

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Sean is exploring a coral reef 91 feet below sea level and liz is hiking 91 feet above sea level. Who is hiking farther away from sea level

Answers

They are about same distance from sea level.

Sean is exploring a coral reel below level= 91 feet

Liz is hiking above sea level= 91 feet

 When, we compare both distance from sea level, both have the sane distance. Although, the distance between both Sean and Liz is 91+91= 182 feet.

When compare the level of both , both are at 91 feet one is below the sea level and another is above the sea level. Hence, both are at the same distance from the sea level.

Hence, the correct answer is both at 91 feet from seal level.

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In the united states, voters who are neither democrat nor republican are called independent. It is believed that 6% of voters are independent. A survey asked 12 people to identify themselves as democrat, republican, or independent. What is the probability that fewer than 4 are independent?.

Answers

The probability that fewer than 4 are independent = 0.971

Let X be a random variable representing the number of independent people out of 12 people.

Then X follows binomial distribution.

A binomial distribution considers two possibilities in 'n' trials -  success or  failure. Here the case of success is being independent and the case of failure is being either republican or democrat.

The probability distribution function of a binomial distribution is,

P(X = x) = ⁿCₓ pˣ (1-p)ⁿ⁻ˣ

Where n is the number of trials, p - the probability of success

Here, n = 12

Since 6% of voters are independent, probability of being an independent = 6/100 = 0.06

Probability that fewer than 4 are independent = P( X = 0 or 1 or 2 or 3)

                                                                             = P( X = 0) + P(X = 1) + P(X = 2) + P(X = 3)

Now, P(X=0) = ¹²C₀ (0.06)⁰ (1-0.06)¹²⁻⁰

                      = 1 x 1 x 0.4759

                      = 0.4759

P(X = 1) = ¹²C₁ (0.06)¹ (1-0.06)¹²⁻¹

           = 12 x 0.06 x 0.94¹¹

           = 0.3645

P(X = 2) = ¹²C₂ (0.06)² (1-0.06)¹²⁻²

             = 66 x (0. 06)² x 0.94¹⁰

            = 0.128

P(X = 3) =  ¹²C₃ (0.06)³ (1-0.06)¹²⁻³

             = 22 x 0.000216 x 0.94⁹

             = 0.00272

Therefore, Probability that fewer than 4 are independent = P( X = 0) + P(X = 1) + P(X = 2) + P(X = 3) =  0.4759 + 0.3645 +  0.128 + 0.00272 = 0.971

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You tie a spherical balloon that is 2 feet in diameter to a
stake in the ground. The string is 15 feet long. The wind
blows and you observe that the top of the balloon is
8 feet over from the stake, as shown in the diagram.
What is the height, b, of the balloon?
Show your work.
15 ft
2 ft
8 ft

Answers

Answer:

Step-by-step explanation:

Which exponential equation is equivalent to this logarithmic equation? log x = 4

Answers

Answer:

\(x=10^{4}\)

Step-by-step explanation:

Switching from Logarithmic to Exponential form:

An exponential base is the inverse of a logarithm with the same base.  Given the equation log x = 4, note that the base of the logarithm isn't written in (it has no subscript).  By default, the base of the logarithm function is base-10.  So, to rewrite the equation using an exponential, we need to undo the logarithm with an exponential of the same base.

\(\log(x)=4\)

\(10^{\log{(x)}}=10^{4}\)

\(x=10^{4}\)

Analogies with Addition/Subtraction

Think about the equation x + 7 = 10.

I could tell you this is the equation in "addition form".  What if I asked you to write an equation in "subtraction form"?  While neither "addition form" nor "subtraction form" have been defined explicitly, one could undo the addition, and get an equation with subtraction in it, which one could argue is a "subtraction form" of the equation.

\(x+7=10\)

Subtracting 7 from both sides to undo the addition...

\((x+7)-7=(10)-7\)

Simplifying the left side since the "+7" and "-7" cancel...

\(x=10-7\)

This is arguably in a "subtraction form" (there's a subtraction in it), whereas the original equation had addition in it.

While we could simplify this particular equation's right-hand side, we might not always be able to (what if the 10 had been a "y"... then the "y" and the "7" aren't like terms, and they would have to remain separate)

Similarly, in the logarithm problem, one could simplify 10^4 (it's 10,000), but one doesn't have to, and one won't always be able to.

For the logarithm problem, x=10^4 is the exponential form, as requested.

#1: Find the slope of the line shown below.

#1: Find the slope of the line shown below.

Answers

Answer:

-3/4

Step-by-step explanation:

Hope this helps. Pls give brainliest.

Answer:

-3/4

Step-by-step explanation:

The prime minister of Ecoland wants to minimize the unemployment rate. a) Use the AD-AS to briefly explain a fiscal policy and a monetary policy that can achieve the prime minister's goal. (5 marks) b) Suppose the central bank of Ecoland helps the prime minister achieve his goal. Predict the impact on the unemployment rate and the inflation rate in the short run. Explain how the slope of the SRAS matters. ( 5 marks) c) The opposition party's leader argues that the prime minister and the central bank's agreement will affect inflation expectations, which will be costly for the country in the long run. Use the AD-AS model to explain the opposition leader's point. (5 marks) d) Suppose the prime minister chooses to use fiscal policy instead to minimize the unemployment rate. The opposition leader argues that doing so will also be costly for the country in the long run. Use concepts from this course to explain the opposition leader's point yet again.

Answers

a) Fiscal policy: Increase government spending or reduce taxes to boost aggregate demand (AD). Monetary policy: Lower interest rates or increase money supply to stimulate AD.

b) Impact depends on SRAS slope. Output ↑, unemployment ↓ in short run. Inflation ↑ if SRAS is steep.

c) Higher inflation expectations from persistent expansionary policies can lead to increased wages and prices, resulting in higher inflation in the long run.

d) Expansionary fiscal policy can lead to budget deficits, crowding out private investment, higher government debt, future tax burdens, and dependency on government intervention.

a) Fiscal policy involves using government spending and taxation to influence aggregate demand (AD) and stabilize the economy. To minimize the unemployment rate, the prime minister could implement expansionary fiscal policy by increasing government spending or reducing taxes. This would lead to an increase in AD, stimulating economic activity, and potentially reducing unemployment. Monetary policy, on the other hand, involves actions taken by the central bank to influence the money supply and interest rates. The prime minister could work with the central bank to implement expansionary monetary policy, such as lowering interest rates or conducting open market operations to increase the money supply. This would encourage borrowing and spending, boosting AD and potentially reducing unemployment.

b) If the central bank helps the prime minister achieve the goal of minimizing the unemployment rate, it can have short-run effects on both the unemployment rate and the inflation rate. Expansionary fiscal and monetary policies can increase AD, leading to increased output and potentially reducing unemployment in the short run. However, the impact on inflation will depend on the slope of the short-run aggregate supply (SRAS) curve. If the SRAS is relatively flat, the increase in output will have a larger impact on reducing unemployment without significantly increasing inflation. Conversely, if the SRAS is steep, the increase in output may lead to a significant increase in inflation with only a modest reduction in unemployment.

c) The opposition leader's argument is related to the long-run implications of the prime minister and central bank's agreement on inflation expectations. According to the AD-AS model, in the long run, the economy will reach the natural rate of unemployment (NRU) where the SRAS curve intersects the long-run aggregate supply (LRAS) curve. If expansionary fiscal and monetary policies are used persistently to reduce the unemployment rate below the NRU, it can create inflationary pressures. This may result in higher inflation expectations among households and businesses, leading to higher wage demands and increased prices.

d) If the prime minister chooses to use fiscal policy to minimize the unemployment rate, the opposition leader argues that it will also be costly in the long run. This is because expansionary fiscal policy, such as increasing government spending or reducing taxes, can lead to budget deficits. Persistent budget deficits can increase government debt and require borrowing, which may lead to higher interest rates and crowding out private investment. Higher government debt can also result in future tax burdens or reduced government spending on other essential areas, impacting long-term economic growth.

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Round 30713.517126 to the nearest hundred.

Answers

Answer:

3,266.53

Step-by-step explanation:

What is the measure of JK?

What is the measure of JK?

Answers

your answer will be B

A square tile mesures 20 cm by 20cm a rectangular tile is 3 cm longer and 2 cm narrower. What is the different in area between the two tiles?

Answers

Answer:

Rectangular tile has 14 cm² larger area

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

Find each area and then find their difference.

A(square) = 20² = 400 cm²A(rectangle) = (20 + 3)(20 - 2) = 23*18 = 414  cm²

The difference is:

414 - 400 = 14 cm²

List 4 true angle facts about the illustration created by
AD intersects FK at point M.

Answers

Acute angles are less than 90 , right angles are 90 , straight lines are 180

A line that intersects a segment at its midpoint and creates a 90 degree angle.

Answers

A perpendicular bisector is a line segment or a ray or a line that intersects a given line segment at a 90-degree, and also it passes through the midpoint of the line segment

At its midway, a segment bisector crosses another segment. A Perpendicular Bisector is a segment, ray, line, or plane that is perpendicular to another segment at its halfway.

A perpendicular bisector is a line that precisely splits a given line segment into two halves, generating a 90-degree angle at the junction point. A perpendicular bisector is a line segment that crosses through the midway. It can be built with a ruler and a compass.

When two lines cross at 90 degrees or at right angles, they are said to be perpendicular to each other. A bisector, on the other hand, is a line that divides a line into two equal halves.

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For what values of a and b is the line 4x y = b tangent to the parabola y = ax2 when x = 5?

Answers

The line 4x + y = 30 is tangent to the parabola \(\(y = \frac{2}{5}x^2\)\) at the point \(\((5, 25\left(\frac{2}{5}\right))\)\).

To determine the values of a and b such that the line 4x + y = b is tangent to the parabola \(\(y = ax^2\)\), we need to find the point of tangency.

Given that the line is tangent to the parabola, the point of tangency will have the same x value for both the line and the parabola.

Let's substitute x = 5 into both equations and equate them:

For the line:

\(\(4(5) + y = b \Rightarrow 20 + y = b \Rightarrow y = b - 20\)\)

For the parabola:

\(\(y = a(5)^2 \Rightarrow y = 25a\)\)

Since the point of tangency has the same x value, we have:

25a = b - 20

To find the values of a and b, we need additional information. Let's assume the line is tangent to the parabola at the point (5, 25a).

The slope of the line is given by the coefficient of x in its equation, which is 4. The derivative of the parabola at the point of tangency will also give us the slope of the tangent line.

The derivative of the parabola \(\(y = ax^2\)\) with respect to x is:

\(\(\frac{dy}{dx} = 2ax\)\)

Evaluating the derivative at x = 5, we get:

\(\(\frac{dy}{dx} = 2a(5) = 10a\)\)

Since the slope of the tangent line is 4, we have:

10a = 4

\(\(a = \frac{4}{10}\)\)

\(\(a = \frac{2}{5}\)\)

Substituting the value of 'a' back into the equation 25a = b - 20, we can solve for b:

\(\(25\left(\frac{2}{5}\right) = b - 20\)\)

10 = b - 20

b = 10 + 20

b = 30

Therefore, the parabola is tangent to the line 4x + y = 30  \(\(y = \frac{2}{5}x^2\)\) at the point \(\((5, 25\left(\frac{2}{5}\right))\)\).

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solve sinx = 2x-3 using false position method

Answers

The root of the equation sinx = 2x-3 is 0.8401 (approx).

Given equation is sinx = 2x-3

We need to solve this equation using false position method.

False position method is also known as the regula falsi method.

It is an iterative method used to solve nonlinear equations.

The method is based on the intermediate value theorem.

False position method is a modified version of the bisection method.

The following steps are followed to solve the given equation using the false position method:

1. We will take the end points of the interval a and b in such a way that f(a) and f(b) have opposite signs.

Here, f(x) = sinx - 2x + 3.

2. Calculate the value of c using the following formula: c = [(a*f(b)) - (b*f(a))] / (f(b) - f(a))

3. Evaluate the function at point c and find the sign of f(c).

4. If f(c) is positive, then the root lies between a and c. So, we replace b with c. If f(c) is negative, then the root lies between c and b. So, we replace a with c.

5. Repeat the steps 2 to 4 until we obtain the required accuracy.

Let's solve the given equation using the false position method.

We will take a = 0 and b = 1 because f(0) = 3 and f(1) = -0.1585 have opposite signs.

So, the root lies between 0 and 1.

The calculation is shown in the attached image below.

Therefore, the root of the equation sinx = 2x-3 is 0.8401 (approx).

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