The cartesian coordinates of the point are (−1,3√). hence, polar coordinates of the point are

Answer:

About 5.0 hours

Step-by-step explanation:

To solve the equation 49x²+56x-64 = 0 by completing the square, we first convert it to the format (ax + b)² = c. It is found that a=1, b=4/7, and c=16/49. Hence, a+b+c = 381/147 or approximately 2.59183673469.

The equation to solve is 49x²+56x-64 = 0. By completing the square, we can rewrite the equation in the form (ax + b)² = c. To get to this form, Po first divided the entire equation by 49, giving x²+8/7x-64/49= 0. Following this, he then took half of the coefficient of x (which is 4/7), squared it (which is 16/49), and added it to both sides of the equation. This transforms the left-hand side of the equation into a perfect square giving us (x+4/7)²=16/49. Hence, we find that a=1, b=4/7, and c=16/49. Therefore a+b+c = 381/147 or approximately 2.59183673469.

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We apply the Pythagorean theorem and differentiate it to relate the rates of the ladder's top slipping and the foot of the ladder moving away from the wall. Substituting given values in the differentiated equation gives us the speed at which the foot of the ladder is moving away.

In this problem, we are dealing with a right triangle formed by the wall, ground and the ladder acting as the hypotenuse. The rate at which the top of the ladder is descending and the height at which the rate needs to be calculated are given. This problem applies the concepts of related rates in calculus.

According to the Pythagorean theorem, for a right triangle, the sum of the square of the two shorter sides is equal to the square of the longest side (the hypotenuse). Here, we have  x² + y² = 15² where x is the distance of foot of the ladder from the wall and y is the height from the ground.

Differentiating both sides with respect to time (t),  we get 2x(dx/dt) + 2y(dy/dt) = 0. Solve this differentiation equation to find dx/dt, the speed of the foot of the ladder moving away from the wall while y is 13.

To solve this, plug y = 13, dy/dt (rate at which top of ladder is descending) = -4 ft/sec into the equation and solve for dx/dt.

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Answer: [tex]84x^{12}[/tex]

Step-by-step explanation:

The given expression  : [tex](4x)(-3x^8) (-7x^3)[/tex]

Open brackets, we get

[tex]4x\cdot-3x^8\cdot-7x^3\\\\=4\cdot-3\cdot-7\cdot x\cdot x^8\cdot x^3[/tex]

Using law of exponents:-

[tex]a^m\cdot a^n=a^{m+n][/tex]

[tex]84\cdot x^{1+8+3}\\\\=84x^{12}[/tex]

Hence, the product [tex](4x)(-3x^8) (-7x^3)=84x^{12}[/tex]

Answer:

C. 84X^12

Step-by-step explanation:

edge 2021

The exponential model provides a reasonable approximation for the world population growth between 1750 and 1800. However, it becomes less accurate for longer time periods due to various factors like technological advancements, medical breakthroughs, and changing social and economic conditions.

1. Define the model:

The general form of an exponential model is:

P(t) = a * b^(t)

where:

P(t) is the population at time t

a is the initial population (at t = 0)

b is the growth factor (greater than 1 for positive growth)

t is the time elapsed (in years, since the initial time)

2. Find the parameters:

We have data for 1750 (t = 0) and 1800 (t = 50):

P(0) = 790 million (initial population)

P(50) = 980 million (population after 50 years)

Using these values, we can solve for a and b:

b = (P(50) / P(0))^(1/t) = 980 / 790)^(1/50) ≈ 1.007

a = P(0) / b^0 = 790 / 1 ≈ 790

3. Predict the population in 1900 and 1950:

Now we can plug the values of a and b into the model to predict the population:

P(150) = 790 * 1.007^(150) ≈ 1912 million (predicted population in 1900)

P(200) = 790 * 1.007^(200) ≈ 3145 million (predicted population in 1950)

4. Comparison with actual data:

The actual population in 1900 was 1650 million and in 1950 was 2560 million. While the model overestimates the population in both cases, it still captures the general trend of growth.

The problem is a simple division process. We set up the equation where the number of buckets, B is calculated by the total quantity of paint in gallons, divided by how many gallons each bucket holds. Solving this equation, we discover that 30,000 gallons of paint can fill 6,000 buckets.

We can solve this problem by using a simple division process. Each bucket holds 5 gallons. So, if we have 30,000 gallons, we need to find out how many 5-gallon buckets this amount equals to.

If we denote the number of buckets by B, we can write an equation as follows:

5B = 30000.

To find B, we solve the equation by dividing both sides by 5: B = 30000/5

So, using a calculator, we find that B = 6000 buckets.

Therefore, the facility would be able to give away 6000 buckets of paint.

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The rule for solving proportions is that the product of the means equals the product of the extremes. This method is used when dealing with categorical data in two categories.

The rule for solving proportions is this: The product of the means is equal to the product of the extremes (option B). When you have a proportion which is often written in the mathematically form 'a/b = c/d', you can use this rule. 'a' and 'd' are the extremes and 'b' and 'c' are the means. Therefore, the rule means that a*d (product of the extremes) is equal to b*c (product of the means).

In terms of identifying when you're dealing with a proportion problem, you're involved in this scenario when the data you're dealing with is of two categories like Yes or No, Success or Failure. This is typically when you're attempting to estimate a population proportion for example, the proportion of the population that smokes or will vote for candidate A.

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Answer:

A. An additional month of growth is associated with an additional 13.5 pounds of weight.

Step-by-step explanation:

4 people x 45 minutes = 180 minutes total to paint 5 walls

180/5 = 36 minutes of man work per wall

36 * 4 walls = 144 total minutes

144/6 people = 24 minutes total

Answer:

The common reasoning that can be use while solving a radical equation are shown below.

Step-by-step explanation:

Radical equations are the equations which contains radical expressions like [tex]\sqrt{x}\text{ and }\sqrt{x+2}[/tex], etc.

If a radical expression is defined as [tex]\sqrt{x}[/tex], then the sign [tex]\sqrt{}[/tex] is the radical and x is radicand.

The common reasoning that can be use while solving a radical equation are:

1. Isolate or separate the radical expression.

2. To remove radical square both sides of the equation.

3. After that solve the equation to find the unknown variable

4. Check the answer for solution or extraneous solution.

For example:

[tex]\sqrt{x+1}+1=x[/tex]

subtract 1 from both sides.

[tex]\sqrt{x+1}=x-1[/tex]

Taking square on both sides.

[tex]x+1=(x-1)^2[/tex]

On simplification we get

[tex]x+1=x^2-2x+1[/tex]

[tex]0=x^2-2x+1-x-1[/tex]

[tex]0=x^2-3x[/tex]

[tex]0=x(x-3)[/tex]

Using zero product property,

[tex]x=0,x-3=0\Rightarrow x=3[/tex]

Check the equation for x=0,

[tex]LHS=\sqrt{0+1}+1=1+1=2\neq 0=RHS[/tex]

Since LHS is not equal to RHS, therefore 0 is an extraneous solution.

Check the equation for x=3,

[tex]LHS=\sqrt{3+1}+1=2+1=3=RHS[/tex]

Since LHS is equal to RHS, therefore 3 is an solution.

Answer:

4 weeks

Step-by-step explanation:

Answer:58

Step-by-step explanation: