A quadratic equation is shown:x2 - 14x + 41 = 0
Which of the following is the first correct step to write the above equation in the form (x - p)2 = 9, where p and q are integers?
x2 - 14x + 41 + 8 = 0 + 8
x2 - 14x + 41 + 9 = 0 + 9
x2 - 14x + 41 - 8 = 0 - 8
x2 – 14x + 41 - 9 = 0 - 9

Answers

Answer 1
Answer:

Answer:

The correct answer is the first option

Step-by-step explanation:

Quadratic Equation

The standard form of a quadratic equation is

ax^2+bx+c=0

Sometimes we need to change the expression of the same equation to the form

(x-p)^2=q

To accomplish that change, we usually modify the left-hand expression to make it look like the square of a binomial.

The given quadratic equation is

x^2-14x+41=0

Recall the square of a binomial is

(x-p)^2=x^2-2px+p^2

The first term is already present. The second term gives us the value of p:

-2px=-14x

Solving

p=7

Now we need to produce the third term p^2=49. We only have 41, thus we need to add 8 to both sides of the equation:

x^2-14x+41+8=0+8

The correct answer is the first option


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A pharmaceutical company ran a clinical trial to test if drug X cures disease Y. A statistician named Z who is taking BIO 211 was given a task to perform a null hypothesis test. The test was perfect, and the null hypothesis was rejected at the alpha = 0.05 significance level. However, unbeknownst to Z, the company ran 39 extra clinical trials and secretly hired Z’s classmates to evaluate data obtained from each independent trial with the same null hypothesis test at the same significance level. a. What is the null hypothesis? Drug X does cure disease Y Drug X does not cure disease Y

Answers

Answer:

The null hypothesis is A) Drug X does cure disease Y

Step-by-step explanation:

Consider the provided information.

If there is no statistical significance in the test then it is know as the null which is denoted by H_0, otherwise it is known as alternative hypothesis which denoted by H_a.

A pharmaceutical company ran a clinical trial to test if drug X cures disease Y.

Since, claim is drug X cures disease.

Therefore, the null hypothesis is A) Drug X does cure disease Y

A certain vibrating system satisfies the equation u'' + γu' + u = 0. Find the value of the damping coefficient γ for which the quasi period of the damped motion is 90% greater than the period of the corresponding undamped motion.

Answers

Final answer:

In damped harmonic motion, we calculate damping coefficient γ by comparing the periods of damped and undamped motion. For the given situation where the quasi-period is 90% greater than the undamped period, the damping coefficient is approximately 0.7416.

Explanation:

The subject of this question involves Damped Harmonic Motion, a concept in Physics, related to vibrations and waves. The equation given, u'' + γu' + u = 0, describes the motion where γ denotes the damping coefficient. Here, we have to calculate this damping coefficient when the quasi period of the damped motion is 90% greater than the period of the corresponding undamped motion.

To solve this, we must use the relationship between damped and undamped periods. The quasi-period T' of a damped harmonic motion relates to the undamped period T as: T' = T/(sqrt(1 - (γ/2)^2)). Now, given that T' = 1.9T, we can but these two equations together:

1.9 = 1/(sqrt(1 - (γ/2)^2))

Solving this for γ, we get γ ≈ 0.7416. Hence, the damping coefficient γ for which the quasi period of the damped motion is 90% greater than the period of the corresponding undamped motion is approximately 0.7416.

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Final answer:

The value of the damping coefficient γ for which the quasi period of the damped motion is 90% greater than the period of the undamped motion is the one that satisfies γ=2*ω*0.9, where ω is the natural frequency of oscillation.

Explanation:

The given equation is for a damped harmonic oscillator, a physical system that oscillates under both a restoring force and a damping force proportional to the velocity of the system. The damping coefficient γ determines the behavior of the system and in this case, we need to find the value of γ such that the quasi period of the damped motion is 90% greater than the period of the undamped motion.

The period of the undamped motion, T₀, is calculated by the formula T₀=2π/sqrt(ω), where ω is the natural frequency of oscillation. The quasi period of the damped motion, Td, is increased by a factor of 1+η (in this case, 1.9 as the increase is 90%) and calculated by the formula Td=T₀(1+η) = T₀*1.9.

The damping ratio η is determined by the damping coefficient γ as η=γ/2ω. Therefore, by combining these expressions and rearranging the terms, we extract γ from these formulas as γ=2ω*η => γ=2*ω*(0.9). Thus, the value of the damping coefficient γ for which the quasi period of the damped motion is 90% greater than the period of the corresponding undamped motion is the one which satisfies γ=2*ω*0.9.

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What does the point (1, 18) represent

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Answers

A graph is the plot of a function or a proportion thus (1,18) represents the number of cookies made by using 1 cup of flour is 18.

What is a graph?

A graph is a diametrical representation of any function between the dependent and independent variables.

For example y = x² form a parabola now by looking at only the graph we can predict that it has only a positive value irrespective of the interval of x.

As per the given graph of the number of cookies and cups of flour.

The coordinate of a point is (x,y) and here x-axis is the cups of flour and the y-axis is the number of cookies.

Since x = 1 so cups of flour are 1.

Since y = 18 so the number of cookies is 18.

Hence "A graph is the plot of a function or a proportion thus (1,18) represents the number of cookies made by using 1 cup of flour is 18".

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1 cup of flour makes 18 cookies

Look at the cone above. If r = 4 cm and h = 4 cm, what is the volume of the cone? (Assume = 3.14) A. 64 cm3 B. 66.99 cm3 C. 64 cm2 D. 100.53 cm3

Answers

Answer:

66.99 cm³

Step-by-step explanation:

the volume = ⅓× 3.14 × 4²× 4 = 3.14 × 64/ 3

= 66.99cm³

Sum of series 1 +1/3 +1/3².... is?​

Answers

Answer:

The sum of the series is 3/2

Step-by-step explanation:

Given

1 + 1/3 + 1/3^2 + ....

Required

The sum of the series

This implies that we calculate the sum to infinity.

We have:

a = 1 -- The first term

First, calculate the common ratio (r)

r = (1)/(3^2) / (1)/(3)

Change to product

r = (1)/(3^2) * (3)/(1)

Solve

r = (1)/(3)

The sum of the series is then calculated as:

S_(\infty) = (a)/(1 - r)

S_(\infty) = (1)/(1 - 1/3)

Solve the denominator

S_(\infty) = (1)/(2/3)

Express as product

S_(\infty) = 1 * (3)/(2)

S_(\infty) = (3)/(2)

Carlos has decided to buy a new mountain bike that costs $295.90 before tax. Sales tax is 4.5%. How much sales tax will he pay?

Answers

All we need to do is multiply the price by the tax:
0.045(29590)
1331.55
13.33155
We can round:
Carlos will pay $13.33 sales tax.