Hey can you please help me posted picture of question

Answers

Answer 1

Answer: The correct answer is option D.

The function has a repeated root. We can find this by factorization.

x² - 2x + 1
= x² - x - x + 1
= x (x - 1) - 1(x - 1)
= (x -1)(x - 1)

This can also be checked by finding the discriminant. The discriminant is zero which shows the function has a repeated root.

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Suppose you are asked to choose a whole number between 1 and 13, inclusive. (a) What is the probability that it is odd? (b) What is the probability that it is even? (c) What is the probability that it is a multiple of 3?

Answers

a. this depends on if 1 and 13 are included. If so, it would be 7 of 13. If not, 5 of 11
b. same thing, depends on if 1 and 13 are included. If so, 6 of 13. If not, 6 of 11
c. again, depends. If so, 4 of 13. If not, 4 of 11

Allison buys a spool of thread for sewing. There are 10 yards of thread on the spool. She uses 9 meters. How much thread is left on thespool in meters? Round your answer to the nearest thousandth, if necessary.

Answers

The amount of meters left is 0.144 meters

First and foremost, it should be noted that: 1 yard = 0.9144 meter

Therefore, 10 yards to meters will be:

= 0.9144 × 10

= 9.144 meters

Since Allison uses 9 meters, the amount of thread that is left on the

spool will be:

= 9.144 meters - 9 meters

= 0.144 meters

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there are 9.144 meters in 10 yards, therefore, there would be .144 meters left of thread.

A Triangle has an angle that measures 137.3 degrees. The other two angles are in a ratio of 3:4. What are the measures of those two angles?

Answers

so we start off by subtracting 137.3 from 180 getting 42.5. If you add the ratios up (3+4) you get 7 and 7 should equal 42.5. thus,

42.5/7= 85/14

(85/14)*3=18.2 or (255/14 to be exact)
(85/14)*4= 24.29 or (170/7 to be exact)

Solve for x. round to the nearest tenth.

Answers

tan (angle = Opposite / adjacent

tan(28) = 18/x

x = 18 / tan(28)

x = 33.85

Rounded to nearest tenth X = 33.9

Final answer:

The student correctly solved the equations given for x. Note that an equation with an unknown variable squared might have two solutions. The way to solve for x alters according to what the equation requires, whether it is adding, subtracting, or dividing.

Explanation:

It seems like the student is trying to solve equations for x. The equations given were all solved correctly. Keep in mind that when an equation contains an unknown variable squared, there could be two solutions, and one or both could be reasonable depending on the problem. For example, consider the equation x² +0.0211x -0.0211 = 0. This could be rearranged to solve for x. Other variables are known unless additional calculations needed if they are not.

Remember that the principle of altering the equation to solve for x is employed, whether we add, subtract or divide by certain values. Like mentioned in the information provided, when dividing by powers of 10, you would move the decimal to the left, corresponding to the number of zeros in the power of ten.

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Find the value of this expression if x = 9. x^2+7/x+2

Answers

Answer:

Step-by-step explanation:

Answer:

Yeah, the answer is 8.

Step-by-step explanation:

I've gotten this question and it's right.

Use the Trapezoidal Rule, the Midpoint Rule, and Simpson's Rule to approximate the given integral with the specified value of n. (Round your answers to six decimal places.) π/2 0 3 1 + cos(x) dx, n = 4

Answers

Split up the integration interval into 4 subintervals:

$\left[0,\frac\pi8\right],\left[\frac\pi8,\frac\pi4\right],\left[\frac\pi4,\frac{3\pi}8\right],\left[\frac{3\pi}8,\frac\pi2\right]$

The left and right endpoints of the $i$ -th subinterval, respectively, are

$\ell_i=\frac{i-1}4\left(\frac\pi2-0\right)=\frac{(i-1)\pi}8$

$r_i=\frac i4\left(\frac\pi2-0\right)=\frac{i\pi}8$

for $1\le i\le4$ , and the respective midpoints are

$m_i=\frac{\ell_i+r_i}2=\frac{(2i-1)\pi}8$

Trapezoidal rule

We approximate the (signed) area under the curve over each subinterval by

$T_i=\frac{f(\ell_i)+f(r_i)}2(\ell_i-r_i)$

so that

$\displaystyle\int_0^(\pi/2)\frac3{1+\cos x}\,\mathrm dx\approx\sum_(i=1)^4T_i\approx\boxed{3.038078}$

Midpoint rule

We approximate the area for each subinterval by

$M_i=f(m_i)(\ell_i-r_i)$

so that

$\displaystyle\int_0^(\pi/2)\frac3{1+\cos x}\,\mathrm dx\approx\sum_(i=1)^4M_i\approx\boxed{2.981137}$

Simpson's rule

We first interpolate the integrand over each subinterval by a quadratic polynomial $p_i(x)$ , where

$p_i(x)=f(\ell_i)((x-m_i)(x-r_i))/((\ell_i-m_i)(\ell_i-r_i))+f(m)((x-\ell_i)(x-r_i))/((m_i-\ell_i)(m_i-r_i))+f(r_i)((x-\ell_i)(x-m_i))/((r_i-\ell_i)(r_i-m_i))$

so that

$\displaystyle\int_0^(\pi/2)\frac3{1+\cos x}\,\mathrm dx\approx\sum_(i=1)^4\int_(\ell_i)^(r_i)p_i(x)\,\mathrm dx$

It so happens that the integral of $p_i(x)$ reduces nicely to the form you're probably more familiar with,

$S_i=\displaystyle\int_(\ell_i)^(r_i)p_i(x)\,\mathrm dx=\frac{r_i-\ell_i}6(f(\ell_i)+4f(m_i)+f(r_i))$

Then the integral is approximately

$\displaystyle\int_0^(\pi/2)\frac3{1+\cos x}\,\mathrm dx\approx\sum_(i=1)^4S_i\approx\boxed{3.000117}$

Compare these to the actual value of the integral, 3. I've included plots of the approximations below.

Final answer:

The question is asking to approximate the definite integral of 1 + cos(x) from 0 to π/2 using the Trapezoidal Rule, the Midpoint Rule, and Simpson's Rule for n=4. These are numerical methods used for approximating integrals by estimating the area under the curve as simpler shapes.

Explanation:

This question asks to use several mathematical rules, specifically the Trapezoidal Rule, the Midpoint Rule, and Simpson's Rule, to approximate the given integral with a specified value of n which is 4. The integral given is the function 1 + cos(x) dx from 0 to π/2. Each of these rules are techniques for approximating the definite integral of a function. They work by estimating the region under the graph of the function and above the x-axis as a series of simpler shapes, such as trapezoids or parabolas, and then calculating the area of these shapes. The 'dx' component represents a small change in x, the variable of integration. The cosine function in this integral is a trigonometric function that oscillates between -1 and 1, mapping the unit circle to the x-axis. The exact solution would require calculus, but these numerical methods provide a close approximation.

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