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sweet-ann [11.9K]
3 years ago
6

Please help with #6. How do I find all of the real zeros? Thank you!!!

Mathematics
2 answers:
seraphim [82]3 years ago
8 0

Answer:

4 distinct zeroes

Step-by-step explanation:

You can not find the zeroes without the equation.

But here, they are asking for the no. of zeroes. Just count the no. of x-intercepts.. which is 4

There are 4 distinct zeroes.

Degree is 5 (odd).

0 is one of the zeroes with multiplicity 2

Other 3 zeroes have a multiplicity of 1

Morgarella [4.7K]3 years ago
7 0

I'm assuming you're referring to problem 6. You are asked to find the number of x intercepts or roots, which is another term for "zero". I prefer the term root or x intercept as "zero" seems misleading. Anyways, all we do is count the number of times the graph crosses the x axis. This happens 4 times as shown in the attached image below. I have marked these points in red. The graph can directly cross over the x axis, or it can touch the x axis and then bounce back. Either way, it is considered an x intercept.

<h3>Answer: there are 4 x intercepts (or 4 roots)</h3>

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The axis of symmetry for the graph of the function is f(x) = x2 + bx + 10 is x = 6. What is the value of b?
joja [24]

Answer:

b=-12

Step-by-step explanation:

we have

f(x)=x^{2}+bx+10

we know that

The equation of a vertical parabola into vertex form is equal to

y=a(x-h)^{2} +k

where

(h,k) is the vertex of the parabola

and the axis of symmetry is equal to x=h

In this problem we have the axis of symmetry x=6

so

the x-coordinate of the vertex is equal to 6  

therefore

For x=6+1=7 -----> one unit to the right of the vertex

Find the value of f(7)

f(7)=7^{2}+b(7)+10

f(7)=59+7b

For x=6-1=5 -----> one unit to the left of the vertex

Find the value of f(5)

f(5)=5^{2}+b(5)+10

f(5)=35+5b

Remember that

f(5)=f(7) ------> the x-coordinates are at the same distance from the axis of symmetry

so

59+7b=35+5b ------> solve for b

7b-5b=35-59

2b=-24

b=-12


3 0
2 years ago
Read 2 more answers
Which of the following is in Integrity but not a whole number A -9.6 B -4 ​
abruzzese [7]

Answer:

B. -4.

Step-by-step explanation:

3 0
2 years ago
Use the Trapezoidal Rule, the Midpoint Rule, and Simpson's Rule to approximate the given integral with the specified value of n.
Vera_Pavlovna [14]

Split up the integration interval into 4 subintervals:

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

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

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

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

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

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

  • Trapezoidal rule

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

T_i=\dfrac{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)\dfrac{(x-m_i)(x-r_i)}{(\ell_i-m_i)(\ell_i-r_i)}+f(m)\dfrac{(x-\ell_i)(x-r_i)}{(m_i-\ell_i)(m_i-r_i)}+f(r_i)\dfrac{(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.

3 0
3 years ago
What’s the answer to this?
Elina [12.6K]

Step-by-step explanation:

Line is passing through the points:

(-2,\:3)=(x_1,\:y_1) \:\&\: (2,\:5)=(x_2 ,\:y_2)

Equation of line in two point form is given as:

\frac{y -y_1 }{y_1 -y_2 } = \frac{x -x_1 }{x_1 -x_2 } \\ \\ \therefore \frac{y -3}{ 3 -5} = \frac{x -(-2) }{-2 -2} \\ \\ \therefore \frac{y -3}{ - 2} = \frac{x -(-2) }{-4} \\ \\ \therefore \frac{y - 3}{1} = \frac{x +2}{2} \\ \\ \therefore \: y-3= \frac{x}{2} + \frac{2}{2} \\ \\\therefore \: y= \frac{x}{2} + 1 +3\\ \\ \huge \red{ \boxed{\therefore \: y= \frac{1}{2} \:x+ 4}}\\ is \: the \: required \: equation \: of \: line.

4 0
2 years ago
Need help question 4
zysi [14]
You need to find what 3 is if 5 is $520,000
$520,000 divided by 5 = 104,000
104,000 x 3 = 312,000

Therefore 3 is 312,000
Hope this helps :3
5 0
3 years ago
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