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2 years ago

Which input value produces the same output value for the two functions on the graph?

Mathematics

1 answer:

GrogVix [38]2 years ago

6 0

Answer:

The image of both graphs can be seen below:

Both functions will have the same output for an input x₀ if:

f(x₀) = g(x₀)

This means that, for that particular value of x₀, the functions will intersect each other.

So we just need to look at the graph and find the x-value where the functions intersect. (Remember that the x-values are in the horizontal axis)

We can see that it happens at x = 1.

Then the input value that produces the same output value for the two functions is:

x = 1

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(x+6)(−x+1)=0 greatest x and least x = 0

Bumek [7]

Answer:

x=-6

×=1

Step-by-step explanation:

remove parentheses

connect like terms

change the signs

calculate the discriminant

simplify

6 0

2 years ago

The line passing through (-2,5) and (2,p) has a gradient of -1/2. Fnd the value of p

makkiz [27]

Given:

The line passing through (-2,5) and (2,p) has a gradient of $-\dfrac{1}{2}$ .

To find:

The value of p.

Solution:

If a line passes through two points, then the slope of the line is:

$m=\dfrac{y_2-y_1}{x_2-x_1}$

The line passing through (-2,5) and (2,p). So, the slope of the line is:

$m=\dfrac{p-5}{2-(-2)}$

$m=\dfrac{p-5}{2+2}$

$m=\dfrac{p-5}{4}$

It is given that the gradient or slope of the line is $-\dfrac{1}{2}$ .

$\dfrac{p-5}{4}=-\dfrac{1}{2}$

On cross multiplication, we get

$2(p-5)=-4(1)$

$2p-10=-4$

$2p=-4+10$

$2p=6$

Divide both sides by 2.

$p=3$

Therefore, the value of p is 3.

4 0

3 years ago

Which of the following statements is true about the division expression 686.54 ÷ a? A. If a is a number greater than 686.54, the

borishaifa [10]

Answer:

D-- if a is a number between 0 and 1, the quotient will be greater

Step-by-step explanation:

5 0

3 years ago

Tyra buys 14 gallons of gas for $35. How could she figure out how much 1 gallon of gas cost

defon

Answer:

The cost of 1 gallon is $2.5

Step-by-step explanation:

Given

Cost of 14 gallons = $35

Required

Determine the cost of 1 gallon

From the given parameters, we have:

$14\ gallons = \$35$

Divide both sides by 14

$\frac{14\ gallons}{14} = \frac{\$35}{14}$

$1\ gallon = \frac{\$35}{14}$

$1\ gallon = \$2.5$

Hence,

The cost of 1 gallon is $2.5

4 0

3 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