<img src="https://tex.z-dn.net/?f=%28%20%7Bx%7D%5E%7B3%7D%20-%208%20%7Bx%7D%5E%7B2%7D%20%20%2B%2019x%20-%209%29%20%5Cdiv%20%28x%

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3 years ago

20-%204%29%20" id="TexFormula1" title="( {x}^{3} - 8 {x}^{2} + 19x - 9) \div (x - 4) " alt="( {x}^{3} - 8 {x}^{2} + 19x - 9) \div (x - 4) " align="absmiddle" class="latex-formula">

Mathematics

1 answer:

Anna [14]3 years ago

6 0

$(x^3-8x^2+19x-9)\div(x-4)=x^2-4x+3\\\underline{-x^3+4x^2}\\=-4x^2+19x\\\underline{\ \ \ \ \ 4x^2-16x}\\.\ \ \ =3x-9\\\underline{\ \ \ \ \ -3x+12}\\.\ \ \ \ \ =\ 3$

$x^3-8x^2+19x-9=(x^2-4x+3)(x-4)+3$

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an airplane has flown 260 miles out of a total trip of 500 miles. What fraction in simplest form of the trip has been completed

solmaris [256]

260/500 = .52
.52 = 13/25
.52 = 52%

4 0

3 years ago

s(t) = 0.29t2 − t + 25 gallons per year (0 ≤ t ≤ 7), where t is time in years since the start of 2007. Use a Riemann sum with n

Sav [38]

Answer: The answer is 300 gallons.

Step-by-step explanation: Riemann sum is a method of calculating the total area under a curve on a graph, which is also known as Integral.

To calculate that area, we divide it into a number of rectangles with one point touching the curve. The curve has a closed interval [a,b] that can be subdivided into n subintervals, each having a width of Δ $x_{k}$ = $\frac{b-a}{n}$

If a function is defined on the closed interval [a,b] and $c_{k}$ is any point in [ $x_{k-1}$ , $x_{k}$ ], then a Riemann Sum is defined as ∑f( $c_{k}$ )Δ $x_{k}$ .

For this question:

Δ $x_{k}$ = $\frac{7-0}{5}$ = 1.4

Now, we have to find s(t) for each valor on the interval:

s(t) = 0.29 $t^{2}$ - t +25

s(0) = 25

s(1) = 24.29

s(2) = 24.16

s(3) = 24.61

s(4) = 25.64

s(5) = 27.25

s(6) = 29.44

s(7) = 32.21

Now, using the formula:

∑f( $c_{k}$ )Δ $x_{k}$ = 1.4(25+24.29+24.16+24.61+25.64+29.44+32.21)

∑f( $c_{k}$ )Δ $x_{k}$ = 1.4(212.6)

∑f( $c_{k}$ )Δ $x_{k}$ ≅ 300

With Riemann Sum, it is estimated the total country's per capita sales of bottled water is 300 gallons.

3 0

3 years ago

Which point is an x-intercept of the quadratic function f(x) = (x – 4)(x + 2)? (–4, 0) (–2, 0) (0, 2) (4, –2)

son4ous [18]

<span>f(x) = (x – 4)(x + 2),
x-intercept means that f(x) = 0.

0 = (x-4)(x+2)
(x-4)=0, x= 4, point (4,0)
(x+2)=0, x = -2, point (-2,0)

This graph has 2 x-intercepts: (4,0) and (-2,0).

From given answers we can choose only </span>(-2,0).

5 0

3 years ago

Read 2 more answers

If a cone with a diameter of 10 m has a surface area of 190.6m2, find its slant height. Round to the nearest tenth.

alukav5142 [94]

Answer: The slant height of the cone is 65.6 m

Step-by-step explanation:

Given: The diameter of a cone = 10 m

Surface area of cone = 190.6 m²

To find: Slant height

Diameter of cone = 10 m

Therefore Radius of cone = $\dfrac{\text {Diameter }}{2} = \dfrac{10}{2} =5m$

As we know that surface area of a cone is given by

$S.A. = \pi r(l+r)$

Where S.A. is surface area , r is the radius of cone and l is the slant height of the cone.

Let Slant height = l

So we have

$190.6 = \dfrac{22}{7} \times 5 ( 5+l)\\\\\Rightarrow 5+l= \dfrac{190.6 \times 7}{22}\\\\\Rightarrow l= \dfrac{1334.2}{22}+5\approx 60.64+5 = 65.64\approx65.6$

Hence the slant height of the cone is 65.6 m

5 0

3 years ago

1. The graph of every exponential function f(x)= ax, a>0, a≠1, passes through what three points(in terms of a)? Explain.

Anvisha [2.4K]

The exponential function
f(x) = a^x
can pass through all points as long as x is any real number

As an example, we can choose values of x.
x = -4, x = 0, x=100

The value of the function in terms of a would be
f(-4) = a^-4
f(0) = a^0 = 1
f(100) = a^100

3 0

3 years ago