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3 years ago

3x^4-7x^2+11 Expression

1 answer:

3 0

Which of the following statements correctly describes the expression below based on its degree and number of terms? 3x^4 - 7x^2 + 11. The expression has four terms and a degree of 6. The expression is a trinomial with a degree of 6. The expression is a trinomial with a degree of 4. The expression has four terms and a degree of 4.

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The sum of two numbers is 75. The second number is 3 less than twice the first

Mandarinka [93]

Answer:

$\large{\textbf{The two numbers are: 26 and 49}.\\}$

Step-by-step explanation:

$\large{\textup{assume the two numbers are $x$ and $y$.}}\\\large{\textup{The given sentences are written in mathematical terms as follows:}\\$$ x + y = 75 \hspace{25mm} (1)$$ $$ y = 2x - 3 \hspace{25mm} (2) $$ \\\textup{Substituting $(2)$ in $(1)$,}\\\begin{align*} & \implies x + 2x - 3 = 75 \\& \implies 3x = 78 \\& \implies x = 26\end{align*}\textup{Substituting $x$ in $(1), \hspace{5mm} y = 49$} }$

7 0

2 years ago

PLZ HELP...Enter in standard form the equation of the line passing through the given point and having the given slope.

Alenkinab [10]

Standard form for the equation of the line is

$$y=-\frac{2}{3} x-\frac{25}{3}$

Solution:

Given point is (2, –5).

slope of the line m = $-\frac{2}{3}$

Here, $x_1=2, y_1=-5$

Equation of a line passing through the point:

$y-y_1=m(x-x_1)$

$$y-(-5)=-\frac{2}{3} (x-(-5))$

$$y+5=-\frac{2}{3} (x+5)$

$$y+5=-\frac{2}{3} x-\frac{10}{3}$

Subtract 15 from both sides of the equation.

$$y+5-5=-\frac{2}{3} x-\frac{10}{3}-5$

$$y=-\frac{2}{3} x-\frac{25}{3}$

Standard form for the equation of the line is

$$y=-\frac{2}{3} x-\frac{25}{3}$

7 0

3 years ago

. A right cylindrical drum is to hold 7.35 cubic feet of liquid. Find the dimensions (radius of the base and height) of the drum

Drupady [299]

Answer:

$r=1.05\ \text{ft}$

$h=2.12\ \text{ft}$

$20.91\ \text{ft}^3$

Step-by-step explanation:

r = Radius

h = Height

Volume of cylinder = $7.35\ \text{ft}^3$

$V=\pi r^2h\\\Rightarrow h=\dfrac{V}{\pi r^2}\\\Rightarrow h=\dfrac{7.35}{\pi r^2}$

Surface area is given by

$A=2\pi r^2+2\pi rh\\\Rightarrow A=2\pi r^2+2\pi r\dfrac{7.35}{\pi r^2}\\\Rightarrow A=2\pi r^2+\dfrac{14.7}{r}$

Differentiating with respect to radius we get

$\dfrac{dA}{dr}=4\pi r-\dfrac{14.7}{r^2}$

Equating with zero we get

$0=4\pi r-\dfrac{14.7}{r^2}\\\Rightarrow 4\pi r=\dfrac{14.7}{r^2}\\\Rightarrow r^3=\dfrac{14.7}{4\pi}\\\Rightarrow r=(\dfrac{14.7}{4\pi})^{\dfrac{1}{3}}\\\Rightarrow r=1.05$

$\dfrac{d^2A}{dr^2}=4\pi-2\times \dfrac{14.7}{r^3}\\\Rightarrow \dfrac{d^2A}{dr^2}=4\pi+2\times \dfrac{14.7}{1.05^3}\\\Rightarrow \dfrac{d^2A}{dr^2}=37.96>0$

So, the value of the function is minimum at $r=1.05$

$h=\dfrac{7.35}{\pi r^2}=\dfrac{7.35}{\pi 1.05^2}\\\Rightarrow h=2.12$

So, the radius and height which would minimize the surface area is 1.05 feet and 2.12 feet respectively.

Surface area

$A=2\pi r^2+2\pi rh\\\Rightarrow A=2\pi \times 1.05^2+2\pi 1.05\times 2.12\\\Rightarrow A=20.91\ \text{ft}^3$

The minimum surface area is $20.91\ \text{ft}^3$ .

8 0

3 years ago

Identify the decimals labeled with the letters A, B, and C on the scale below. Letter A represents the decimal Letter B represen

Yuliya22 [10]

$10$ divisions between $389$ and $390$ so each division is $\frac{390-389}{10}=0.1$

A is 8 division from $389$, so, A is $389+8\times 0.1=389.8$

similarly, C is one division behind $389$ so it is $389-1\times 0.1=388.9$

and B is $390.3$

8 0

3 years ago

The equation of a parabola is given.y=1/8x^2+4x+20 What are the coordinates of the focus of the parabola?

Lena [83]

He equation of a parabola is x = -4(y-1)^2. What is the equation of the directrix?
You may write the equation as 
(y-1)^2 = (1) (x+4) 
(y-k)^2 = 4p(x-h), where (h,k) is the vertex 
4p=1 
p=1/4 
k=1 
h=-4 

The directrix is a vertical line x= h-p 
x = -4-1/4 
x=-17/4 

------------------------------- 
What is the focal length of the parabola with equation y - 4 = 1/8x^2 
(x-0)^2 = 8(y-4) 
The vertex is (0,4) 
4p=8 
p=2 (focal length) -- distance between vertex and the focus 
------------------------------- 
(y-0)^2 = (4/3) (x-7) 
vertex = (7,0) 
4p=4/3 
p=1/3 
focus : (h+p,k) 
(7+1/3, 0)

8 0

3 years ago

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