How many feet in a rod?

2.5

4.5

8.5

16.5

Answers

Answer 1

Answer: 1 rod is equal to 16.5 feet

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What are the domain and range of the function f(x) = 3^x + 5

Answers

Answer:

Hence,

Domain: (-∞,∞)

Range: (5,∞)

Step-by-step explanation:

The domain of the function is the possible set of values at which the function is defined.

and the range of the function is the corresponding function values at the points of the domain.

e are given a function f(x) as:

$f(x)=3^x+5$

Clearly the function $3^x$ is defined for all the real values.

Hence, the function:

$f(x)=3^x+5$ is defined for all the real numbers.

Hence the domain of the function is: (-∞,∞) i.e. all of the real line.

Also we know that:

$3^x>0$ for all x.

Hence,

$3^x+5>5$ for all x.

Hence, the range of the function is:

(5,∞).

Hence,

Domain: (-∞,∞)

Range: (5,∞)

The range is y values and domain is x values

y intercept here is 5 and since the function is increasing thus the range would be all real values bigger than or equal to 5

And the domain would be all real numbers.

Which of the following expressions is larger? 3.67 x 10^2 or 1.9 x 10^2

Answers

Answer:

3.67 x 10^2 is larger

Step-by-step explanation:

Answer:

3.67 x 10^2 is larger than 1.9 x 10^2

Step-by-step explanation: Multiply

The planets in our solar system do not travel in circular paths. Rather, their orbits are elliptical. The Sun is located at a focus of the ellipse. The perihelion is the point in a planet’s orbit that is closest to the Sun. So, it is the endpoint of the major axis that is closest to the Sun.

The aphelion is the point in the planet’s orbit that is furthest from the Sun. So, it is the endpoint of the major axis that is furthest from the Sun.

The closest Mercury comes to the Sun is about 46 million miles. The farthest Mercury travels from the Sun is about 70 million miles.

1. What is the distance between the perihelion and the aphelion?

2. What is the distance from the center of Mercury’s elliptical orbit and the Sun?

3. Write the equation of the elliptical orbit of Mercury, where the major axis runs horizontally. Allow a and b to be measured in millions of miles. Use the origin as the center of the

Answers

Answer:

(1) 83.764 million miles

(2) 52.766 million miles

(3) $(x^2)/(4900)+(y^2)/(2116)=1.$

Step-by-step explanation:

Let the origin C(0,0) be the center of the elliptical path as shown in the figure, where the location of the sun is at one of the two foci, say f.

The standard equation of the ellipse having the center at the origin is

$(x^2)/(a^2)+(y^2)/(b^2)=1\;\cdots(i)$

where $a$ and $b$ are the semi-axes of the ellipse along the x-axis and y-axis respectively.

Let the points P and A represent the points of perihelion (nearest to the sun) and the aphelion (farthest to the sun) of the closest planet Mercury.

Given that,

CP=46 million miles and

CA=70 million miles.

So, $CP=b$ is the semi-minor axis and $CA=a$ is the semi-major axis.

Let the distances on the axes are in millions of miles. So, the coordinates of the point P and A are $P(0,46)$ and $A(70,0)$ respectively.

(1) From the distance formula, the distance between the perihelion and the aphelion is

$PA=√((0-70)^2+(46-0)^2)=83.764$ million miles.

(2) Location of the Sun is at focus, $f$ , of the elliptical path.

From the standard relation, the distance of the focus from the center of the ellipse, c, is

$c=ae\;\cdots(ii)$

where $a$ and $e$ are the semi-major axis and the eccentricity of the ellipse.

The eccentricity of the ellipse is

$e=\sqrt{1-(b^2)/(a^2)}$

$\Rightarrow e=\sqrt{1-(46^2)/(70^2)}=0.7538$ .

Hence, from the equation (i) the distance of the Sun from the center of the elliptical path of the Mercury is

$c=70*0.7538=52.766$ million miles.

(3) From the equation (i), the equation of the elliptical orbit of Mercury is

$(x^2)/(70^2)+(46^2)/(b^2)=1$

$\Rightarrow (x^2)/(4900)+(y^2)/(2116)=1.$

Which of the following numbers has 4 significant figures? A. 3020.5 B. 0.003020 C. 3.2005 D. 0.0325

Answers

Answer:

Step-by-step explanation:

This is because the leading zero isn't counted, but the trailing zero after the decimal point is, making it four.

What times what equals 96

Answers

The requried 96 can be expressed as the product of two numbers in five different ways,

96 = 2 x 48

96 = 3 x 32

96 = 4 x 24

96 = 6 x 16

96 = 8 x 12

What is the factors?

A number or algebraic expression that evenly divides another number or expression—i.e., leaves no remainder—is referred to as a factor.

Here,
To find two numbers that multiply to 96, we can factorize 96 into its prime factors:

96 = 2 x 2 x 2 x 2 x 2 x 3

Now we can group these factors into pairs, where each pair multiplies to 96,

2 x 48 = 96

3 x 32 = 96

4 x 24 = 96

6 x 16 = 96

8 x 12 = 96

Learn more about Factors here:
brainly.com/question/24182713
#SPJ5

Factors of 96: 1,2,3,4,6,8,12,16,24,32,48,96

So 48 x 2 = 96

Solve 9x2 + 12x + 4 = 0. By using the quadratic formula

Answers

so 9x^2+12x+4=0

so the quadratic formulat is (-b+/-(squrt(b^2-4ac)))/(2a)=x
subsitute
ax^2+bx+c=

9=a
12=b
4=c

(-12+/-(squrt(12^2-4(9)(4))))/(2(9))=x
(-12+/-(squrt(144^2-144)))/18)=x

(-12+/-0)/18)=x
-12/18=x
-2/3=x

$Discriminant= b^(2)-4.a.c \n \n We\:need\:to:-b+ √(discriminant) /2a \n \n 9x^(2) +12x+4=0 \n => 12^(2) -4.9.4 \n 144-144=0 \n √(0) =0 \n \n -12+ 0/18= (-12)/(18) = (-2)/(3) \n \n That`s\: enough=>x= (-2)/(3) \n \n \framebox[1.1\width]{Good Luck!} \par$