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2 years ago

Write the ratio 3 : 12 in its simplest form

Mathematics

2 answers:

Agata [3.3K]2 years ago

5 0

3:12
3/12=1:4

This, 1:4 is your answer

ohaa [14]2 years ago

4 0

Answer:

3 : 12

1 : 6

The final result is 1 : 6

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For the function y=3x2: (a) Find the average rate of change of y with respect to x over the interval [3,6]. (b) Find the instant

nirvana33 [79]

Answer:

The instantaneous rate of change of $y$ with respect to $x$ at the value $x = 3$ is 18.

Step-by-step explanation:

a) Geometrically speaking, the average rate of change of $y$ with respect to $x$ over the interval by definition of secant line:

$r = \frac{y(b) -y(a)}{b-a}$ (1)

Where:

$a$ , $b$ - Lower and upper bounds of the interval.

$y(a)$ , $y(b)$ - Function exaluated at lower and upper bounds of the interval.

If we know that $y = 3\cdot x^{2}$ , $a = 3$ and $b = 6$ , then the average rate of change of $y$ with respect to $x$ over the interval is:

$r = \frac{3\cdot (6)^{2}-3\cdot (3)^{2}}{6-3}$

$r = 27$

The average rate of change of $y$ with respect to $x$ over the interval $[3,6]$ is 27.

b) The instantaneous rate of change can be determined by the following definition:

$y' = \lim_{h \to 0}\frac{y(x+h)-y(x)}{h}$ (2)

Where:

$h$ - Change rate.

$y(x)$ , $y(x+h)$ - Function evaluated at $x$ and $x+h$ .

If we know that $x = 3$ and $y = 3\cdot x^{2}$ , then the instantaneous rate of change of $y$ with respect to $x$ is:

$y' = \lim_{h \to 0} \frac{3\cdot (x+h)^{2}-3\cdot x^{2}}{h}$

$y' = 3\cdot \lim_{h \to 0} \frac{(x+h)^{2}-x^{2}}{h}$

$y' = 3\cdot \lim_{h \to 0} \frac{2\cdot h\cdot x +h^{2}}{h}$

$y' = 6\cdot \lim_{h \to 0} x +3\cdot \lim_{h \to 0} h$

$y' = 6\cdot x$

$y' = 6\cdot (3)$

$y' = 18$

The instantaneous rate of change of $y$ with respect to $x$ at the value $x = 3$ is 18.

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2 years ago

316.7 gallons to pints

svet-max [94.6K]

316.7 gal = 2533.6 pints.

8 0

3 years ago

Read 2 more answers

What is the term, coefficient, constant, and factor of 1/2(base1 + base2)h? (Formula used to find area of trapezoid)

vovangra [49]

Answer:

i. Term = $\frac{b_{1}h }{2}$ + $\frac{b_{2}h }{2}$

ii. Coefficient = $\frac{1}{2}$

iii. Constant = $\frac{1}{2}$

iv. Factor = $\frac{h}{2}$

Step-by-step explanation:

A trapezoid is a quadrilateral which has its base parallel to the opposite side. It's area can be determined by;

Area of trapezium = $\frac{1}{2}$ ( $b_{1}$ + $b_{2}$ )h

Where $b_{1}$ is the measure of length of its fist base, $b_{2}$ is the measure of its second base and h is its height.

Considering the given question,

Term = $\frac{b_{1}h }{2}$ + $\frac{b_{2}h }{2}$

Coefficient = $\frac{1}{2}$

Constant = $\frac{1}{2}$

Factor = $\frac{h}{2}$

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2 years ago

There are 5 green balls, 2 orange balls, 4 purple balls, and 1 pink ball in a bucket. You pick 1 ball from

bagirrra123 [75]

B
The purple balls constitute 1/3 of the amount of balls there, so you’re that likely to pluck one out.

8 0

2 years ago

Please help with this question I will pass if I get it right

Alex17521 [72]

9514 1404 393

Answer:

∠K = ∠M = 55°

Step-by-step explanation:

The two marked angles are opposite the sides marked as congruent. That means the angles are congruent, so we have ...

4x -1 = 2x +27

2x = 28 . . . . . . . . add 1-2x to both sides

x = 14

4x -1 = 4(14) -1 = 55

The measures of the angles are ...

∠K = ∠M = 55°

4 0

2 years ago