MATHEMATICS COLLEGE

The difference between seven and triple the input

Answers

Answer 1

Answer:

Answer: 3x - 7

x = some input number

3x = triple the input

3x - 7 = difference of triple the input and 7

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A piece of rope there is 28 feet long is cut into two pieces. One is use to form a circle and others used to form a square. Write a function G representing the area of the square as a function of the radius of the circle R

Answers

The function g representing the area of the square as a function of the radius of the circle r is given as:

$g(r) = 49 - 22r + (121r^2)/(49)$

Solution:

Given that,

length of rope = 28 feet

Let "c" be the circumference of circle

Let "p" be the perimeter of square

Therefore,

length of rope = circumference of circle + perimeter of square

c + p = 28 ------- eqn 1

The circumference of circle is given as:

$c = 2 \pi r$

Where, "r" is the radius of circle

Substitute the above circumference in eqn 1

$2 \pi r + p = 28$

$p = 28 - 2 \pi r$ ----------- eqn 2

If "a" is the length of each side of square, then the perimeter of sqaure is given as:

p = 4a

Substitute p = 4a in eqn 2

$4a = 28 - 2 \pi r\n\na = (28 - 2 \pi r)/(4)\n\na = 7 - ( \pi r)/(2)$

The area of square is given as:

$area = (side)^2\n\narea = a^2$

Substitute the value of "a" in above area expression

$area = (7 - ( \pi r)/(2))^2$ ------ eqn 3

We know that,

$(a - b)^2 = a^2 - 2ab + b^2$

Therefore eqn 3 becomes,

$area = 7^2 -2(7)((\pi r)/(2)) + (( \pi r)/(2))^2\n\narea = 49 - 7 \pi r + ( (\pi)^2 r^2 )/(4)$

$\text{ substitute } \pi = (22)/(7)$

$area = 49 - 7 * (22)/(7) * r + ((22)/(7))^2 * (r^2 )/(4)\n\narea = 49 - 22r + (121)/(49) * r^2\n\narea = 49 - 22r + (121r^2)/(49)$

Let g(r) represent the area of the square as a function of the radius of the circle r, then we get

$g(r) = 49 - 22r + (121r^2)/(49)$

Thus the function is found

Find the area of the triangle Please help

Answers

Answer:

14m^2

Step-by-step explanation:

Area of a triangle is - 1/2 base times hight

two triangels find the srea of both and add them

4x4x1/2 = 16x1/2 = 8m

3x4x1/2 = 12x1/2 = 6m

6m + 8m = 14m

Which of the following scatterplots would have a trend line with a positive slope?

Answers

the first one will be positive!

Answer:

It's the first answer.

Step-by-step explanation:

As demonstrated through the image, the slope increases. Thus making it a positive slope.

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Answers

Answer:

c. One sided t-test

Step-by-step explanation:

One sided t test because we want to compare two means and alternative hypothesis is directional.

Using the unit circle, determine the value of sin 450°

Answers

Answer:

Step-by-step explanation:

To find the value of sin 450 degrees using the unit circle, represent 450° in the form (1 × 360°) + 90° [∵ 450°>360°] ∵ sine is a periodic function, sin 450° = sin 90°.

Rotate ‘r’ anticlockwise to form a 90° or 450° angle with the positive x-axis.

The sin of 450 degrees equals the y-coordinate(1) of the point of intersection (0, 1) of unit circle and r.

Hence the value of sin 450° = y = 1

Answer:

To find the value of sin 450 degrees using the unit circle, represent 450° in the form (1 × 360°) + 90° [∵ 450°>360°] ∵ sine is a periodic function, sin 450° = sin 90°.

Jenny's chocolate bar is 34% cocoa. If the weight of the chocolate bar is 66 grams, how many grams of cocoa does it contain? Round youranswer to the nearest tenth.

Answers

Answer:

22.4 grams

Step-by-step explanation:

66 times 0.34 is 22.44

22.44 rounded to the nearest tenth is 22.4

hope i helped :)

Answer:

22.4 grams

Step-by-step explanation:

34% = 0.34

66 grams x 0.34 = 22.4 grams

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