All categories

2 years ago

Evaluate the expression. (13^2 - 12^2) ÷ 5

Mathematics

1 answer:

otez555 [7]2 years ago

5 0

Answer:

5

Step-by-step explanation:

(13^2 - 12^2) ÷ 5

(169 - 144) ÷ 5

25 ÷ 5

5

You might be interested in

If the area of the outer square is 4x2, then the area of the inner square is

konstantin123 [22]

<span>Answered by the following sums - Outer square area = 4x^2 side of the square = 2x which is equal to diameter of circle == diameter of inner square. radius of circle = x diameter of outer square = 2*sqrt(2)*x consider side of inner square = a so a^2 + a^2 = (2x)^2 2a^2 = 4x^2 a = x*sqrt(2) So area of inner square will be = 2x^2</span>

6 0

3 years ago

Please help. What is the range of f(x)=20x+4

Advocard [28]

Answer:

(−∞,∞)

Step-by-step explanation:

THe range is Infinity

7 0

2 years ago

Find the volume V of the solid obtained by rotating the region bounded by the given curves about the specified line.? y = 2 + se

sertanlavr [38]

Answer:

The volume of the solid is: $\mathbf{V = \pi [ \dfrac{8 \pi}{3} - 2\sqrt{3}]}$

Step-by-step explanation:

GIven that :

$y = 2 + sec \ x , -\dfrac{\pi}{3} \leq x \leq \dfrac{\pi}{3} \\ \\ y = 4\\ \\ about \ y \ = 2$

This implies that the distance between the x-axis and the axis of the rotation = 2 units

The distance between the x-axis and the inner ring is r = (2+sec x) -2

Let R be the outer radius and r be the inner radius

By integration; the volume of the of the solid can be calculated as follows:

$V = \pi \int\limits^{\dfrac{\pi}{3}}_{\dfrac{-\pi}{3}} [(4-2)^2 - (2+ sec \ x -2)^2]dx \\ \\ \\ V = \pi \int\limits^{\dfrac{\pi}{3}}_{\dfrac{-\pi}{3}} [(2)^2 - (sec \ x )^2]dx \\ \\ \\ V = \pi \int\limits^{\dfrac{\pi}{3}}_{\dfrac{-\pi}{3}} [4 - sec^2 \ x ]dx$

$V = \pi [4x - tan \ x]^{\dfrac{\pi}{3}}_{\dfrac{-\pi}{3}} \\ \\ \\ V = \pi [4(\dfrac{\pi}{3}) - tan (\dfrac{\pi}{3}) - 4(-\dfrac{\pi}{3})+ tan (-\dfrac{\pi}{3})] \\ \\ \\ V = \pi [4(\dfrac{\pi}{3}) - tan (\dfrac{\pi}{3}) + 4(\dfrac{\pi}{3})- tan (\dfrac{\pi}{3})] \\ \\ \\ V = \pi [8(\dfrac{\pi}{3}) - 2 \ tan (\dfrac{\pi}{3}) ]$

$\mathbf{V = \pi [ \dfrac{8 \pi}{3} - 2\sqrt{3}]}$

7 0

3 years ago

What is the result when the number 24 is increased by 6%?

Delicious77 [7]

Answer:

24 increased by 6% = 25.44

Step-by-step explanation:

Introduction. Percent, p%

'Percent (%)' means 'out of one hundred':

p% = p 'out of one hundred',

p% is read p 'percent',

p% = p/100 = p ÷ 100.

6% = 6/100 = 6 ÷ 100 = 0.06.

100% = 100/100 = 100 ÷ 100 = 1.

ncrease the number by 6% of its value.

Percentage increase = 6% × 24

New value = 24 + Percentage increase

Calculate the New Value

New value =

24 + Percentage increase =

24 + (6% × 24) =

24 + 6% × 24 =

(1 + 6%) × 24 =

(100% + 6%) × 24 =

106% × 24 =

106 ÷ 100 × 24 =

106 × 24 ÷ 100 =

2,544 ÷ 100 =

25.44

Calculate absolute change (actual difference)

Absolute change (actual difference) =

New value - 24 =

25.44 - 24 =

1.44

Proof.

Calculate percentage increase...

... And see if we get as a result

the absolute change (actual difference).

Percentage increase =

6% × 24 =

6 ÷ 100 × 24 =

6 × 24 ÷ 100 =

144 ÷ 100 =

1.44

So we have proven that the calculations are correct.

For positive numbers

Absolute change (actual difference) =

Percentage increase

Answer:

24 increased by 6% = 25.44

Absolute change (actual difference):

25.44 - 24 = 1.44

8 0

2 years ago

Read 2 more answers

Megan and Suzanne each have a plant. They track the growth of their plants for four weeks.

Alenkinab [10]

Answer: Megan's at 3 inches per week

3 0

2 years ago

Evaluate the expression. (13^2 - 12^2) ÷ 5​

Evaluate the expression. (13^2 - 12^2) ÷ 5