All categories

3 years ago

The difference between a number divided by 3 and 4 is 21

Mathematics

1 answer:

Alona [7]3 years ago

8 0

Answer:

3*4=12

12+12=24

24-3=21

You might be interested in

Consider the curve defined by the equation y=6x2+14x. Set up an integral that represents the length of curve from the point (−2,

torisob [31]

Answer:

32.66 units

Step-by-step explanation:

We are given that

$y=6x^2+14x$

Point A=(-2,-4) and point B=(1,20)

Differentiate w.r. t x

$\frac{dy}{dx}=12x+14$

We know that length of curve

$s=\int_{a}^{b}\sqrt{1+(\frac{dy}{dx})^2}dx$

We have a=-2 and b=1

Using the formula

Length of curve= $s=\int_{-2}^{1}\sqrt{1+(12x+14)^2}dx$

Using substitution method

Substitute t=12x+14

Differentiate w.r t. x

$dt=12dx$

$dx=\frac{1}{12}dt$

Length of curve= $s=\frac{1}{12}\int_{-2}^{1}\sqrt{1+t^2}dt$

We know that

$\sqrt{x^2+a^2}dx=\frac{x\sqrt {x^2+a^2}}{2}+\frac{1}{2}\ln(x+\sqrt {x^2+a^2})+C$

By using the formula

Length of curve= $s=\frac{1}{12}[\frac{t}{2}\sqrt{1+t^2}+\frac{1}{2}ln(t+\sqrt{1+t^2})]^{1}_{-2}$

Length of curve= $s=\frac{1}{12}[\frac{12x+14}{2}\sqrt{1+(12x+14)^2}+\frac{1}{2}ln(12x+14+\sqrt{1+(12x+14)^2})]^{1}_{-2}$

Length of curve= $s=\frac{1}{12}(\frac{(12+14)\sqrt{1+(26)^2}}{2}+\frac{1}{2}ln(26+\sqrt{1+(26)^2})-\frac{12(-2)+14}{2}\sqrt{1+(-10)^2}-\frac{1}{2}ln(-10+\sqrt{1+(-10)^2})$

Length of curve= $s=\frac{1}{12}(13\sqrt{677}+\frac{1}{2}ln(26+\sqrt{677})+5\sqrt{101}-\frac{1}{2}ln(-10+\sqrt{101})$

Length of curve= $s=32.66$

5 0

3 years ago

Leon scored 20 points in yesterday's game.That was 2 more than twice the number of points Trey scored.Write and solve an equatio

Sveta_85 [38]

Answer:

The best answer is C.

Step-by-step explanation:

8 0

4 years ago

Order these equations to match the steps used to solve the equation

gtnhenbr [62]

Answer:

x = 7/5

Step-by-step explanation:

2(5x - 3) = 8

Step 1: Distributive property

10x - 6 = 8

Step 2: Addition property of equality

Add 6 to both sides of the equation

10x - 6 + 6 = 8 + 6

10x = 14

Step 3: Division property of equality

Divide both sides by 10

10x/10 = 14/10

x = 7/5

8 0

3 years ago

Read 2 more answers

Estimate the time juanita will arive at her aount's home 320 miles away if she leaves at 9:00 am.,drives about 60 miles per hour

Airida [17]

She would get there around 3:30pm

8 0

3 years ago

Explain the process for solving this logarithmic equation.

alexdok [17]

Log3(x)+log3(4)-2log3(3)=2using properties of multiplication of logarithms,log3(x)+log3(4)-log3(3^2)=2log3(x)+log3(4)-log3(9)=2using properties of addition of logarithms,log3(x*4/9)=2raise both sides to exponent of base 33^log3(x*4/9)=3^24x/9=9x=81/4

7 0

3 years ago