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2 years ago

The length of a rectangle is five inches more than four times it’s width. If the perimeter is 90 inches, find its dimensions

1 answer:

3 0

90 = 2(x + 5 + 4x)

90 = 2(5x + 5)

90 = 10x + 10

80 = 10x

x = 8

So the width is 8 and the length is 37
I hope this helps.

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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

2 years ago

List the steps used to solve the equation below.

pychu [463]

Answer:

- 1

Step-by-step explanation:

2x + 3 = x - 4

2x - x = - 4 + 3

x = - 1

The solution to the above equation is - 1.

4 0

3 years ago

2a-6=4a Solve for a Check your work

algol [13]

Answer:

-3

Step-by-step explanation:

2a - 6 = 4a

subtract 2a giving you -6 = 2a

divide by 2 from both sides so that a will be by itself

giving you -6 ÷ 2 = a

-6 ÷ 2 = -3

so a = -3

5 0

2 years ago

How to solve 4(a-2)=3(a+4)

Blababa [14]

Use the distributive property.
4a - 8 = 3a + 12
Arrange the like terms.
4a - 3a = 12 + 8
a = 20
That is the answer. ☺️✌️

5 0

3 years ago

Which number line best shows how to solve -4-(-8)

Rama09 [41]

Answer:

The first point should be plotted at -4, then there should be a line that goes up 8 units and gives us a final destination of 4.

7 0

2 years ago