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3 years ago

The area of a lawn is 500 square feet the length is 5 feet longer then the width what are the length and width of the lawn

Mathematics

2 answers:

Oliga [24]3 years ago

6 0

Answer:

width: 20, length: 25

Step-by-step explanation:

area = length x width

since length is 5 feet longer than the width, length = width + 5

so we can replace length with width + 5

500 = (width + 5) x width

500 = w^2 + 5w

0 = w^2 + 5w - 500

w = 20, w = -25

width cannot bc -25 since you cannot have negative width

since width is 20, length is 25 since length = width + 5

width = 20, length = 25

Alona [7]3 years ago

5 0

Step-by-step explanation:

area is base x height so 5 x 100 because as I said area is base x height.

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If u = 2i - j; v= -5i + 4j and w = j find 4u (v -w).

Sedaia [141]

Answer:

-40

Explanation:

Given

u = 2i - j; v= -5i + 4j and w = j

Required

4u(v-w)

4u = 4(2i) = 8i

v - w = -5i + 4j - j

v - w = -5i + 3j

Substitute

4u(v-w)

= 8i(-5i+3j)

= -40(i*i) [since i*i = 1]

= -40

Hence the required solution is -40

5 0

1 year ago

PLEASE HELP

Studentka2010 [4]

The side length for a cube
with volume 8000cm3 = 8000^(1/3)= 20 m
Cheers,
Stan H.8000=S^38000=20^3
so the answer will be B

3 0

3 years ago

(10 points) Consider the initial value problem y′+3y=9t,y(0)=7. Take the Laplace transform of both sides of the given differenti

Rashid [163]

Answer:

The solution

$Y (s) = 9( -1 +3 t + e^{-3 t} ) + 7 e ^{-3 t}$

Step-by-step explanation:

Explanation:-

Consider the initial value problem y′+3 y=9 t,y(0)=7

Step(i):-

Given differential problem

y′+3 y=9 t

Take the Laplace transform of both sides of the differential equation

L( y′+3 y) = L(9 t)

Using Formula Transform of derivatives

L(y¹(t)) = s y⁻(s)-y(0)

By using Laplace transform formula

$L(t) = \frac{1}{S^{2} }$

Step(ii):-

Given

L( y′(t)) + 3 L (y(t)) = 9 L( t)

$s y^{-} (s) - y(0) + 3y^{-}(s) = \frac{9}{s^{2} }$

$s y^{-} (s) - 7 + 3y^{-}(s) = \frac{9}{s^{2} }$

Taking common y⁻(s) and simplification, we get

$( s + 3)y^{-}(s) = \frac{9}{s^{2} }+7$

$y^{-}(s) = \frac{9}{s^{2} (s+3}+\frac{7}{s+3}$

Step(iii):-

By using partial fractions , we get

$\frac{9}{s^{2} (s+3} = \frac{A}{s} + \frac{B}{s^{2} } + \frac{C}{s+3}$

$\frac{9}{s^{2} (s+3} = \frac{As(s+3)+B(s+3)+Cs^{2} }{s^{2} (s+3)}$

On simplification we get

9 = A s(s+3) +B(s+3) +C(s²) ...(i)

Put s =0 in equation(i)

9 = B(0+3)

B = 9/3 = 3

Put s = -3 in equation(i)

9 = C(-3)²

C = 1

Given Equation 9 = A s(s+3) +B(s+3) +C(s²) ...(i)

Comparing 'S²' coefficient on both sides, we get

9 = A s²+3 A s +B(s)+3 B +C(s²)

0 = A + C

put C=1 , becomes A = -1

$\frac{9}{s^{2} (s+3} = \frac{-1}{s} + \frac{3}{s^{2} } + \frac{1}{s+3}$

Step(iv):-

$y^{-}(s) = \frac{9}{s^{2} (s+3}+\frac{7}{s+3}$

$y^{-}(s) =9( \frac{-1}{s} + \frac{3}{s^{2} } + \frac{1}{s+3}) + \frac{7}{s+3}$

Applying inverse Laplace transform on both sides

$L^{-1} (y^{-}(s) ) =L^{-1} (9( \frac{-1}{s}) + L^{-1} (\frac{3}{s^{2} }) + L^{-1} (\frac{1}{s+3}) )+ L^{-1} (\frac{7}{s+3})$

By using inverse Laplace transform

$L^{-1} (\frac{1}{s} ) =1$

$L^{-1} (\frac{1}{s^{2} } ) = \frac{t}{1!}$

$L^{-1} (\frac{1}{s+a} ) =e^{-at}$

Final answer:-

Now the solution , we get

$Y (s) = 9( -1 +3 t + e^{-3 t} ) + 7 e ^{-3t}$

5 0

3 years ago

________________________

xenn [34]

✩ Answer:

✧･ﾟ: *✧･ﾟ:*✧･ﾟ: *✧･ﾟ:*✧･ﾟ: *✧･ﾟ:*

$\bold{Hello!}\\\bold{Your~answer~is~below!}$

✩ Step-by-step explanation:

✧･ﾟ: *✧･ﾟ:*✧･ﾟ: *✧･ﾟ:*✧･ﾟ: *✧･ﾟ:*

✺ Divide both sides by −3. Since −3 is negative, the inequality direction is changed:

-3 ÷ -3 = Cancels Out
Turns into: $\frac{-9}{-3} >5x-2$

✺ Divide −9 by −3 to get 3. Since they are both negatives it turns into a positive:

-9 ÷ -3 = 3
Turns into: $3 > 5x - 2$

✺ Swap sides so that all variable terms are on the left hand side. This changes the sign direction once more:

Turns into: $5x-2$

✺ Add 2 to both sides:

Turns into: $5x$

✺ Add 3 and 2 to get 5:

3 + 2 = 5
Turns into: $5x$

✺ Divide both sides by 5. Since 5 is positive, the inequality direction remains the same:

5 ÷ 5 = Cancels Out
Turns into: $x$

✺ Divide 5 by 5 to get 1:

5 ÷ 5 = 1

✺ So your answer is B, $\boxed{x$ .

(Number line is below.)

$Hope~this~helps~and,\\Best~of~luck!\\\\~~~~~-TotallyNotTrillex$

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How do you solve 4x+2=1/2x+17

DochEvi [55]

1) 4x + 2 = 1/2x + 17
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4) (3.5x)/3.5 = 15/ 3.5
5) x = 4.29 (rounded)

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3 years ago

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