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3 years ago

The length of a rectangle is five centimeters less than width. Find the dimensions of the

Mathematics

1 answer:

kondaur [170]3 years ago

8 0

Answer:

w is 10 and l is 5

Step-by-step explanation:

l=w-5

lw=50

w^2-5w-50=(w-10)(w+5) since the negative solution does not make sense w=10 and therefore l is 5 so the length is 5 while the width is 10

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A ladder 20 feet long is leaning against the wall of a house. The base of the ladder is pulled away from the wall at a rate of 2

alukav5142 [94]

Answer:

0.17 °/s

Step-by-step explanation:

Since the ladder is leaning against the wall and has a length, L and is at a distance, D from the wall. If θ is the angle between the ladder and the wall, then sinθ = D/L.

We differentiate the above expression with respect to time to have

dsinθ/dt = d(D/L)/dt

cosθdθ/dt = (1/L)dD/dt

dθ/dt = (1/Lcosθ)dD/dt where dD/dt = rate at which the ladder is being pulled away from the wall = 2 ft/s and dθ/dt = rate at which angle between wall and ladder is increasing.

We now find dθ/dt when D = 16 ft, dD/dt = + 2 ft/s, and L = 20 ft

We know from trigonometric ratios, sin²θ + cos²θ = 1. So, cosθ = √(1 - sin²θ) = √[1 - (D/L)²]

dθ/dt = (1/Lcosθ)dD/dt

dθ/dt = (1/L√[1 - (D/L)²])dD/dt

dθ/dt = (1/√[L² - D²])dD/dt

Substituting the values of the variables, we have

dθ/dt = (1/√[20² - 16²]) 2 ft/s

dθ/dt = (1/√[400 - 256]) 2 ft/s

dθ/dt = (1/√144) 2 ft/s

dθ/dt = (1/12) 2 ft/s

dθ/dt = 1/6 °/s

dθ/dt = 0.17 °/s

8 0

3 years ago

Please help! I dont understand this!

deff fn [24]

75 is equivalent to 0.75 and

3 devided by 4 is 0.75 i would choose A and B

3 0

3 years ago

NEED NOW PLEASE..........

Arada [10]

Answer: C. -12 - 3 + 9

Step-by-step explanation:

-12 because the fish are 12 m below the ocean.

-3 because the fish swim down.

+9 because the fish swim up.

8 0

3 years ago

Help solve this equation

Sveta_85 [38]

Answer:

If you're supposed to use elimination to find (x, y) the answer is (6, 1)

Step-by-step explanation:

Add:

2x+3y=15

x-3y= 3

y cancels out and left with...

2x=15

x=3

that becomes

3x=18

find x

18/3= 6

x=6

Then plug in x (which is 6) to one of the equations to solve for y

6- 3y= 3

-3y= 3-6

-3y= -3

y= 1

(x, y) equals (6, 1)

3 0

3 years ago

Betsy, a recent retiree, requires $6,000 per year in extra income. She has $70,000 to invest and can invest in B-rated bonds pay

viva [34]

Answer:

The amount of money invested at 13% is $39,000 while the amount of money invested at 3% is $31,000

Step-by-step explanation:

Extra income required per year $6,000

Total investment = $70,000

Let x = amount of money Invested at 13% ;

Then 70,000 - x = amount of money Invested at 3%

Total interest required = $6,000

Thus;

x × 0.13 + (70,000 - x) × 0.03 = 6,000

⇒ 0.13x + 2100 - 0.03x = 6,000

0.13x - 0.03x + 2100 = 6,000

0.1x = 6,000 - 2100

0.1x = 3,900

x = 3,900/0.1

x = $39,000

Thus, what this means is that the amount of money invested at 13% is $39,000 while the amount of money invested at 3% is $70,000 - $39,000 = $31,000

PS ; IN CASE YOU ARE WONDERING WHERE 1.3 AND 0.3 CAME INTO THE CALCULATION, 13% IS (13/100 = 0.13) WHILE 3% IS (3/100 = 0.03)

8 0

3 years ago