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stira [4]
2 years ago
5

Find the dimensions of a rectangle with perimeter 76 m whose area is as large as possible. m (smaller value) m (larger value)

Mathematics
1 answer:
Sladkaya [172]2 years ago
5 0

Answer:

19 m

Step-by-step explanation:

Perimeter = 2(length + width) ; P = 2(l+w) - - (1)

Area = Length * width ; A = l*w - - - (2)

76 = 2(l+w)

76/2 = l+w

l+w = 38

l = 38 - w

Put l = 38 - w in (1)

A = (38-w)*w

A = 38w - w²

At maximum point:

dA/dw = 0

dA/dw = 38 - 2w

38 - 2w = 0

38 = 2w

w = 38/2

w = 19

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Which point corresponds to the real zero of the graph of y = log3 (x+2) - 1?
brilliants [131]

Answer:

(1, 0 )

Step-by-step explanation:

using the rule of logarithms

log_{b} x = n ⇒ x = b^{n} , then

y = log_{3} (x + 2) - 1

to find the zero let y = 0 , that is

log_{3} (x + 2) - 1 = 0 ( add 1 to both sides )

log_{3} (x + 2) = 1 , then

x + 2 = 3^{1} = 3 ( subtract 2 from both sides )

x = 1

the zero is (1, 0 )

8 0
2 years ago
fiona is going to jog once around the block she lives on. The block is retangular, and it is 180 yards long and 200 feet wide. H
prisoha [69]

Answer:

1480 feet

Step-by-step explanation:

180yd x 2 = 360yd

change to feet: 360 x 3 = 1080 feet

200ft x 2 = 400ft

1080 + 400 = 1480ft

5 0
3 years ago
Hi can anyone help me with this please ​
kupik [55]

Answer:

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Step-by-step explanation:

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6 0
3 years ago
Read 2 more answers
Write an equation of a line passing through the point (4,-9) and parallel to the line 3x-6y=30
sesenic [268]

The equation of a line in the slope intercept form is expressed as

y = mx + c

Where

m represents slope

c represents y intercept

The equation of the given line is expressed as

3x - 6y = 30

Rearranging it so that it will look like the slope intercept form, it becomes

6y = 3x - 30

Dividing both sides by 6, it becomes

6y/6 = 3x/6 - 30/6

y = x/2 - 5

Looking at the equation, slope, m = 1/2

If two lines are parallel, it means that they have equal slope. This means that the slope of the line parallel to the given line is 1/2

To determine the y intercept, c of the line passing through the point (4, - 9), we would substitute

x = 4, y = - 9 and m = 1/2 into the slope intercept equation. It becomes

- 9 = 1/2 * 4 + c

- 9 = 2 + c

c = - 9 - 2

c = - 11

By substtuting m = 1/2 and c = - 11 into the slope intercept equation, the equation of the line would be

y = x/2 - 11

7 0
1 year ago
three apples and four bananas cost $4.85 . three apples and ten bananas cost $8.75.Find the cost of an apple.
konstantin123 [22]
8.75-4.85= 3.90= cost of 6 bananas
3.9/6=0.65= cost of one banana
.65*4=2.60= cost of 4 bananas
4.85-2.60= 2.25= cost of 3 apples
2.25/3=.75= cost of an apple
5 0
3 years ago
Read 2 more answers
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