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maks197457 [2]
3 years ago
9

.

Mathematics
1 answer:
babunello [35]3 years ago
4 0
<span>From the problem, you can get this equation:
Jane is 2 years older than Sally
J=z+2
David is 4 times older than Jane.
D=4J

</span>Write two equivalent expressions that represent David’s age in terms of Sally’s age, z, and explain how the two expressions relate to one another.<span>Sally is z years old.
From the 2 equation above, you can get:
</span>D=4J
D=4(z+2)
D=4z+8

D-8=4z
(D-8)/4=z
The two equivalent expression would be D=4z+8 and (D-8)/4=z

The expression that more usefull would be D=4z+8 if you want to determine David age.
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Step-by-step explanation:

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The square root of 78 is a number which when multiplied by itself results in 78. The square root of 78 is denoted by √78. 78 can be expressed as 78 = 2 × 3 × 13. Hence, on simplifying square root of 78 is written as √78

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8 0
3 years ago
You have a wire that is 20 cm long. You wish to cut it into two pieces. One piece will be bent into the shape of a square. The o
Aleksandr [31]

Answer:

Therefore the circumference of the circle is =\frac{20\pi}{4+\pi}

Step-by-step explanation:

Let the side of the square be s

and the radius of the circle be r

The perimeter of the square is = 4s

The circumference of the circle is =2πr

Given that the length of the wire is 20 cm.

According to the problem,

4s + 2πr =20

⇒2s+πr =10

\Rightarrow s=\frac{10-\pi r}{2}

The area of the circle is = πr²

The area of the square is = s²

A represent the total area of the square and circle.

A=πr²+s²

Putting the value of s

A=\pi r^2+ (\frac{10-\pi r}{2})^2

\Rightarrow A= \pi r^2+(\frac{10}{2})^2-2.\frac{10}{2}.\frac{\pi r}{2}+ (\frac{\pi r}{2})^2

\Rightarrow A=\pi r^2 +25-5 \pi r +\frac{\pi^2r^2}{4}

\Rightarrow A=\pi r^2\frac{4+\pi}{4} -5\pi r +25

For maximum or minimum \frac{dA}{dr}=0

Differentiating with respect to r

\frac{dA}{dr}= \frac{2\pi r(4+\pi)}{4} -5\pi

Again differentiating with respect to r

\frac{d^2A}{dr^2}=\frac{2\pi (4+\pi)}{4}    > 0

For maximum or minimum

\frac{dA}{dr}=0

\Rightarrow \frac{2\pi r(4+\pi)}{4} -5\pi=0

\Rightarrow r = \frac{10\pi }{\pi(4+\pi)}

\Rightarrow r=\frac{10}{4+\pi}

\frac{d^2A}{dr^2}|_{ r=\frac{10}{4+\pi}}=\frac{2\pi (4+\pi)}{4}>0

Therefore at r=\frac{10}{4+\pi}  , A is minimum.

Therefore the circumference of the circle is

=2 \pi \frac{10}{4+\pi}

=\frac{20\pi}{4+\pi}

4 0
2 years ago
What do I do here is the math equation : Evan walked his dog 2.8 kilometers around the perimeter of a park.The is four time as m
Morgarella [4.7K]

Answer:

2.8÷4

Step-by-step explanation:

if 2.8 is the 4th lap, you have to divide it by 4 to get the 1st lap.

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