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3 years ago

Jamal planted 53 fewer flowers than Heidi. Write an expression to show how many flowers Heidi planted.

Mathematics

2 answers:

Sergeu [11.5K]3 years ago

6 0

Answer:

y = x + 53

Step-by-step explanation:

Let x be the number of flowers Jamal planted and y the number of flowers Heidi planted.

Jamal planted 53 fewer flowers than Heidi:

x = y - 53

Isolate the y.

x + 53 = y (Change the - sign to + sign when switching from different sides of an equation)

y = x + 53

Dovator [93]3 years ago

3 0

Answer: $j=h-53$

Step-by-step explanation:

Let h be the number of flowers Heidi planted, and j the number for Jamal.

$j=h-53$

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The circumference of a sphere was measured to be 76 cm with a possible error of 0.5 cm. (a) Use differentials to estimate the ma

andreev551 [17]

The maximum error in the calculated surface area is 24.19cm² and the relative error is 0.0132.

Given that the circumference of a sphere is 76cm and error is 0.5cm.

The formula of the surface area of a sphere is A=4πr².

Differentiate both sides with respect to r and get

dA÷dr=2×4πr

dA÷dr=8πr

dA=8πr×dr

The circumference of a sphere is C=2πr.

From above the find the value of r is

r=C÷(2π)

By using the error in circumference relation to error in radius by:

Differentiate both sides with respect to r as

dr÷dr=dC÷(2πdr)

1=dC÷(2πdr)

dr=dC÷(2π)

The maximum error in surface area is simplified as:

Substitute the value of dr in dA as

dA=8πr×(dC÷(2π))

Cancel π from both numerator and denominator and simplify it

dA=4rdC

Substitute the value of r=C÷(2π) in above and get

dA=4dC×(C÷2π)

dA=(2CdC)÷π

Here, C=76cm and dC=0.5cm.

Substitute this in above as

dA=(2×76×0.5)÷π

dA=76÷π

dA=24.19cm².

Find relative error as the relative error is between the value of the Area and the maximum error, therefore:

$\begin{aligned}\frac{dA}{A}&=\frac{8\pi rdr}{4\pi r^2}\\ \frac{dA}{A}&=\frac{2dr}{r}\end$

As above its found that r=C÷(2π) and r=dC÷(2π).

Substitute this in the above

$\begin{aligned}\frac{dA}{A}&=\frac{\frac{2dC}{2\pi}}{\frac{C}{2\pi}}\\ &=\frac{2dC}{C}\\ &=\frac{2\times 0.5}{76}\\ &=0.0132\end$

Hence, the maximum error in the calculated surface area with the circumference of a sphere was measured to be 76 cm with a possible error of 0.5 cm is 24.19cm² and the relative error is 0.0132.

Learn about relative error from here brainly.com/question/13106593

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1. Which addition fact can

Andrews [41]

Answer:

The Answer is B 8+ 6=14

Step-by-step explanation:

14-8=6

8+6=14

14-6=8

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1 year ago

Work out m and c for the line: 2 x + 3 y + 4 = 0

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Answer:

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Answer:

m = - , c = -

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

Given

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3 years ago

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A shipping container in the shape of a rectangular solid must have a volume of 84 cubic meters. The client tells the manufacture

Zolol [24]

Answer:

The Length , width and height of solid are 4 feet , 3 feet and 7 feet respectively.

Step-by-step explanation:

Let the width of rectangular solid be x

We are given that the length of the container must be one meter longer than the width

So, Length of solid = x+1

We are also given that height must be one meter greater than twice the width

So, Height of solid = 2x+1

So, Volume of solid = $Length \times Width \times height$

Volume of solid = $(x+1) \times x \times (2x+1)$

Volume of solid = $(x^2+x)(2x+1)$

Volume of solid = $2x^3+x^2+2x^2+x=2x^3+3x^2+x$

We are given that a rectangular solid must have a volume of 84 cubic meters

So, $2x^3+3x^2+x=84\\2x^3+3x^2+x-84=0\\(x-3)(2x^2+9x-28)=0\\$

On equating

x-3=0

x=3

So, Length of solid = x+1=3+1 = 4 feet

Height of solid = 2x+1 =2(3)+1=7 feet

Width of solid = 3 feet

Hence The Length , width and height of solid are 4 feet , 3 feet and 7 feet respectively.

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3 years ago