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3 years ago

10

Maths Helppppp plsssss

1 answer:

Alexandra [31]3 years ago

7 0

Gradient in the UK = slope in the U.S.

The gradients of perpendicular lines are negative reciprocals.
That means the gradients of perpendicular lines are two numbers whose product is -1.

If you know the gradient of a line, to find the gradient of a perpendicular to that line, write the gradient as a fraction. Flip the fraction. Change the sign.

a) gradient = 4 = 4/1
flip the fraction: 1/4
change the sign: -1/4
The gradient of the perpendicular is -1/4

b) gradient = -3 = -3/1
flip the fraction: -1/3
change the sign: 1/3
The gradient of the perpendicular is 1/3

c) gradient = 2/3 (already a fraction)
flip the fraction: 3/2
change the sign: -3/2
The gradient of the a perpendicular is -3/2

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What equals 62? and what factors equal 62

nexus9112 [7]

The only factors that equal 62 are

62 • 1 = 62
and
31 • 2 = 62.

Hope this helps!

3 0

4 years ago

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Determine the dimensions of a rectangular solid (with a square base) with maximum volume if its surface area is 181.5 square cen

3241004551 [841]

Answer:

The base and height of the solid is 5.5cm

<em></em>

Step-by-step explanation:

Given

$Surface\ Area = 181.5cm^2$

Required

Determine the dimensions that maximizes the volume

Let the base dimension be x and the height be h

The volume is calculated as:

$Volume =x^2 * h$

$Volume =x^2h$

181.5 =x^2h

The surface area (S) is calculated as this:

$S = 2(x^2 + xh + xh)$

$S = 2(x^2 + 2xh)$

$S = 2x^2 + 4xh$

Substitute 181.5 for S

$181.5 = 2x^2 + 4xh$

Make h the subject:

$4xh = 181.5 - 2x^2$

$h = \frac{181.5 - 2x^2}{4x}$

Substitute $h = \frac{181.5 - 2x^2}{4x}$ in $Volume =x^2h$

$V = x^2(\frac{181.5 - 2x^2}{4x})$

$V = x(\frac{181.5 - 2x^2}{4})$

$V = \frac{1}{4}(x)(181.5 - 2x^2)$

$V = \frac{181.5x}{4} - \frac{2x^3}{4}$

$V = \frac{181.5x}{4} - \frac{x^3}{2}$

To get the maximum, we differentiate V with respect to t and set the differentiation to 0

$dV = \frac{181.5}{4} - \frac{3x^2}{2}$

Set to 0

$0 = \frac{181.5}{4} - \frac{3x^2}{2}$

$\frac{3x^2}{2} = \frac{181.5}{4}$

Multiply through by 4

$4 * \frac{3x^2}{2} = \frac{181.5}{4} * 4$

$2*3x^2 = 181.5$

$6x^2 = 181.5$

$x^2 = \frac{181.5}{6}$

$x^2 = 30.25$

$x = \sqrt{30.25$

$x = 5.5$

Recall that:

$h = \frac{181.5 - 2x^2}{4x}$

$h = \frac{181.5 - 2 * 5.5^2}{4 * 5.5}$

$h = \frac{181.5 - 60.5}{22}$

$h = \frac{121}{22}$

$h = 5.5$

So, we have:

$h = 5.5$

$x = 5.5$

<em>Hence, the base and height of the solid is 5.5cm</em>

7 0

3 years ago

Micah needs to buy some new shoes for football. At the sporting goods store, he finds 2 shoe pairs on sale for $24.80 each. He b

NikAS [45]

Answer:

$35.99

Step-by-step explanation:

He saved 22.38 so divide by two and you get 11.19 and add that to the price of each shoe on sale you get 35.99

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3 years ago

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blsea [12.9K]

Answer:

Step-by-step explanation:

Yeo

3 0

3 years ago

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What is the property of 93+(68+7)

inysia [295]

I'm pretty sure it's the Associative Property.

4 0

4 years ago