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3 years ago

What is an equation of the line that passes through

Mathematics

1 answer:

lys-0071 [83]3 years ago

3 0

Answer:

Step-by-step explanation:

For the perpendicular of an equation you need to flip the fraction and change the sign from positive to negative or if it's negative to positive. 3/2 is changed to -2/3 which when multiplied by -2 gives you 4/3 and 4/3+5/3 is equal to 3.

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A piece of cardboard measures 10 ft by 10 ft. Four equal squares of size x are removed from the corners. After removing the squa

Gnesinka [82]

Answer:

The value of x would be $\frac{5}{3}$

Step-by-step explanation:

Given,

The dimension of the cardboard = 10 ft by 10 ft,

∵ After removing four equal squares of size x ( in ft ) from the corners,

The dimension of the resultant box would be,

Length = ( 10 - 2x ) ft,

Width = ( 10 - 2x ) ft,

Height = x ft,

The volume of box,

$V=(10-2x)\times (10 - 2x)\times x=x(10-2x)^2 = x(100 - 40x + 4x^2)=100x - 40x^2 + 4x^3$

Differentiating with respect to x,

$V'=100 - 80x + 12x^2$

Again differentiating with respect to x,

$V''=-80 + 24x$

For maxima or minima,

$V'=0$

$\implies 100 - 80x + 12x^2 = 0$

$\implies 3x^2 - 20x + 25=0$

By quadratic formula,

$x=\frac{20\pm \sqrt{20^2-4\times 3\times 25}}{6}$

$x=\frac{20\pm \sqrt{400 - 300}}{6}$

$x=\frac{20\pm \sqrt{100}}{6}$

$x=\frac{20\pm 10}{6}$

$\implies x = \frac{10}{6}=\frac{5}{3}\text{ or } x = 5$

For x = 5/3, V'' = negative,

While for x = 5, V'' = Positive,

Hence, the value of x would be 5/3 ft for maximising the volume.

8 0

3 years ago

45% of all 1st graders at Sierra Elementary School are female students. This year there are 54 female 1st graders at Sierra Elem

Anit [1.1K]

Answer:

There are 120 1st graders at Sierra Elementary School this year

Step-by-step explanation:

Let n represent the total number of 1st graders at Sierra Elementary School

Since 45% of all 1st graders at Sierra Elementary School are female students and this year there are 54 female 1st graders, 45% of n is equal to 54

→ n( $\frac{45}{100}$ ) = 54

→ 45n = 5400

→ n = 120

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Marrrta [24]

The answer is
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