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2 years ago

Joseph has 22 gallons of fertilizer. He uses 7 quarts to fertilize his plants.

Mathematics

1 answer:

nata0808 [166]2 years ago

5 0

Joseph would have 81 quarts of fertilizer left

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3 years ago

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s2008m [1.1K]

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Step-by-step explanation:

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2 years ago

Read 2 more answers

Rachel multiplied each side of x ≥ 2 by 3. She wrote the result as 3x ≤ 6. Explain the error Rachel made.

andrey2020 [161]

Answer:

Her mistake was to change the inequality sign from ≥ to ≤.

The sign only changes when you multiply or divide both sides of an inequality by a negative number.

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2 years ago

A rectangular storage container with an open top is to have a volume of 24 cubic meters. The length of its base is twice the wid

Mariana [72]

Answer:

419.25

Step-by-step explanation:

The calculation of the cost of materials for the cheapest such container is shown below:-

We assume

Width = x

Length = 2x

Height = h

where, length = $2 \times width$

Base area = lb

= $2x^2$

Side area = 2lh + 2bh

= 2(2x)h + 2(x)h

= 4xh + 2xh

Volume = 24 which is lbh = 24

$h = \frac{24}{2x^2} \\\\ h = \frac{12}{x^2}$

Now, cost is

$= 13(2x^2) + 9(4xh + 2xh)\\\\ = 13(2x^2) + 9(4x + 2x)\times \frac{12}{x^2} \\\\ = 26x^2 + \frac{648}{x}$

now we have to minimize C(x)

So, we need to compute the C'(x)

$= 52x - \frac{648}{x^2}$

C"(x) $= 52x - \frac{1,296}{x^3}$

now for the critical points, we will solve the equation C'(x) = 0

$= 52x - \frac{648}{x^2} = 0\\\\ x = \frac{648}{52}^{\frac{1}{3}}$

$C" = ((\frac{648}{52} ^{\frac{1}{3} } = 52 + \frac{1296}{(\frac{648}{52})^\frac{1}{3} )^3}\\\\ = 52 + \frac{1296}{\frac{648}{52} } >0$

So, x is a point of minima that is

= $(\frac{648}{52} )^\frac{1}{3}$

Now, Base material cost is

$= 13(2x^2)\\\\ = 26(\frac{648}{52} )^\frac{2}{3}$

= 139.75

Side material cost is

$= \frac{648}{x} \\\\ = \frac{648}{(\frac{648}{52})^\frac{1}{3} }$

= 279.50

and finally

Total cost is

= 139.75 + 279.50

= 419.25

4 0

3 years ago

What is the total surface area

Stels [109]

We have two right triangles and three different rectangles.

The formula of an area of a right triangle:

$A_T=\dfrac{1}{2}l_1l_2$

l₁, l₂ - legs

We have l₁ = 20cm and l₂ = 21cm. Substitute:

$A_T=\dfrac{1}{2}(20)(21)=(10)(21)=210\ cm^2$

The formula of an area of a rectangle:

$A_R=lw$

l - length

w - width

We have:

rectangle #1: l = 22cm, w = 29cm

$A_{R1}=(22)(29)=638\ cm^2$

rectangle #2: l = 22cm, w = 21cm

$A_{R2}=(22)(21)=462\ cm^2$

rectangle #3: l = 22cm, w = 20cm

$A_{R3}=(22)(20)=440\ cm^2$

The total Surface Area of the triangular prism:

$S.A.=2A_T+A_{R1}+A_{R2}+A_{R3}\\\\S.A.=2\cdot210+638+462+440=1960\ cm^2$

3 0

2 years ago