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lesya [120]
2 years ago
12

A dairy needs 357 gallons of milk containing 5% butterfat. How many gallons each of milk containing 7% butterfat and milk contai

ning 1% butterfat must be used to obtain the desired 357 gallons?
Mathematics
1 answer:
IrinaVladis [17]2 years ago
6 0

9514 1404 393

Answer:

  • 238 gallons 7%
  • 119 gallons 1%

Step-by-step explanation:

Let h represent the number of gallons of high butterfat content milk. Then 357-h will be the number of gallons of 1% milk. The total amount of butterfat in the mix is ...

  0.07h +0.01(357 -h) = 0.05(357)

  0.06h = 14.28 . . . . . . . . . . subtract 3.57, collect terms

  h = 238 . . . . . . . . . .  divide by 0.06

  357-h = 357 -238 = 119

238 gallons of 7% and 119 gallons of 1% are needed.

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Simplify the following radical <br> Sqrt 126x^13
fenix001 [56]

Answer:

\large\boxed{\sqrt{126x^{13}}=3x^6\sqrt{14x}}

Step-by-step explanation:

Domain:\ x\geq0\\\\\sqrt{126x^{13}}=\sqrt{9\cdot14\cdot x^{12+1}}\\\\\text{use}\ a^n\cdot a^m=a^{n+m}\\\\=\sqrt{9\cdot14\cdot x^{12}\cdot x^1}=\sqrt{9\cdot14\cdot x^{6\cdot2}\cdot x}\\\\\text{use}\ \sqrt{ab}=\sqrt{a}\cdot\sqrt{b}\ \text{and}\ (a^n)^m=a^{nm}\\\\=\sqrt9\cdot\sqrt{14}\cdot\sqrt{(x^6)^2}\cdot\sqrt{x}\\\\\text{use}\ \sqrt{a^2}=a\ \text{for}\ a\geq0\\\\=3\cdot\sqrt{14}\cdot x^6\cdot\sqrt{x}=3x^6\sqrt{14x}

3 0
3 years ago
From a circular cylinder of diameter 10 cm and height 12 cm are conical cavity of the same base radius and of the same height is
Nataliya [291]
<h3>Volume of the remaining solid = 628 cm^2</h3>

<h3>Whole surface area = 659.4 cm^2</h3>

Step-by-step explanation:

Now, Given that:-

Diameter (d) = 10 cm

So, Radius (r) = 10/2 = 5cm

Height of the cylinder = 12cm.

volume \: of \: the \: cylinder \:  =  \pi {r}^{2} h

=  > \pi \times  {5}^{2} \times  12 {cm}^{3}   = 300\pi {cm}^{3}

Radius of the cone = 5 cm.

Height of the cone = 12 cm.

slant \: height \: of \: the \: cone \:  =  \sqrt{ {h}^{2}  + \:  {r}^{2} }

=  >  \sqrt{ {5}^{2}+{12}^{2} } cm \:  = 13cm

Volume of the cone = 1/3 *πr^2h

=  >  \frac{1}{3} \pi \times  {5}^{2}   \times 12 {cm}^{3}  = 100\pi {cm}^{3}

therefore, the volume of the remaining solid

= 300\pi {cm}^{3}  - 100\pi {cm}^{3}  \\  = 200 \times 3.14 {cm}^{3}  = 628 {cm}^{3}

Curved surface of the cylinder =

2\pi \: rh \:  = 2\pi \times 5 \times 12 {cm}^{2}  \\  = 120\pi {cm}^{2} .

curved \: surface \: of \: the \: cone \:  = \pi \: rl \\  = \pi \times 5 \times 13 {cm}^{2}  \\  = 65\pi {cm }^{2} \\ area \: of \: (upper)circular \: base \: \\  of \: cylinder \:  =  \\ =  \pi \:  {r}^{2}  = \pi \times  {5}^{2}

therefore, The whole surface area of the remaining solid

= curved surface area of cylinder + curved surface area of cone + area of (upper) circular base of cylinder

= 120\pi {cm}^{2}  + 65\pi {cm }^{2}  + 25 \pi {cm}^{2}  \\  = 210 \times 3.14 {cm}^{2}  = 659.4 {cm}^{2}

<h3>Hope it helps you!!</h3>

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Step-by-step explanation:

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Answer:

0.7 or 5/7

Step-by-step explanation:

(1 3/7) ÷ 2 =

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