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andrew11 [14]
3 years ago
13

Can someone use FOIL for this? pls help

Mathematics
1 answer:
Reptile [31]3 years ago
8 0

Answer:

xy^4+2x^3y^2+xy

Step-by-step explanation:

shown above. Hope this helps :]

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Given that 3^x = 4^y = 12^z, show that z = (xy)/(x+y).
irinina [24]
3^{x} = 4^{y} = 12^{z}
3^{x} = 4^{y} = (4 \cdot 3)^{z}
3^{x} = 4^{y} = 4^{z} \cdot 3^{z}

\text{Let a } = 3^{x} = 4^{y} = 4^{z} \cdot 3^{z}
log_3a = x
log_4a = y
log_{(4 \cdot 3)}a = z

Using change of base:
x = \frac{lna}{ln3}
y = \frac{lna}{ln4}
z = \frac{lna}{ln(4 \cdot 3)}

ln3 = \frac{lna}{x}
ln4 = \frac{lna}{y}
ln(4 \cdot 3) = \frac{lna}{z}

Now, ln(4 · 3) = ln(4) + ln(3)

\frac{lna}{z} = \frac{lna}{x} + \frac{lna}{y}
\frac{1}{z} = \frac{1}{x} + \frac{1}{y}
\frac{1}{z} = \frac{x + y}{xy}

\therefore z = \frac{xy}{x + y}
8 0
4 years ago
If the height of the cone, h, is 10 millimeters and the diameter of the base, d, is 30 millimeters, what is the volume of the co
nirvana33 [79]
750 pi mm cubed
1\3 (pi) r^2 h
8 0
3 years ago
For what value of the variable will the expression 8b-27 <br><br> -11
raketka [301]

Answer: 8b - 38

Step-by-step explanation:

8 0
3 years ago
At a gas station during a road trip, Gerard has $32.00 to spend on fuel and windshield washer fluid for his car. Fuel costs $2.7
Lemur [1.5K]

Answer:

Step-by-step explanation:

Total amount with Gerald = $32

Cost of fuel per gallon = $2.75

Cost of each bottle of windshield = $3

38 miles per gallon. If Gerard must fill his car with enough fuel to drive 250 miles,

Total gallons of fuel = 250 miles / 38 miles

= 6.5789473684210 gallons

Total cost of fuel = Total gallons of fuel × cost per gallon

= 6.5789473684210 × $2.75

= $18.1

Amount left for windshield = Total amount with Gerald - Total cost of fuel

= $32 - $18.1

= $13.9

what is the maximum number of bottles of windshield washer fluid Gerard can buy?

= Amount left for windshield / Cost of each bottle of windshield

= $13.9 / $3

= 4.6333333333333 bottles

Maximum number of bottles =

4 bottles

5 0
3 years ago
Find the dimensions of the regular corral split into 2 pens of the same size producing the greatest possible enclosed area given
mrs_skeptik [129]

Answer:

Length = 225 ft

Width = 150 ft

Step-by-step explanation:

If L is the length and W is the width, then:

900 = 2L + 3W

A = LW

Solve for W in the first equation:

3W = 900 − 2L

W = 300 − ⅔ L

Substitute into the area equation:

A = L (300 − ⅔ L)

A = 300L − ⅔ L²

Use calculus to find dA/dL and set to 0, or use the formula for vertex of a parabola.

Using calculus:

dA/dL = 300 − 4/3 L

0 = 300 − 4/3 L

L = 225

Using vertex formula:

L = -b / (2a)

L = -300 / (-4/3)

L = 225

Find the width:

W = 300 − ⅔ L

W = 150

You got the right answers, but the problem says to assume that the length is greater than the width.

3 0
3 years ago
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