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Svet_ta [14]
3 years ago
7

A^2(64a^2-3)/3=27-4a^2/4

Mathematics
1 answer:
frutty [35]3 years ago
7 0
The answer is a = 3/4 = 0.75

First get rid of the paranthesis,
{a}^{2} (64 {a}^{2}  - 3) = 64 {a}^{4} -  3 {a}^{2}
Then set the denominators equal:
\frac{ 256 {a}^{4}  - 12 {a}^{2}}{12}  =  \frac{81 - 12 {a}^{2} }{12}
Then remove the denominators and solve:
256 {a}^{4}  - 12 {a}^{2}  = 81 - 12 {a}^{2}
Eliminate -12a^2 by adding 12a^2 to both sides:
256 {a}^{4}  = 81
Take the fourth root of them or take the square root twice:
\sqrt[4]{256 {a}^{4} }  =  \sqrt[4]{81}   \\  4a = 3
Divide both sides by 4:
a =  \frac{3}{4}  = 0.75
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William has a lemonade stand. It costs him $0.30 to make 3 cups of lemonade. Find the rate of change of his cost and respect to
Snowcat [4.5K]

Answer:

I'm a bit confused, but it would cost $1.20 to make a dozen cups of lemonade

Step-by-step explanation:

0.30 divided by 3 is 0.10, and a dozen is twelve which makes the problem 0.10x12 which equals $1.20

8 0
3 years ago
Find the values of x and y that make the following quadrilateral a parallelogram.
lidiya [134]

Answer:

x = 3 and y = 14

Step-by-step explanation:

opposite angles of a parallelogram are congruent. Hence,

1) 7y + 2 = 6y + 16

I. e. 7y - 6y = 16 - 2

I. e. y = 14

2) 8x + 8 = 6x + 14

I. e. 8x - 6x = 14 - 8

I. e. 2x = 6

I. e. x = 6/2

I. e. x = 3

7 0
3 years ago
In which of the following units is acceleration expressed? A. Newtons B. Kilograms C. Foot-pounds D. Meters per second squared
ELEN [110]

Answer:

D. Meters per second

Step-by-step explanation:

here's  why the answer is D even though they arent the best explanations but none the less the answer is still right.

1. Newton = force

2.kilo = mass

3. foot-pound = force

4. Meters Per sec = speed/acceleration

3 0
3 years ago
The pyramid shown has a square base that is 14 centimeters on each side. The slant height is 15 centimeters. What is the surface
Ksenya-84 [330]
We know that

surface area=area of the base+4*[area of one lateral triangle side]

area of the base=b²
b is the side length of the square
b=14 cm
area of the base=14²-----> 196 cm²

area of one lateral triangle side=b*h/2
b is the side length of the square
b=14 cm
h is the height of the lateral triangle side
h is equal to the slant height 
h=15 cm

area of one lateral triangle side=14*15/2----> 105 cm²

surface area=196+4*[105]------> 616 cm²

the answer is
the surface area is 616 cm²
7 0
3 years ago
What is the result of a dilation of scale factor 3 centered at the origin of the line 2y + 3x=10?? PLEASE HELP PLEASEEEEEEEEE
maks197457 [2]

Given:

The equation of a line is:

2y+3x=10

The line is dilated by factor 3.

To find:

The result of dilation.

Solution:

The equation of a line is:

2y+3x=10

For x=0,

2y+3(0)=10

2y+0=10

y=\dfrac{10}{2}

y=5

For x=2,

2y+3(2)=10

2y+6=10

2y=10-6

2y=4

Divide both sides by 2.

y=\dfrac{4}{2}

y=2

The given line passes through the two points A(0,5) and B(2,2).

If the line dilated by factor 3 with origin as center of dilation, then

(x,y)\to (3x,3y)

Using this rule, we get

A(0,5)\to A'(3(0),3(5))

A(0,5)\to A'(0,15)

Similarly,

B(2,2)\to B'(3(2),3(2))

B(2,2)\to B'(6,6)

The dilated line passes through the points A'(0,15) and B'(6,6). So, the equation of dilated line is:

y-y_1=\dfrac{y_2-y_1}{x_2-x_1}(x-x_1)

y-15=\dfrac{6-15}{6-0}(x-0)

y-15=\dfrac{-9}{6}(x)

y-15=\dfrac{-3}{2}x

Multiply both sides by 2.

2(y-15)=-3x

2y-30=-3x

2y+3x=30

Therefore, the equation of the line after the dilation is 2y+3x=30.

3 0
3 years ago
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