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2 years ago

7.9y-2-3.2y-10=2.8+y

Mathematics

1 answer:

Katyanochek1 [597]2 years ago

3 0

Answer:

y=4

Step-by-step explanation:

7.9y-2-3.2y-10=2.8+y

group like variables

4.7y -12 = 2.8 +y

isolate the variable (y)

3.7y = 14.8

solve for y through division

14.8/3.7=y

4=y

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Simplify the expression: 1/4+4/5(3/4x-1 1/9)

sweet-ann [11.9K]

Answer:

108x + 29

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180

Step-by-step explanation:

6 0

3 years ago

Read 2 more answers

Your favorite craft store had a weekend sale. On the first day, all $10 items were 70% off. You bought some number of these of t

Svet_ta [14]

For the first day we have the following function:
f (n) = (0.3 * 10) n + 8
For the second day we have the following function:
f (n) = (0.4 * 10) n + 5
You spent the same amount of money as the day before:
(0.3 * 10) n + 8 = (0.4 * 10) n + 5
3n + 8 = 4n + 5
n = 8-5
n = 3 items
We evaluate each function for n = 3
f (3) = (0.3 * 10) * 3 + 8 = 17 $
f (3) = (0.4 * 10) * 3 + 5 = 17 $
The total amount of money is:
17 + 17 = 34 $
Answer:
you purchase 6 items
you spend at the craft store during the sale $ 34

8 0

3 years ago

A solid is formed by adjoining two hemispheres to the ends of a right circular cylinder. An industrial tank of this shape must h

mestny [16]

Answer:

Radius =6.518 feet

Height = 26.074 feet

Step-by-step explanation:

The Volume of the Solid formed = Volume of the two Hemisphere + Volume of the Cylinder

Volume of a Hemisphere $=\frac{2}{3}\pi r^3$

Volume of a Cylinder $=\pi r^2 h$

Therefore:

The Volume of the Solid formed

$=2(\frac{2}{3}\pi r^3)+\pi r^2 h\\\frac{4}{3}\pi r^3+\pi r^2 h=4640\\\pi r^2(\frac{4r}{3}+ h)=4640\\\frac{4r}{3}+ h =\frac{4640}{\pi r^2} \\h=\frac{4640}{\pi r^2}-\frac{4r}{3}$

Area of the Hemisphere = $2\pi r^2$

Curved Surface Area of the Cylinder = $2\pi rh$

Total Surface Area=

$2\pi r^2+2\pi r^2+2\pi rh\\=4\pi r^2+2\pi rh$

Cost of the Hemispherical Ends = 2 X Cost of the surface area of the sides.

Therefore total Cost, C

$=2(4\pi r^2)+2\pi rh\\C=8\pi r^2+2\pi rh$

Recall: $h=\frac{4640}{\pi r^2}-\frac{4r}{3}$

Therefore:

$C=8\pi r^2+2\pi r(\frac{4640}{\pi r^2}-\frac{4r}{3})\\C=8\pi r^2+\frac{9280}{r}-\frac{8\pi r^2}{3}\\C=\frac{9280}{r}+\frac{24\pi r^2-8\pi r^2}{3}\\C=\frac{9280}{r}+\frac{16\pi r^2}{3}\\C=\frac{27840+16\pi r^3}{3r}$

The minimum cost occurs at the point where the derivative equals zero.

$C^{'}=\frac{-27840+32\pi r^3}{3r^2}$

$When \:C^{'}=0$

$-27840+32\pi r^3=0\\27840=32\pi r^3\\r^3=27840 \div 32\pi=276.9296\\r=\sqrt[3]{276.9296} =6.518$

Recall:

$h=\frac{4640}{\pi r^2}-\frac{4r}{3}\\h=\frac{4640}{\pi*6.518^2}-\frac{4*6.518}{3}\\h=26.074 feet$

Therefore, the dimensions that will minimize the cost are:

Radius =6.518 feet

Height = 26.074 feet

5 0

2 years ago

What is the complex formula for dilation with scale factor 2 and rotation by 90

zhuklara [117]

Answer:

z' = 2iz +11 -2i

Step-by-step explanation:

Dilation multiplies each point by the scale factor. Rotation by 90° CCW is equivalent to multiplication by i.

When the center is not the origin, the transformation is applied to the difference from the center, then the result is added to the center.

z' = 2i(z -(3+4i)) + (3+4i)

Simplifying gives ...

z' = 2iz -6i +8 +3 +4i

z' = 2iz +11 -2i

_____

<em>Check</em>

For example, consider the point 1 unit east of the center of dilation/rotation. That point is z = 4+4i. Applying the transformation moves this point to ...

z' = 2i(4 +4i) +11 -2i = 8i -8 +11 -2i

z' = 3 +6i . . . . . 2 units north of the center of dilation/rotation

This is where it is expected to be after dilation by a scale factor of 2 and rotation 90° CCW.

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2 years ago

The large Ferris wheel makes a revolution in 60 seconds. The small Ferris wheel makes one revolution in 20 seconds. How many sec

Wewaii [24]

Answer:

120 seconds

Step-by-step explanation:

60 20

120 40

180 60

100

120

4 0

3 years ago