Answer:
The number of big pictures are 49 and number of small pictures are 48 .
Step-by-step explanation:
Let us assume that the number of big pictures are x .
Let us assume that the number of small pictures are y .
As given
Big pictures are 56$ each small ones are 34$.
97 were sold at the total of $4,376.
Equations becomes
x + y = 97
56x + 34y = 4376
Multiply x + y = 97 by 56 and subtracted from 56x + 34y = 4376 .
56x - 56x + 34y - 56y = 4376 - 5432
-22y = - 1056
22y = 1056
y = 48
Put value of y in the equation x + y = 97
x + 48 =97
x = 97 - 48
x = 49
Therefore the number of big pictures are 49 and number of small pictures are 48 .
Answer:
x= -15 or (7x+5)
Step-by-step explanation:
Simplifying
4x + 10 = 3x + -5
Reorder the terms:
10 + 4x = 3x + -5
Reorder the terms:
10 + 4x = -5 + 3x
Solving
10 + 4x = -5 + 3x
Solving for variable 'x'.
Move all terms containing x to the left, all other terms to the right.
Add '-3x' to each side of the equation.
10 + 4x + -3x = -5 + 3x + -3x
Combine like terms: 4x + -3x = 1x
10 + 1x = -5 + 3x + -3x
Combine like terms: 3x + -3x = 0
10 + 1x = -5 + 0
10 + 1x = -5
Add '-10' to each side of the equation.
10 + -10 + 1x = -5 + -10
Combine like terms: 10 + -10 = 0
0 + 1x = -5 + -10
1x = -5 + -10
Combine like terms: -5 + -10 = -15
1x = -15
Divide each side by '1'.
x = -15
Simplifying
x = -15
1 quart is approximately 9.464 x 10⁻⁴ cubic meter, so the amount of oil that was spilled is about
0.50 qt = (0.50 qt) * (0.0009464 m³/qt) = 4.732 x 10⁻⁴ m³
The pool has a cross sectional area of (25.0 m) * (30.0 m) = 750 m² = 7.5 x 10² m².
Assuming the oil spreads completely across the surface of the pool, you can get its thickness by dividing the volume of oil by this cross sectional area.
(4.732 x 10⁻⁴ m³) / (7.5 x 10² m²) = 4.732/7.5 x 10⁻⁶ m ≈ 6.309 x 10⁻⁷ m
1 m is exactly 100 cm, so multiply this result by 100 = 10² to get a thickness of
6.309 x 10⁻⁷ m = (6.309 x 10⁻⁷ m) * (10² cm/m) = 6.309 x 10⁻⁵ cm
or 0.00006309 cm.
Part 1
V = pi*r^2*h .... volume of a cylinder
250 = pi*r^2*h
h = 250/(pi*r^2)
Plug this into the surface area of a cylinder equation
SA = 2*pi*r^2 + 2*pi*r*h
SA = 2*pi*r^2 + 2*pi*r*( 250/(pi*r^2) )
SA = 2*pi*r^2 + 500/r
Now replace every copy of r with x to get this function
f(x) = 2*pi*x^2 + 500/x
x = radius
y = f(x) = surface area
Next we'll use Desmos to graph this function. See the screenshot below. It produces some kind of curve that has two pieces to it. We'll only focus on the curve where x > 0 and y > 0. It makes no sense to have a negative radius, and we cannot have a negative surface area either.
Click on the lowest point of the parabolic looking shaped piece (it's not really a parabola, but we'll imagine that it is for the sake of simplicity).
The coordinates of that local min point will show up and they are (3.414, 219.689)
We have (x,y) = (3.414, 219.689) lead to r = 3.414 and SA = 219.689
This means that a radius of approximately r = 3.414 cm leads to the smallest surface area of approximately 219.689 square cm. This is when the amount of material is minimized.
Use this value of r to find h
h = 250/(pi*r^2)
h = 250/(pi*3.414^2)
h = 6.828
Desmos not only graphs, but it is also a standard calculator. The calculation is also shown in the screenshot.
<h3>Answer: This can has a radius of roughly 3.414 cm and height 6.828 cm.</h3>
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Part 2
- Find the three side lengths of each triangle. So you should have 6 sides total. Then divide the corresponding sides to see if you get the same ratio. If so, then the triangles are similar by the side side side (SSS) similarity theorem. Another method is to find the angle between two sides and use the SAS (side angle side) similarity theorem. This is when the two pairs of sides form the same ratio, and the angles mentioned are congruent to each other. The angles must be between the sides used.
- A proportion can be used to solve equations based on similar polygons. For example, we could have the proportion x/2 = 30/10 which solves to x = 6.
- The first step is to multiply the two numbers. Then apply the square root to them. Example: The geometric mean of 4 and 9 is 6 because
