Answer:
The correct option is;
21 ft
Step-by-step explanation:
The equation of the parabolic arc is as follows;
y = a(x - h)² + k
Where the height is 25 ft and the span is 40 ft, the coordinates of the vertex (h, k) is then (20, 25)
We therefore have;
y = a(x - 20)² + 25
Whereby the parabola starts from the origin (0, 0), we have;
0 = a(0 - 20)² + 25
0 = 20²a + 25 → 0 = 400·a + 25
∴a = -25/400 = -1/16
The equation of the parabola is therefore;
[tex]y = (-\frac{1}{16})(x-20)^2 + 25[/tex]
To find the height 8 ft from the center, where the center is at x = 20 we have 8 ft from center = x = 20 - 8 = 12 or x = 20 + 8 = 28
Therefore, plugging the value of x = 12 or 28 in the equation for the parabola gives;
[tex]y = (-\frac{1}{16})(12-20)^2 + 25 = (-\frac{1}{16})(-8)^2 + 25 = 21 \ ft[/tex].
Final answer:
By creating and solving the equation of a parabola which matches the description of the arch, it is found that the height of the arch 8 feet from the center is 21 feet.
Explanation:
To determine how high the parabolic arch is 8 feet from each side of the center, we can use the properties of a parabola to set up an equation. The vertex of the parabola (the highest point) is in the center of the arch, so we know that the parabola is symmetrical about the vertex.
The general form of a parabolic equation is y = ax^2 + bx + c. In this scenario:
The vertex is at the origin (0,25).
The arch has a span (width) of 40 feet, so its x-intercepts, or roots, are at (-20,0) and (20,0).
To find the parabolic constant, a, we use the x-intercepts to establish the equation 0 = a(20)^2, which simplifies to a = -25/400 = -1/16 because we know that the height at the x-intercepts is 0.
The parabolic equation for the arch is then y = -1/16x^2 + 25. To find the height 8 feet from the center, we substitute x with 8:
y = -1/16(8)^2 + 25 = -1/16(64) + 25 = -4 + 25 = 21
Therefore, the arch is 21 feet high 8 feet from each side of the center.
A fish population in a lake decreases by 2% each year. What is the common ratio? (Write your answer as a decimal)
Answer:
the common ratio is 0.98.
Step-by-step explanation:
A fish population in a lake decreases by 2% each year. We are asked to find the common ratio.
The decrease of population of fish 2% annually means the population becomes next year 100% - 2% = 98%
Therefore, the common ratio would be 98%. Upon converting 98 percent to a decimal we will get,
98% = [tex]\frac{98}{100}=0.98[/tex]
Therefore, the common ratio or decay factor is 0.98.
Answer:
D. .98
Step-by-step explanation:
Just got it right on the test
A rectangle or piece of paper has a width is 3 inches less than its link it is cut in half along a diagonal to create two congruent right triangles with areas of 44 in.²
The length and width of the rectangle is 11 in and 8 in respectively.
Step-by-step explanation:
Given,
The width of a rectangle is 3 in less than the length.
The area of each congruent right angle triangle = 44 in²
To find the length and width of the rectangle.
Formula
The area of a triangle with b base and h as height = [tex]\frac{1}{2}[/tex]bh
Now,
Let, the width = x and the length = x+3.
Here, for the triangle, width will be its base and length will be its height.
According to the problem,
[tex]\frac{1}{2}[/tex]×(x+3)×x = 44
or, [tex]x^{2} +3x = 88[/tex]
or,[tex]x^{2} +3x-88 = 0[/tex]
or, [tex]x^{2}[/tex]+(11-8)x-88 = 0
or, [tex]x^{2}[/tex]+11x-8x-88 =0
or, x(x+11)-8(x+11) = 0
or, (x+11)(x-8) = 0
So, x = 8 ( x≠-11, the length or width could no be negative)
Hence,
Width = 8 in and length = 8+3 = 11 in
2. What is 75% of 300?
Answer:6.25
Step-by-step explanation:divide 75 of 300
Answer:
210
Step-by-step explanation:
70% of 300
70%= 0.7
0.7*300
=210
Does anyone know this?!
Answer:
i think b
Step-by-step explanation:
tell me if im wrong
Amelie is making a recipe that uses 134 cups flour. She is making 212 times the original recipe. Amelie draws this model to represent the number of cups of flour she needs. How many cups of flour does Amelie need? Enter your answer as a mixed number in simplest form by filling in the boxes.
Amelie needs [tex]\( 28\frac{1}{4} \)[/tex] cups of flour for her recipe.
Amelie's recipe uses [tex]\( \frac{1}{4} \)[/tex] cups of flour and she's making [tex]\( 2\frac{1}{2} \)[/tex]times the original recipe. To find the total amount of flour needed, we multiply the two quantities:
1. Original Quantity of Flour: [tex]\( \frac{1}{4} \)[/tex] cups
2.Multiply by the Recipe Multiplier: [tex]\( 2\frac{1}{2} \times \frac{1}{4} \)[/tex]
3.Convert Mixed Number to Improper Fraction: [tex]\( 2\frac{1}{2} = \frac{5}{2} \)[/tex]
4. Perform the Multiplication:
[tex]\[ \frac{5}{2} \times \frac{1}{4} = \frac{5}{8} \][/tex]
Since Amelie is using [tex]\( \frac{5}{8} \)[/tex] of the grid and each square represents 1 cup, we can calculate the total cups by multiplying the number of squares in the grid by [tex]\( \frac{5}{8} \)[/tex]:
5.Total Squares in the Grid: [tex]\( 8 \times 4 = 32 \)[/tex]
6.Total Flour Needed:
[tex]\[ 32 \times \frac{5}{8} = 4 \times 5 = 20 \text{ cups} \][/tex]
However, since the grid seems to represent a multiplication model for the entire recipe amount, and we've been given that she's using[tex]\( 1\frac{3}{4} \)[/tex] cups and multiplying it by [tex]\( 2\frac{1}{2} \)[/tex], we should calculate as follows:
1. Convert [tex]\( 1\frac{3}{4} \)[/tex] cups to an improper fraction: [tex]\( \frac{7}{4} \)[/tex] cups.
2. Multiply[tex]\( \frac{7}{4} \) by \( 2\frac{1}{2} \)[/tex] (which is [tex]\( \frac{5}{2} \)[/tex] as an improper fraction):
[tex]\[ \frac{7}{4} \times \frac{5}{2} = \frac{35}{8} \][/tex]
3. Convert \( \frac{35}{8} \) to a mixed number:
[tex]\[ \frac{35}{8} = 4\frac{3}{8} \text{ cups} \][/tex]
Looking at the model provided, the total grid represents[tex]\( 2\frac{1}{2} \)[/tex]times the original recipe, which is [tex]\( 1\frac{3}{4} \)[/tex] cups of flour. The full grid has [tex]\( 8 \times 4 = 32 \)[/tex]squares, where each square represents [tex]\( \frac{1}{4} \)[/tex] cup of flour, giving us a total of 8 cups represented by the full grid. Since we want [tex]\( 2\frac{1}{2} \) or \( \frac{5}{2} \)[/tex] of this grid, we multiply:
[tex]\[ \text{Total flour} = 8 \times \frac{5}{2} = 4 \times 5 = 20 \text{ cups} \][/tex]
However, the discrepancy arises because the image shows a grid that is partially shaded, suggesting that we're looking at a portion of the full recipe's flour amount. Without clear visibility or description of the image, the precise interpretation of the grid is ambiguous.
Given this, the correct interpretation based on the model provided would be to calculate as follows:
[tex]\[ \frac{32}{4} \times \frac{5}{2} = 8 \times \frac{5}{2} = 20 \text{ cups} \][/tex]
If the grid is fully shaded, which means the entire grid is being used to represent the amount of flour, then Amelie needs 20 cups of flour for her recipe. If the grid is partially shaded and we are to use the fraction[tex]\( \frac{35}{8} \) (or \( 4\frac{3}{8} \) cups)[/tex] from the shaded portion, then the amount of flour needed would be [tex]\( 4\frac{3}{8} \)[/tex] cups. The mixed number in simplest form for the latter calculation would be [tex]\( 4\frac{3}{8} \)[/tex] cups.
complete question given below:
Amelie is making a recipe that uses 1 3/4 cups flour. She is making 2 1/2 times the original recipe.Amelie draws this model to represent the number of cups of flour she needs.How many cups of flour does Amelie need?Enter your answer as a mixed number in simplest form by filling in the boxes.