Mathematics, 19.11.2020 18:40 suzyleonardsl0

Sue wants to build a model of the Skyway Bridge for a school project. She decides that her scale model needs to be 1/10th the size of the real bridge. When she looked online, she found that the base of the bridge is 4000 ft long and 100 ft wide. If she uses a scale of inches to feet, what are the dimensions of her model? (you will have TWO answers)

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Answer from: groovyghoulie5630

400 inches by 10 inches

Step-by-step explanation:

Length of the bridge = 4000feet

Width of the bridge = 100 feet

Since Sue decides that her scale model needs to be 1/10th the size of the real bridge.

If she uses a scale of inches to feet, the dimensions of her model will be:

Length = 4000 × 1/10 = 400 inches

Width = 100 × 1/10 = 10 inches.

Therefore, the dimensions are 400 inches by 10 inches

Answer from: Quest

a, b, c, d are correct.

step-by-step explanation:

we have g(x) = 3 $\sqrt{x}$ and are required to find which option is a translation of g(x).

now, 'translation' is a transformation which means to shift the function in any direction and the general form of translation is g(x) + k, where k is any real number.

so, according to the options we see that all are correct as they satisfy the general form of translation.

also, it can be seen from the graph below that the function g(x) = 3 $\sqrt{x}$ is shifted from its position in all the four options.

Answer from: Quest

a. geometricb. g[h] = (3/4)·g[h-1]; g[1] = 384c. g[h] = 384·(3/4)^(h-1)d. g[12] ≈ 16.2183 gallonse. g[12] ≈ 64.8732 quarts

step-by-step explanation:

part a. the differences are decreasing, so we know the sequence is not arithmetic. the ratios are constant (=3/4), so we know the sequence is geometric.

part b. from part a, we know the common ratio is 3/4, so each term is 3/4 of the one before. the initial term is the number of gallons at h=1.

g[h] = (3/4)·g[h-1]

g[1] = 384 . . . . initial value required for a recursive definition

part c. the general formula for a geometric sequence is

a[n] = a[1]·r^(n-1)

we have a[1] = 384, r = 3/4, and the term number given by h. the formula that follows is

g[h] = 384·(3/4)^(h-1)

part d. filling in the value and doing the arithmetic, we have

g[12] = 384·(3/4)^11 ≈ 384·0.042235136 ≈ 16.2183 . . gallons

part e. each gallon is 4 quarts, so

16.2183 gal × 4 qt/gal = 64.8732 qt

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