Select all the graphs that are proportional.help me please

A parabolic arch has a height of 25 feet and a span of 40 feet. How high is the arch 8 feet from each side of the center?

Llana [10]

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;

$y = (-\frac{1}{16})(x-20)^2 + 25$

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;

$y = (-\frac{1}{16})(12-20)^2 + 25 = (-\frac{1}{16})(-8)^2 + 25 = 21 \ ft$ .

4 0

3 years ago

Determine the simple interest when: principal: $205,435 interest rate: 2.8%, time: 15 year

Vesna [10]

Step-by-step explanation:

<h3>principle (p) = $205,435</h3><h3>rate (r) = 2.8%</h3><h3>time (t) = 15 years</h3><h3>simple interest = (p × r × t) ÷ 100</h3><h3> = (205,435 × 2.8 × 15) ÷ 100</h3><h3> = 8,628,270 ÷ 100</h3><h3> = 86282.7</h3>

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4 0

3 years ago

The population of Henderson City was 3,381,000 in 1994, and is growing at an annual rate 1.8%

liq [111]

<h2>In the year 2000, population will be 3,762,979 approximately. Population will double by the year 2033.</h2>

Step-by-step explanation:

Given that the population grows every year at the same rate( 1.8% ), we can model the population similar to a compound Interest problem.

From 1994, every subsequent year the new population is obtained by multiplying the previous years' population by $\frac{100+1.8}{100}$ = $\frac{101.8}{100}$ .

So, the population in the year t can be given by $P(t)=3,381,000\textrm{x}(\frac{101.8}{100})^{(t-1994)}$

Population in the year 2000 = $3,381,000\textrm{x}(\frac{101.8}{100})^{6}$ = $3,762,979.38$

Population in year 2000 = 3,762,979

Let us assume population doubles by year $y$ .

$2\textrm{x}(3,381,000)=(3,381,000)\textrm{x}(\frac{101.8}{100})^{(y-1994)}$

$log_{10}2=(y-1994)log_{10}(\frac{101.8}{100})$

$y-1994=\frac{log_{10}2}{log_{10}1.018}=38.8537$

$y$ ≈ $2033$

∴ By 2033, the population doubles.

4 0

3 years ago

The fith term of a G.P is 8 times the 2nd term find its common ratio

Dovator [93]

Answer:

Common ratio r = 2

Step-by-step explanation:

$\because$ the fith term of a G.P is 8 times the 2nd term.

$\therefore \: t_5 = 8\times t_2 \\ \therefore \: ar^{5-1}=8\times \: ar^{2-1} \\ \therefore \: r^{4}=8\times \: r^{1} \\ \therefore \: r^{3}=8 \\ \therefore \:r^{3}= {2}^{3} \\ \hspace{20 pt}\huge \red{ \boxed{\therefore \:r= {2}}} \\$

Hence, common ratio is 2.

6 0

3 years ago

Read 2 more answers

A slope of 0.5 with an x-intercept of (28,0)

quester [9]

Step-by-step explanation:

m/slope=0.5

(28,0)

y=mx+b

0=0.5(28)+b

0=14+b

-14=b

y=0.5x -14

8 0

3 years ago

Select all the graphs that are proportional.help me please​

Select all the graphs that are proportional.help me please