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Burka [1]
1 year ago
8

A car dealership has 24 feet of dividers with which to enclose a rectangular play space in a corner

Mathematics
1 answer:
blondinia [14]1 year ago
7 0

Answer:Answer:a) Area=f(x)= 24x-x^2

b) f(x) ranges from 0 to 144

c) Area max = 144 ft^2

Step-by-step explanation: shown in the attachment

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when a plane flies with the wind, it can travel 1980 miles in 4.5 hours. when the plane flies in the opposite direction, against
Romashka-Z-Leto [24]
Velocity with wind = 1,980 / 4.5 = 440 mph
Velocity against wind =1,980 / 5.5 = 360 mph
Plane in still air - wind speed = 360
Plane in still air + wind speed =440
Adding both equations:
2*Plane in still air = 800
Plane in still air = 400 mph
Plane in still air + wind speed =440
Therefore, wind speed = 40 mph

7 0
2 years ago
Use Simpson's Rule with n = 10 to estimate the arc length of the curve. Compare your answer with the value of the integral produ
SOVA2 [1]

y=\ln(6+x^3)\implies y'=\dfrac{3x^2}{6+x^3}

The arc length of the curve is

\displaystyle\int_0^5\sqrt{1+\frac{9x^4}{(6+x^3)^2}}\,\mathrm dx

which has a value of about 5.99086.

Let f(x)=\sqrt{1+\frac{9x^4}{(6+x^3)^2}}. Split up the interval of integration into 10 subintervals,

[0, 1/2], [1/2, 1], [1, 3/2], ..., [9/2, 5]

The left and right endpoints are given respectively by the sequences,

\ell_i=\dfrac{i-1}2

r_i=\dfrac i2

with 1\le i\le10.

These subintervals have midpoints given by

m_i=\dfrac{\ell_i+r_i}2=\dfrac{2i-1}4

Over each subinterval, we approximate f(x) with the quadratic polynomial

p_i(x)=f(\ell_i)\dfrac{(x-m_i)(x-r_i)}{(\ell_i-m_i)(\ell_i-r_i)}+f(m_i)\dfrac{(x-\ell_i)(x-r_i)}{(m_i-\ell_i)(m_i-r_i)}+f(r_i)\dfrac{(x-\ell_i)(x-m_i)}{(r_i-\ell_i)(r_i-m_i)}

so that the integral we want to find can be estimated as

\displaystyle\sum_{i=1}^{10}\int_{\ell_i}^{r_i}p_i(x)\,\mathrm dx

It turns out that

\displaystyle\int_{\ell_i}^{r_i}p_i(x)\,\mathrm dx=\frac{f(\ell_i)+4f(m_i)+f(r_i)}6

so that the arc length is approximately

\displaystyle\sum_{i=1}^{10}\frac{f(\ell_i)+4f(m_i)+f(r_i)}6\approx5.99086

5 0
1 year ago
Caswell started studying how the number of branches on his tree grows over time. The relationship between the elapsed time ttt,
ipn [44]

Answer:

t =log(20) / 0.3 = 10*log(20) / log(1,000) - years - when the tree will have 100 branches.

Step-by-step explanation:

100 = 5 * 10^(0.3t), solve for t

Divide both sides by 5:

20 =10^(0.3t)

Take the log of both sides:

0.3t =log(20)

Divide both sides by 0.3:

Multiply the RHS by 10 / 10

t =log(20) / 0.3 = 10*log(20) / log(1,000) - years - when the tree will have 100 branches.

8 0
1 year ago
Read 2 more answers
Use the function below to find F(3).<br> F(x) = 3x
Vikki [24]

The value of F(3) = 27.

Step-by-step explanation:

Step 1:

F(x) is dependent on the value of x.

So x is independent while F(x) is dependent on x i.e. the value of F(x) depends on the value of x.

Step 2:

F(x) = 3^{x}, if we have the x's value we can calculate the F(x)'s value.

Here the value of x is given as 3 so F(x) when x equals 3 can be calculated.

F(x) = 3^{x} , F(3) = 3^{3} = 27.

So F(3) = 27.

7 0
1 year ago
While remodeling her kitchen Angela is repainting. She estimates that she paints 55 square feet every half-hour. How many square
madreJ [45]
110 square feet. 55x2=100
5 0
1 year ago
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