Question 4

Mathematics

2 answers:

natali 33 [55]2 years ago

8 0

0 2 gallons is the answer

ICE Princess25 [194]2 years ago

6 0

Answer:

There is a little over 1 gallon

Step-by-step explanation:

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If 1 inch on a map represents 20 miles, what is the mileage represented by 2.5 inches?

SOVA2 [1]

Answer:

50 miles(D)

Step-by-step explanation:

20 x 2.5

5 0

2 years ago

Find the exact length of the curve. x=et+e−t, y=5−2t, 0≤t≤2 For a curve given by parametric equations x=f(t) and y=g(t), arc len

Rama09 [41]

The length of a curve C parameterized by a vector function r(t) = x(t) i + y(t) j over an interval a ≤ t ≤ b is

$\displaystyle\int_C\mathrm ds = \int_a^b \sqrt{\left(\frac{\mathrm dx}{\mathrm dt}\right)^2+\left(\frac{\mathrm dy}{\mathrm dt}\right)^2} \,\mathrm dt$

In this case, we have

x(t) = exp(t ) + exp(-t ) ==> dx/dt = exp(t ) - exp(-t )

y(t) = 5 - 2t ==> dy/dt = -2

and [a, b] = [0, 2]. The length of the curve is then

$\displaystyle\int_0^2 \sqrt{\left(e^t-e^{-t}\right)^2+(-2)^2} \,\mathrm dt = \int_0^2 \sqrt{e^{2t}-2+e^{-2t}+4}\,\mathrm dt$

$=\displaystyle\int_0^2 \sqrt{e^{2t}+2+e^{-2t}} \,\mathrm dt$

$=\displaystyle\int_0^2\sqrt{\left(e^t+e^{-t}\right)^2} \,\mathrm dt$

$=\displaystyle\int_0^2\left(e^t+e^{-t}\right)\,\mathrm dt$

$=\left(e^t-e^{-t}\right)\bigg|_0^2 = \left(e^2-e^{-2}\right)-\left(e^0-e^{-0}\right) = \boxed{e^2-\frac1{e^2}}$

5 0

2 years ago

Solve the system of linear equations below.

Olegator [25]

Answer:

B. x = 2, y = 6

Step-by-step explanation:

$2x + 5y = 34...(1) \\ \\ x + 2y = 14 \\ \therefore \: x = 14 - 2y...(2) \\ \\ from \: equations \: (1) \: and \: (2) \\ \\ 2(14 - 2y) + 5y = 34 \\ \therefore \: 28 - 4y + 5y = 34 \\ \therefore \: 28 + y = 34 \\ \therefore \: y = 34 - 28 \\ \huge \red{ \boxed{\therefore \: y = 6}} \\ substituting \: y = 6 \: in \: equation \: (2) \\ x = 14 - 2 \times 6 \\ \therefore \: x =14 - 12 \\ \huge \purple{ \boxed{\therefore \: x =2}} \\ \\ \huge \orange{ \boxed{ \therefore \: x = 2, \: \: y = 6}} \\$