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1 year ago

A²+b²=c² to find the base of the right triangle. 1600 ft 500 ft

Mathematics

2 answers:

Brut [27]1 year ago

5 0

Answer:

side 2 ( $b^{2}$ ) = 1519.87

hypotenuse ( $c^{2}$ )= 1676.31

Explanation:

If 1600 ft = hypotenuse and 500 ft = side

$1600^{2}$ = $500^{2}$ + $b^{2}$

2560000 = 250000 + $b^{2}$

2560000 - 250000 = $b^{2}$

2310000 = $b^{2}$

$\sqrt{2310000}$ = $\sqrt{b^{2} }$

$b$ = 1519.87

side 2 = 1519.87

If 1600 ft = side 1 and 500 ft = side 2

$1600^{2}$ + $500^{2}$ = $c^{2}$

2560000 + 250000 = $c^{2}$

2810000 = $c^{2}$

$\sqrt{2810000}$ = $\sqrt{c^{2} }$

$c$ = 1676.31

hypotenuse = 1676.31

sammy [17]1 year ago

5 0

Answer:

b=1519.87? (If not correct please clarify what sides the 1600 and 500 ft are on. In my answer the 1600 ft was the hypotenuse since it was the longest of the two and it said to find the base of the triangle. This means the 500 ft is the side adjacent to 90 degrees and 1600 ft is the hypotenuse. Sorry if it's not clear!)

Step-by-step explanation:

$500^{2} +b^2=1600^2\\250000+b^2=2560000\\b^2=2560000-250000\\b^2=2310000\\\sqrt{b^2}=\sqrt{2310000}\\ b=1519.87$

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sukhopar [10]

Let

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When x = 0, we observe that y(0) = a₀ and y'(0) = a₁ can act as initial conditions.

Substitute these into the given differential equation:

$\displaystyle \sum_{n=0}^\infty (n+2)(n+1) a_{n+2} x^n - \sum_{n=0}^\infty a_nx^n = 0$

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Then the coefficients in the power series solution are governed by the recurrence relation,

$\begin{cases}a_0 = y(0) \\ a_1 = y'(0) \\\\ a_{n+2} = \dfrac{a_n}{(n+2)(n+1)} & \text{for }n\ge0\end{cases}$

Since the n-th coefficient depends on the (n - 2)-th coefficient, we split n into two cases.

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$k=0 \implies n=0 \implies a_0 = a_0$

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$k=3 \implies n=6 \implies a_6 = \dfrac{a_4}{6\cdot5} = \dfrac{a_0}{6\cdot5\cdot4\cdot3\cdot2\cdot1}$

It should be easy enough to see that

$a_{n=2k} = \dfrac{a_0}{(2k)!}$

• If n is odd, then n = 2k + 1 for some k ≥ 0. Then

$k = 0 \implies n=1 \implies a_1 = a_1$

$k = 1 \implies n=3 \implies a_3 = \dfrac{a_1}{3\cdot2}$

$k = 2 \implies n=5 \implies a_5 = \dfrac{a_3}{5\cdot4} = \dfrac{a_1}{5\cdot4\cdot3\cdot2}$

$k=3 \implies n=7 \implies a_7=\dfrac{a_5}{7\cdot6} = \dfrac{a_1}{7\cdot6\cdot5\cdot4\cdot3\cdot2}$

so that

$a_{n=2k+1} = \dfrac{a_1}{(2k+1)!}$

So, the overall series solution is

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$\boxed{\displaystyle y(x) = a_0 \sum_{k=0}^\infty \frac{x^{2k}}{(2k)!} + a_1 \sum_{k=0}^\infty \frac{x^{2k+1}}{(2k+1)!}}$

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Rainbow [258]

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The length of a rectangle is 9 cm more then half the width. Find the length of the perimeter is 60cm

stira [4]

length = 1/2 w+9

perimeter= 60 =2(l+w)

substitute in for length

60 = 2(1/2 w +9 +w)

60 = 2 (3/2 w +9)

distribute

60 = 3w + 18

subtract 18 from each side

42 = 3w

divide by 3 on each side

14 = w

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length = 1/2 (14) +9

7 + 9

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