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2 years ago

What are solutions to the equation 9x2-7x-4=0

Mathematics

1 answer:

11111nata11111 [884]2 years ago

3 0

Answer:

Step-by-step explanation:

x =(7-√193)/18=-0.383

x =(7+√193)/18= 1.161

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Find T, N, and kappa for the plane curve Bold r left parenthesis t right parenthesis equalsleft parenthesis 7 Bold cos t plus

pickupchik [31]

Answer:

Step-by-step explanation:

r(t) = (7 cost + 7t sin t)i + (7 sin t - 7t cos t)j

$\frac{d \bar r t}{dt} =(7\frac{d}{dt}\cos t + 7\frac{d}{dt} (t \sin t)i+(7\frac{d}{dt} \sin t-7\frac{d}{dt} t \cos t)j$

$=(7(-\sin t)+7(1* \sin t+t \cos t))i+(7 \cost -7(1*\cos t - t \sin t))j\\\\=7((-\sin t+\sin t+t \cos t)i+(\cos t-\cos t+t \sin t)j)\\\\=7((t\cos t)i+(t\sin t)j)$

$\bar r'(t)=\frac{d \bar r t}{dt} =(7t\cos t)i+(7t\sin t)j---(1)\\\\11\bar r(t)=\sqrt{(7t\cos t)^2+(7t\sin t)^2}\\\\=\sqrt{49t^2(\cos^2t+\sin^2 t)} \\\\=7t$

$\bar T (t)=\frac{\bar r'(t)}{11\bar r(t)11} =\frac{(7t\cos t)i+(7t\sin t)j}{7t} \\\\\barT(t)=(\cos t)i+(\sin t)j$

$\bar T'(t)=\frac{d}{dt} (\cos t)i+\frac{d}{dt} (\sin t) j\\\\\bar T'(t)=(-\sin t)i+(\cos t)j---(2)\\\\11\bar T'(t)=\sqrt{(-\sin t)^2+(\cos t)^2} \\\\=\sqrt{\sin^2t+\cos^2t} \\\\=1$

$\bar N(t)=\bar T'(t)=\frac{(-\sin t)i+(\cos t)j}{(1)} \\\\ \large \boxed {\bar N(t)=(-\sin t)i+(\cos t)j}$

$K(t)=\frac{|\b\r T'(t)|}{\bar r (t)|} \\\\=\frac{|-\sin t i+\cos t j|}{|7t\cos t +7t \sin t j|}$

Using eq (1) and (2)

$K(t)=\frac{\sqrt{(-\sin t)^2+(\cos t)^2} }{\sqrt{(7t\cos t)^2+(7t\sin t)^2} }\\\\=\frac{\sqrt{\sin^2 t+\cos^2t} }{\sqrt{49t^2(\cos^2 t+\sin^2t)} }\\\\=\frac{\sqrt{1} }{\sqrt{49t^2\times 1} } \\\\ \large \boxed {K(t)=\frac{1}{7t} }$

7 0

3 years ago

Y+4−1=18 i need help plz

d1i1m1o1n [39]

Answer:

y=15

Step-by-step explanation:

3 0

3 years ago

Read 2 more answers

Rank and alice are penguins. at birth, frank's beak was 1.95 inches long, while alice's was 1.50 inches long. homework help ✎ fr

miskamm [114]

<span>F for Frank, A or Alice. F(initial)=1.95 inches A(initial)=1.50 inches Frank's equation at .25 inches per year and t representing year variable. F=1.95+.25t Alice's equation at .40 inches per year and t representing year variable. A=1.5+.40t To figure out how old they will be when their beaks are the same lengths set the equations equal to eachother as the equations are length. 1.95+.25t=1.5+.40t .45=.15t t=3 years</span>

5 0

2 years ago

You notice a hot air balloon descending. The elevation h

ANEK [815]

Answer:

the domain is 0 x 45 and the range is 0 h 360. The slope is -8, so the change in the height of the ballon is -8 feet per second. The h-intercept is 360, so the height of the ballon when the first noticed it was 360 feet. The x-intercept is 45, so the time it took the hot air balloon to reach the ground was 45 seconds.

Step-by-step explanation:

8 0

3 years ago

Use matrix inversion to solve the collection of systems of linear equations. HINT [See Example 4.] (a) −x − 4y + 2z = −10 x + 2y

omeli [17]

Answer:

Step-by-step explanation:

given is a system of linear equations in 3 variables as

$-x - 4y + 2z = −10\\ x + 2y - z = 11 \\x + y - z = 14$

This can be represented in matrix form as

AX=B Or

$\left[\begin{array}{ccc}-1&-4&2\\1&2&-1\\1&1&-1\end{array}\right] *\left[\begin{array}{ccc}x\\y\\z\end{array}\right] =\left[\begin{array}{ccc}-10\\11\\14\end{array}\right]$

So solution set

X would be $A^{-1} B$

|A|=-1(-1)+4(0)+2(-1)=--1

Cofactors of A are

-1 0 -1

-2 -1 -3

0 1 2

So inverse of A is

1 2 0

0 1 -1

1 3 -2

Solution set would be

x=12

y=-3

z=-5

8 0

2 years ago