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Fiesta28 [93]
3 years ago
7

The area of a square garden is 81 feet. If you want to put a fence on only 3 sides of the garden, how many feet of fence will yo

u need to purchase?
Mathematics
1 answer:
sergeinik [125]3 years ago
4 0
Length of each side
=  \sqrt{81}  \\  = 9
Fence needed=9×3=27 ft
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Help :::))) ;) asapppppp :)
stealth61 [152]
Multiply 3 with 7.
3 * 7 = 21
The value of the gift card changed by -$21 dollars.
8 0
3 years ago
The line tangent to the graph of g(x) = x^{3}-4x+1 at the point (2, 1) is given by the formula
Usimov [2.4K]

well, about A and D, I just plugged the values on the slope formula of

\bf \begin{array}{llll} g(x)=x^3-4x+1\\ L(x) = 8(x-2)+1 \end{array} \qquad \begin{cases} x_1=1.9\\ x_2=2.1 \end{cases}\implies \cfrac{f(b)-f(a)}{b-a}

for A the values are 8.01 and 8.0, so indeed those "slopes" are close. \textit{\huge \checkmark}

for D the values are -2.25 and 8.0, so no dice on that one.

for B, let's check the y-intercept for g(x), by setting x = 0, we end up g(0) = 0³-4(0)+1, which gives us g(0) = 1.

checking L(x) y-intercept, well, L(x) is in slope-intercept form, thus the +1 sticking out on the far right is the y-intercept, so, dice. \textit{\huge \checkmark}

for C, well, the slope if L(x) is 8, since it's in slope-intercept form, the derivative of g(x) is g'(x) = 3x² - 4, and thus g'(0) = -4, so no dice.

for E, do they intercept at (2,1)?  well, come on now, L(x) is a tangent line to g(x), so that's a must for a tangent. \textit{\huge \checkmark}

for F, we know the slope of the line L(x) is 8, is g'(2) = 8?  let's check

recall that g'(x) = 3x² - 4, so g'(2) = 3(2)² - 4, meaning g'(2) = 8, so, dice. \textit{\huge \checkmark}

6 0
3 years ago
What is the difference between bernoulii equation and riccati equation
melisa1 [442]
The Bernoulli equation is almost identical to the standard linear ODE.

y'=P(x)y+Q(x)y^n

Compare to the basic linear ODE,

y'=P(x)y+Q(x)

Meanwhile, the Riccati equation takes the form

y'=P(x)+Q(x)y+R(x)y^2

which in special cases is of Bernoulli type if P(x)=0, and linear if R(x)=0. But in general each type takes a different method to solve. From now on, I'll abbreviate the coefficient functions as P,Q,R for brevity.

For Bernoulli equations, the standard approach is to write

y'=Py+Qy^n
y^{-n}y'=Py^{1-n}+Q

and substitute v=y^{1-n}. This makes v'=(1-n)y^{-n}y', so the ODE is rewritten as

\dfrac1{1-n}v'=Pv+Q

and the equation is now linear in v.

The Riccati equation, on the other hand, requires a different substitution. Set v=Ry, so that v'=R'y+Ry'=R'\dfrac vR+Ry'. Then you have

y'=P+Qy+Ry^2
\dfrac{v'-R'\dfrac vR}R=P+Q\dfrac vR+R\dfrac{v^2}{R^2}
v'=PR+\left(Q+\dfrac{R'}R\right)v+v^2

Next, setting v=\dfrac{u'}u, so that v'=\dfrac{uu''-(u')^2}{u^2}, allows you to write this as a linear second-order equation. You have

\dfrac{uu''-(u')^2}{u^2}=PR+\left(Q+\dfrac{R'}R\right)\dfrac{u'}u+\dfrac{(u')^2}{u^2}
u''-\left(Q+\dfrac{R'}R\right)u'+PRu=0
u''+Su'+Tu=0

where S=-\left(Q+\dfrac{R'}R\right) and T=PR.
3 0
3 years ago
Muscles, a membership-only gym is hoping to open a new branch in a small city in Pennsylvania that currently has no fitness cent
Cloud [144]

Answer:

  B) 504

Step-by-step explanation:

They should expect 30% of 40 out of every 300 of the 12,600, so ...

  0.30 × 40/300 × 12,600 = 504

About 504 residents might be expected to join.

7 0
2 years ago
Jason and Adam are using a kit to build their own electronics board for a computer project. They use a scale drawing included in
jenyasd209 [6]

Answer:

the area is 1800

Step-by-step explanation:

ik this doesn't answer the full question but hope it helps <3

4 0
2 years ago
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