What is the solution to f (x)=g (x), if f (x)=-x and g (x)=x

What is the most precise name for a quadrilateral with the following vertices:

Luba_88 [7]

Answer:

<em>Parallelogram</em>

Step-by-step explanation:

The image below shows that it most likely looks like a <em>Parallelogram</em>.

5 0

3 years ago

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Use Lagrange multipliers to find the maximum and minimum values of f(x,y)=x+4y subject to the constraint x2+y2=9, if such values

Vesnalui [34]

The Lagrangian is

$L(x,y,\lambda)=x+4y+\lambda(x^2+y^2-9)$

with critical points where the partial derivatives vanish.

$L_x=1+2\lambda x=0\implies x=-\dfrac1{2\lambda}$

$L_y=4+2\lambda y=0\implies y=-\dfrac2\lambda$

$L_\lambda=x^2+y^2-9=0$

Substitute $x,y$ into the last equation and solve for $\lambda$ :

$\left(-\dfrac1{2\lambda}\right)^2+\left(-\dfrac2\lambda\right)^2=9\implies\lambda=\pm\dfrac{\sqrt{17}}6$

Then we get two critical points,

$(x,y)=\left(-\dfrac3{\sqrt{17}},-\dfrac{12}{\sqrt{17}}\right)\text{ and }(x,y)=\left(\dfrac3{\sqrt{17}},\dfrac{12}{\sqrt{17}}\right)$

We get an absolute maximum of $3\sqrt{17}\approx12.369$ at the second point, and an absolute minimum of $-3\sqrt{17}\approx-12.369$ at the first point.

4 0

3 years ago

For three consecutive plays, the Patriots gained

seraphim [82]

Answer:

The overall change in field position is 7yds, 0 - 5 + 12 = 7, if that isn't a "sum of integers" I apologize.

Step-by-step explanation:

6 0

3 years ago

A brand of clay brick tiles has the dimensions 3 5 8 by 7 5 8 by 1 2 inch. These thin bricks are commonly used for floors. Estim

raketka [301]

Answer: The cost to tile the floor is $318.24.

Step-by-step explanation:

Since we have given that

Dimensions of floor is 12 by 17 foot.

So, Area of floor would be

$12\times 17\\\\=204\ sq.\ foot$

As we know that 1 foot = 12 inch

So, Area of floor would be

$204\times (12)^2\\\\=204\times 144\\\\=29376\ sq.\ foot$

Dimension of brick tiles is given by

$3\dfrac{5}{8}\ by\ 7\dfrac{5}{8}\ by\ \dfrac{1}{2}$

So, Area of brick tiles is given by

$2(lb+bh+lh)\\\\=2(\dfrac{29}{8}\times \dfrac{61}{8}+\dfrac{61}{8}\times \dfrac{1}{2}+\dfrac{29}{8}\times \dfrac{1}{2})\\\\=2(\dfrac{1769}{64}+\dfrac{61}{16}+\dfrac{29}{16})\\\\=2\times \dfrac{1769+244+116}{64}\\\\=\dfrac{2129}{32}$

So, Number of clay brick would be

$29376\div \dfrac{2129}{32}\\\\=29376\times \dfrac{32}{2129}\\\\=\dfrac{29376\times 32}{2129}\\\\=441.53\\\\\approx 442$

cost of each clay brick = $0.72

So, Total cost of flooring would be

$442\times 0.72\\\\=\$318.24$

Hence, The cost to tile the floor is $318.24.

7 0

3 years ago

Please Help Me! It’s Math! Please!

nadezda [96]

Answer:

D. About 800 years

Step-by-step explanation:

Use the half-life equation:

A = A₀ (½)ⁿ

where A is the final amount,

A₀ is the initial amount,

and n is the number of half-lives.

0.90A₀ = A₀ (½)ⁿ

0.90 = (½)ⁿ

To solve for n, take log of both sides:

log 0.9 = n log 0.5

n = (log 0.9) / (log 0.5)

n = 0.152

It takes 0.152 half-lives. The half-life of carbon-14 is 5730 years.

0.152 × 5730 years = 871 years

The closest answer is D.

8 0

3 years ago

What is the solution to f (x)=g (x), if f (x)=-x and g (x)=x​

What is the solution to f (x)=g (x), if f (x)=-x and g (x)=x