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2 years ago

Please help ill mark brainliest!!!

Mathematics

1 answer:

Bingel [31]2 years ago

8 0

Triangle QST is similar to triangle PQR

We are given that measure of angle SRP is 90°

Q is the point of the hypotenuse SP

Segment QR is perpendicular to PS and T is a point outside the triangle on the left of s

We need to find which triangle is similar to triangle PQR

So,

Using Angle - Angle - Angle Criterion We can say that

m∠PQR = m∠SQR (AAA similarity)

m∠SQR=m∠SQT (AAA similarity)

Where m∠Q =90° in ΔQST and PQR

Therefore ΔQST is similar to ΔPQR

Learn more about similarity of triangles here

brainly.com/question/24184322

#SPJ4

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Find the minimum and maximum of f(x,y,z)=x^2+y^2+z^2 subject to two constraints, x+2y+z=4 and x-y=8.

Alika [10]

The Lagrangian for this function and the given constraints is

$L(x,y,z,\lambda_1,\lambda_2)=x^2+y^2+z^2+\lambda_1(x+2y+z-4)+\lambda_2(x-y-8)$

which has partial derivatives (set equal to 0) satisfying

$\begin{cases}L_x=2x+\lambda_1+\lambda_2=0\\L_y=2y+2\lambda_1-\lambda_2=0\\L_z=2z+\lambda_1=0\\L_{\lambda_1}=x+2y+z-4=0\\L_{\lambda_2}=x-y-8=0\end{cases}$

This is a fairly standard linear system. Solving yields Lagrange multipliers of $\lambda_1=-\dfrac{32}{11}$ and $\lambda_2=-\dfrac{104}{11}$ , and at the same time we find only one critical point at $(x,y,z)=\left(\dfrac{68}{11},-\dfrac{20}{11},\dfrac{16}{11}\right)$ .

Check the Hessian for $f(x,y,z)$ , given by

$\mathbf H(x,y,z)=\begin{bmatrix}f_{xx}&f_{xy}&f_{xz}\\f_{yx}&f_{yy}&f_{yz}\\f_{zx}&f_{zy}&f_{zz}\end{bmatrix}=\begin{bmatrix}=\begin{bmatrix}2&0&0\\0&2&0\\0&0&2\end{bmatrix}$

$\mathbf H$ is positive definite, since $\mathbf v^\top\mathbf{Hv}>0$ for any vector $\mathbf v=\begin{bmatrix}x&y&z\end{bmatrix}^\top$ , which means $f(x,y,z)=x^2+y^2+z^2$ attains a minimum value of $\dfrac{480}{11}$ at $\left(\dfrac{68}{11},-\dfrac{20}{11},\dfrac{16}{11}\right)$ . There is no maximum over the given constraints.

7 0

4 years ago

Sarah Sandoval is a coffee farmer trying to decide how many tons of coffee to produce. She can sell each ton of coffee for $2,40

Alexandra [31]

Answer:

Sarah should produce four tons of coffee and total cost for four ton is $6,000.

Step-by-step explanation:

According to the scenario, calculation of the given data are as follows,

Selling price per ton = $2,400

Cost of production is increasing by $600 for each ton.

So, Cost of production first ton = $600

Cost of production for second ton = $600 + $600 = $1,200

Similarly, Cost of production for third ton = $1,200 + $600 = 1,800

Cost of production of fourth ton = $1,800 + $600 = $2,400

Here, Sarah can produce coffee till selling price = cost of production.

As, cost of production of four ton = selling price, then Sarah can produce only four tons of coffee.

Total cost for four ton coffee = $600 + $1,200 + $1,800 + $2,400

= $6,000

8 0

3 years ago

Here is the dialations that i need help on

Rasek [7]

I really don’t know sorry bro

8 0

4 years ago

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The coefficient of determination is used to: compute correlations for truncated ranges. compare the relative strength of coeffic

kozerog [31]

Answer: compare the relative strength of coefficients.

Step-by-step explanation: The Coefficient of determination usually denoted as R^2 is obtained by taking the squared value of the correlation Coefficient (R). It's value ranges from 0 to 1 and the value obtained gives the proportion of variation in the dependent variable which could be attributed to it's correlation or relationship to th independent variable. With a R^2 value close to 1, this means a large portion of Variation in a variable A could be explained due to changes in variable B while a low value signifies a low variance between the variables. Hence, the Coefficient of determination is used in comparing the relative strength of the Coefficients in other to establish whether a weak or strong relationship exist.

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3 years ago

Fiona y sus amigas fueron a una tienda de batidos. Pidieron tres batidos de fresa y dos batidos de proteínas por un total de $ 2

jeka94

Answer:

Un batido de proteínas cuesta $ 5,25.

Step-by-step explanation:

El sistema de ecuaciones descrito al final del enunciado coincide con lo descrito al comienzo del mismo, de modo que podemos concentraron casi exclusivamente en la resolución del sistema en cuestión, la cual se describe a continuación:

Este es el sistema a resolver:

$x + 4\cdot y = 25,50$ (1)