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3 years ago

How do u find angle mesurements in a triangle

Mathematics

1 answer:

alexgriva [62]3 years ago

3 0

The sum of all the angles must be 180 degrees.

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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

2 years ago

Math SAT: Suppose the national mean SAT score in mathematics was 510. In a random sample of 50 graduates from Stevens High, the

sukhopar [10]

Answer:

Mean SAT score for Stevens High graduates are not the same as the national average.

Step-by-step explanation:

We are given the following information in question:

Population mean, μ = 510

Sample mean, $\bar{x}$ = 501

Sample size, n = 50

Alpha, α = 0.10

Sample standard deviation, s = 30

First, we design the null and the alternate hypothesis

$H_{0}: \mu = 510\\H_A: \mu \neq 510$

We use Two-tailed t test to perform this hypothesis.

Formula:

$t_{stat} = \displaystyle\frac{\bar{x} - \mu}{\frac{\sigma}{\sqrt{n-1}} }$ Putting all the values, we have,

$t_{stat} = \displaystyle\frac{501 - 510}{\frac{30}{\sqrt{49}} } = -2.1$ Now,

$t_{critical} \text{ at 0.10 level of significance, 49 degree of freedom } = \pm 1.6765$ Since,

$t_{stat} < t_{critical}$

We reject the null hypothesis and fail to accept it.

We accept the alternate hypothesis and mean SAT score for Stevens High graduates are not the same as the national average.

3 0

3 years ago

What is the value ?????

worty [1.4K]

Cos x = 15÷17
because cos is adjacent side over hypotenuse.

6 0

3 years ago

Lisa used the rule "Red, Yellow, Yellow, Yellow" to make a bracelet with a repeating pattern. She

konstantin123 [22]

Answer:

28 beads were used to make the bracelet. 7 beads were not yellow.

Step-by-step explanation:

3/4 beads used to make the bracelet are yellow

If 21 beads are 3/4 of the bracelet and yellow

1/3 of the 21 beads would be 1/4 of the bracelet

7 beads are 1/3 of 21 beads

7 × 4 = 28 beads

8 0

3 years ago

A clinical test on humans of a new drug is normally done in three phases. Phase I is conducted with a relatively small number of

navik [9.2K]

Answer:

A clinical test on humans of a new drug is normally done in three phases. Phase I is conducted with a relatively small number of healthy volunteers. For example, a phase I test of a specific drug involved only 7 subjects.

Step-by-step explanation:

6 0

3 years ago