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1 month ago

The segments shown below could form a triangle.

Mathematics

1 answer:

AnnZ [12.3K]1 month ago

5 0

Answer:

A. True

Step-by-step explanation:

The Triangle Inequality Theorem establishes that the sum of two sides must exceed the length of the third side. Let’s verify this.

a + b

9 + 1 = 10>9

a + c

9 + 9 = 18>1

c + b

9 + 1 = 10>9

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Find the dimensions of the closed rectangular box with maximum volume that can be inscribed in the unit sphere.

Inessa [12570]

Answer:

Wyjaśnienie krok po kroku:

Załóżmy, że prostokąt ma wierzchołki (x,y,z) w dodatnim oktancie. Prostokątny pudełko musi być symetryczne względem wszystkich trzech osi.

Wtedy jego boki to

$2x,2y,2z$

Objętość = $8xyz$

Maksymalizuj objętość przy założeniu

$x^2+y^2+z^2 =1$

tj. $g(x,y,z) = x^2+y^2+z^2 -1=0$

Użyj mnożników Lagrange'a, mamy

$∇f(x,y,z)=λ∇g(x,y,z)$ przy maksimum

$∇f(x,y,z)=λ∇g(x,y,z) =(8yz,8xz,8xy)\\∇g(x,y,z)=(2x,2y,2z)$

$8yz=2λx8xz=2λy8xy=2λz$

Dzieląc otrzymujemy

$\frac{y}{x} =\frac{x}{y} \\x^2=y^2$

Podobnie $y^2=z^2$

Zatem otrzymujemy $3x^2 =1\\x = \frac{1}{\sqrt{3} }$

Stąd wymiary to

(2x,2y,2z)

$\frac{2}{\sqrt{3} },\frac{2}{\sqrt{3} },\frac{2}{\sqrt{3} } )$

</pzatem>

3 0

1 month ago

A merry-go-round has a radius of 18 feet. If a passenger gets on a

Zina [12379]

Answer:

The rotation angle measures 2.11 °

Step-by-step explanation:

Stated as follows:

The radius of the circular path = r = 18 feet

The distance rolled by the wheel = l = 38 feet

Let us denote the angle of rotation as Ф

Now, according to the problem:

∵ the length of an arc at the center corresponds to an angle Ф

Thus,

distance rolled by the wheel = π × radius × $\frac{\Theta }{180^{\circ}}$

As 180° represents π radians

And π approximates to 3.14

Thus, distance rolled by the wheel = 180 °× radius × $\frac{\Theta }{180^{\circ}}$

That is l = r × Ф

So, Ф = $\frac{l}{r}$

Consequently, Ф = $\frac{38 feet}{18 feet}$

Therefore, Ф = 2.11 °

Thus, the rotation angle is Ф = 2.11 °

Hence, the rotation angle is 2.11 ° Answer

6 0

2 months ago

Heights of adult males are known to have a normal distribution. a researcher claims to have randomly selected adult males and me

Leona [12618]

Answer:

The total probability exceeds 100%, indicating a problem with the findings; moreover, the distribution shows excessive uniformity which disqualifies it as a normal distribution.

Detailed explanation:

The sum of probabilities should be exactly 100%. When you add the probabilities of this distribution:

22+24+21+26+28 = 46+21+26+28 = 67+26+28 = 93+28 = 121

This exceeds 100%, highlighting a significant error in the results.

A typical normal distribution possesses a bell curve. If we plot the probabilities for this distribution, we'd see bars at 22, 24, 21, 26, and 28.

The bars would fail to form a bell-shaped curve, confirming that this is not a normal distribution.

3 0

1 month ago

Read 2 more answers

The parent cosecant function is shifted 4 units right and 3 units up. Which of the following is the graph of the transformed fun

AnnZ [12381]

We can use a graphing tool to plot the <span> cosecant function
</span>check the attached image

the answer corresponds to option B

4 0

26 days ago

Read 2 more answers

A music buff wants to estimate the percentage of students at a midwestern university who believe that elvis is still alive. how

Leona [12618]

Lacking information on the proportion, we will assume the sample proportion is 0.50

thus,
p = 0.50
The margin of error is set at 10 percentage points. This indicates that the error on either side of the population proportion is 5%, so E = 0.05
z = 1.645 (Z value for a confidence level of 90%)

The calculation for the margin of error when estimating population proportions follows:

$E=z* \sqrt{ \frac{p(1-p)}{n} } \\ \\ 
 \frac{E}{z} = \sqrt{ \frac{p(1-p)}{n} } \\ \\ 
( \frac{E}{z} )^{2}= \frac{p(1-p)}{n} \\ \\ 
n= p(1-p)* (\frac{z}{E})^{2} \\ \\ 
n=271$

Consequently, 271 students need to be part of the sample.

5 0

1 month ago