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3 years ago

The vertices A B C of a triangle are (2,-1,-3) (4,2,3) and (6,3,4) respectively. Show that vector AB=(2,3,6) and AC=9.

Mathematics

1 answer:

Rzqust [24]3 years ago

8 0

Try this option:

1) vector AB=(2;3;6).

$(X_B-X_A;Y_B-Y_A;Z_B-Z_A); \ => (4-2;2+1;3+3); \ =>(2;3;6).$

2) |AC|=9.

$|AC|=\sqrt{(X_C-X_A)^2+(Y_C-Y_A)^2+(Z_C-Z_A)^2}=\sqrt{(6-2)^2+(3+1)^2+(4+3)^2}=\sqrt{81}=9.$

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hammer [34]

Answer:

The test statistic is z=2.5.

The null hypothesis is rejected.

There is enough evidence to support the claim that more than 10% of the 16 ounce cups are underfilled.

Step-by-step explanation:

This is a hypothesis test for a proportion.

The claim is that more than 10% of the 16 ounce cups are underfilled.

Then, the null and alternative hypothesis are:

$H_0: \pi=0.1\\\\H_a:\pi>0.1$

The significance level is assumed to be 0.05.

The sample has a size n=100.

The sample proportion is p=0.18.

$p=X/n=18/100=0.18$

The standard error of the proportion is:

$\sigma_p=\sqrt{\dfrac{\pi(1-\pi)}{n}}=\sqrt{\dfrac{0.1*0.9}{100}}\\\\\\ \sigma_p=\sqrt{0.001}=0.03$

Then, we can calculate the z-statistic as:

$z=\dfrac{p-\pi-0.5/n}{\sigma_p}=\dfrac{0.18-0.1-0.5/100}{0.03}=\dfrac{0.075}{0.03}=2.5$

This test is a right-tailed test, so the P-value for this test is calculated as:

$P-value=P(z>2.5)=0.006$

As the P-value (0.006) is smaller than the significance level (0.05), the effect is significant.

The null hypothesis is rejected.

There is enough evidence to support the claim that more than 10% of the 16 ounce cups are underfilled.

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ella [17]

Answer:

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Step-by-step explanation:

Aqui, usando a função de análise, queremos saber a quantidade de dinheiro que deve ser investido para fornecer o número de visualizações.

A maneira como podemos resolver isso é através da substituição. Precisamos apenas substituir F (x) na equação e resolver x, o que nos dará a idéia da quantidade de dinheiro a ser investido.

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F (x) = 40x + 80

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Blababa [14]

Answer:

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Step-by-step explanation:

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3 years ago

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Nimfa-mama [501]

Answer:

Step-by-step explanation:

Look for the GCF and then divide every term by the GCF to see what remains

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7(4-x)

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3 years ago

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Mashutka [201]

Answer:

This question is solved in detail below. Please refer to the attachment for better understanding of an Ellipse.

Step-by-step explanation:

In this question, there is a spelling mistake. This is vertices not verticles.

So, I have attached a diagram of an ellipse in which it is clearly mentioned where are the vertices of an ellipse.

Vertices of an Ellipse: There are two axes in any ellipse, one is called major axis and other is called minor axis. Where, minor is the shorter axis and major axis is the longer one. The places or points where major axis and minor axis ends are called the vertices of an ellipse. Please refer to the attachment for further clarification.

Equations of an ellipse in its standard form:

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This is the case when major axis the longer one is on the x-axis centered at an origin.

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This is the case when major axis the longer one is on the y-axis centered at an origin.

where major axis length = 2a

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3 years ago

The vertices A B C of a triangle are (2,-1,-3) (4,2,3) and (6,3,4) respectively. Show that vector AB=(2,3,6) and AC=9.​

The vertices A B C of a triangle are (2,-1,-3) (4,2,3) and (6,3,4) respectively. Show that vector AB=(2,3,6) and AC=9.