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3 years ago

Please solve this following question in the picture.

Mathematics

1 answer:

umka2103 [35]3 years ago

7 0

Answer:

I don't know this

Step-by-step explanation:

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In a right triangle ABC, CD is an altitude, such that AD=BC. Find AC, if AB=3 cm, and CD= 2 cm.

konstantin123 [22]

Consider right triangle ΔABC with legs AC and BC and hypotenuse AB. Draw the altitude CD.

1. Theorem: The length of each leg of a right triangle is the geometric mean of the length of the hypotenuse and the length of the segment of the hypotenuse adjacent to that leg.

According to this theorem,

$BC^2=BD\cdot AB.$

Let BC=x cm, then AD=BC=x cm and BD=AB-AD=3-x cm. Then

$x^2=(3-x)\cdot 3,\\ \\x^2=9-3x,\\ \\x^2+3x-9=0,\\ \\D=3^2-4\cdot (-9)=9+36=45,\\ \\\sqrt{D}=\sqrt{45}=3\sqrt{5},\\ \\x_1=\dfrac{-3-3\sqrt{5} }{2}0.$

Take positive value x. You get

$AD=BC=\dfrac{-3+3\sqrt{5} }{2}\ cm.$

2. According to the previous theorem,

$AC^2=AD\cdot AB.$

Then

$AC^2=\dfrac{-3+3\sqrt{5} }{2}\cdot 3=\dfrac{-9+9\sqrt{5} }{2},\\ \\AC=\sqrt{\dfrac{-9+9\sqrt{5} }{2}}\ cm.$

Answer: $AC=\sqrt{\dfrac{-9+9\sqrt{5} }{2}}\ cm.$

This solution doesn't need CD=2 cm. Note that if AB=3cm and CD=2cm, then

$CD^2=AD\cdot DB,\\ \\2^2=AD\cdot (3-AD),\\ \\AD^2-3AD+4=0,\\ \\D$

This means that you cannot find solutions of this equation. Then CD≠2 cm.

8 0

3 years ago

Read 2 more answers

55.8 is 62% of what number

8_murik_8 [283]

All you have to do is multiply 55.8 by .62 to get the answer which is 34.596 but I rounded up it to 34.60

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3 years ago

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The width of a DNA molecule is about 2.5 nanometers. A nanometer is 0.000000001 meter. Write the width of a DNA molecule in scie

Molodets [167]

Hey there!!

Scientific notation of 0.000000001 :

0.1 ⁻⁷

Hope it helps!

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3 years ago

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A wildlife preserve features a crocodile with a documented age of 24 years, believed to be one of the oldest crocodiles in capti

zysi [14]

Answer:

0.0104

Step-by-step explanation:

Given that, the lifespans of crocodiles have an approximately Normal distribution, with a mean of 18 years and a standard deviation of 2.6 years.

So, mean, $\mu=18$

and standard deviation, $\sigma=2.6$

The z-score, for any arbitrary life span of x year, is given by

$z=\frac{x-\mu}{\sigma}$

By using the given values, we have

$z=\frac{x-18}{2.6} \cdots(i)$

The z-score for x=24, by using equation (i), is

$z=\frac{24-18}{2.6}=\frac{6}{2.6}=2.31$

From the table, the area to the left side of z=2.31 =0.98956

But, the proportion of crocodiles have lifespans of at least 24 years

= Area to the right side of the z=2.31

=1- (Area to the left side of the z=2.31)

=1-0.98956

=0.01044

So, the proportion of crocodiles that have lifespans of at least 24 years is 0.0104.

Hence, option (a) is correct.

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3 years ago

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True or false?is the point(16,4) included in this function: Y=2x or Y=x2 or y= x+12 or y=x-12

Gelneren [198K]

Answer:

True

Step-by-step explanation:

It is true because the graph of $y=x-12$ passes through the point $(16,4)$

x = 16

y = 4

Substitute

4 = 16 - 12

4 = 4

Therefore, the answer is true.

8 0

3 years ago