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lakkis [162]
3 years ago
15

...............................

Mathematics
1 answer:
antoniya [11.8K]3 years ago
4 0

Answer:

<h2>2 \sqrt{10}</h2>

Option C is the correct option.

Step-by-step explanation:

√ 8 • √ 5

Calculate the product

=  \sqrt{40}

Simplify the radical expression

=  \sqrt{2 \times 2 \times 10}

= 2 \sqrt{10}

Hope this helps...

Best regards!!

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Paul and jose are trying to measure the height of a tree. paul is standing 19m from the foot of the tree and measures the angle
Nina [5.8K]
The firts thig we are going to do is create tow triangles using the angles of elevation of Paul and Jose. Since the problem is not giving us their height we'll assume that the horizontal line of sight of both of them coincide with the base of the tree.
We know that Paul is 19m from the base of the tree and its elevation angle to the top of the tree is 59°. We also know that the elevation angle of Jose and the top of the tree is 43°, but we don't know the distance between Paul of Jose, so lets label that distance as x.
Now we can build a right triangle between Paul and the tree and another one between Jose and the tree as shown in the figure. Lets use cosine to find h in Paul's trianlge:
cos(59)= \frac{19}{h}
h= \frac{19}{cos(59)}
h=36.9
Now we can use the law of sines to find the distance x between Paul and Jose:
\frac{sin(43)}{36.9} = \frac{sin(16)}{x}
x= \frac{36.9sin(16)}{sin(43)}
x=14.9

Now that we know the distance between Paul and Jose, the only thing left is add that distance to the distance from Paul and the base of the tree:
19m+14.9=33.9m

We can conclude that Jose is 33.9m from the base of the tree.

3 0
3 years ago
Find the distance between the points <br><br>(−5,2) and (9.2)<br>​
forsale [732]

Step-by-step explanation:

<u>Formula</u><u> </u><u>U</u><u>s</u><u>e</u><u>d</u>

<u>By distance formula,</u>

  • d (A,B)=√[(x₁ - x₂)² + (y₁ - y₂)²]

\sf \longmapsto \: D = √(x2-x1)²+(y2-y1)²

\sf \longmapsto= √(9+5)²+(2-2)²

\sf \longmapsto= = √14²+09

\sf \red \longmapsto \boxed{= 14}

4 0
2 years ago
A manufacturer determines that the number of toys it can sell is given by the formula
otez555 [7]

Answer:

The price where the manufacture sells the maximum number of toys is $20

Step-by-step explanation:

The given equation for that represents the number of toys the manufacturer can sell is given as follows;

T = -4·p² + 160·p - 305

Where;

p = The price of the toys in dollars

At the point where the manufacture sells the maxim number of toys on the graph of the equation T = -4·p² + 160·p - 305, which is the top of the graph, the slope = 0

Therefore, at the maximum point;

The slope = 0 = dT/dp = d(-4·p² + 160·p - 305)/dp = -8·p + 160

∴ -8·p + 160 = 0

160 = 8·p

8·p = 160

p = 160/8 = 20

The price where the manufacture sells the maximum number of toys is = p = 20 dollars

4 0
2 years ago
Which describes the correct procedure when converting a number from scientific notation to standard notation if the power of 10
jenyasd209 [6]

Answer:

A. Move the decimal point to the left

Step-by-step explanation:

Given that:

The scientific notation = 10⁻¹⁰

Let recall;

That the standard notation usually took the form of an inverse:

For example;

Let say 10⁻¹ will be \dfrac{1}{10} in scientific notation;

SO, \dfrac{1}{10} = 0.1

Now; we are given 10⁻¹⁰ as a scientific notation,

To standard notation, we get:

10^{-10} = \dfrac{1}{100}

= 0.01

Thus, it is true to say that the decimal point will be moved to the left side when converting a number from scientific notation to standard notation if the power of 10 is  -10.

4 0
2 years ago
An Air Force plane flew to the
Free_Kalibri [48]

Answer:

5 hours

Step-by-step explanation:

Time taken for trip : t + 1

Time taken for return : t

Avg. speed (trip) : 256 km/h

Avg. speed (return) : 320 km/h

The distances covered on both trips are equal.

⇒ Distance (trip) = Distance (return)

⇒ Speed (trip) × time (trip) = Speed (return) × time (return)

⇒ (256)(t + 1) = (320)(t)

⇒ 256t + 256 = 320t

⇒ 64t = 256

⇒ t = 4 hours

<u>Time (trip)</u> = t + 1 = 4 + 1 = 5 hours

4 0
2 years ago
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