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MAVERICK [17]
3 years ago
12

George is 1.94 meters tall and wants to find the height of a tree in his yard. He started at the base of the tree and walked 10.

20 meters along the shadow of the tree until his head was in a position where the tip of his shadow exactly overlaps the end fo the tree top's shadow. He is now 5.1 meters from the end of the shadows. How tall is the tree?

Mathematics
1 answer:
Free_Kalibri [48]3 years ago
7 0
Draw a diagram to illustrate problem as shown below.

Let h = the height of the tree.

Because ΔABC ~ ΔADE, therefore
DE/BC = AD/AB

That is,
h/1.94 = (5.1 + 10.2)/5.1 = 3
h = 1.94*3 = 5.82 m

Answer: 5.82 m

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Pls help me with this question​
RoseWind [281]

Answer:

the answer is 3 and 90 that's all

8 0
2 years ago
Read 2 more answers
Triangle VXW is similar to triangle ZXY. Triangle V X W. Side V W is 12 miles and side V X is 14 miles. Triangle Z X Y. Side Y Z
amid [387]

Answer: Kara should have written the proportion in step 1 as;

Start Fraction 12 Over 72 End Fraction = Start Fraction 14 Over x End Fraction (that is 12/72 = 14/x)

Step-by-step explanation: The two similar triangles are given with the following dimensions;

Triangle VXW with side VW = 12 and side VX = 14. Also Triangle ZXY with side YZ = 72 and side XZ = x.

For two triangles to be similar, then there must be a similarity ration that is consistent with all sides in both triangles. This means if in the first triangle a side measures  1 unit and the similar side in the other triangle measures 5 units, then the ratio of similarity of corresponding sides shall be ratio 1 : 5. So for every corresponding side in the second triangle the measurement shall be times five of the side that corresponds in the first triangle.

Therefore, in triangle VXW and triangle ZXY, the corresponding sides are as follows;

VX = ZX

VW = ZY

XW = XY

What Kara did was as follows;

VX/ZY = VW/ZX

Which translates to 14/72 = 12/x

This was a wrong calculation because the side that corresponds to VX is ZX and not ZY.

The correct step should therefore have been;

VW/ZY = VX/ZX

12/72 = 14/x (Step 1)

12x = (72) (14) {Step 2}

x = 1008/12 (Step 3)

x = 84 (Step 4)

5 0
3 years ago
Read 2 more answers
The following integral requires a preliminary step such as long division or a change of variables before using the method of par
shtirl [24]

Division yields

\dfrac{x^4+7}{x^3+2x} = x-\dfrac{2x^2-7}{x^3+2x}

Now for partial fractions: you're looking for constants <em>a</em>, <em>b</em>, and <em>c</em> such that

\dfrac{2x^2-7}{x(x^2+2)} = \dfrac ax + \dfrac{bx+c}{x^2+2}

\implies 2x^2 - 7 = a(x^2+2) + (bx+c)x = (a+b)x^2+cx + 2a

which gives <em>a</em> + <em>b</em> = 2, <em>c</em> = 0, and 2<em>a</em> = -7, so that <em>a</em> = -7/2 and <em>b</em> = 11/2. Then

\dfrac{2x^2-7}{x(x^2+2)} = -\dfrac7{2x} + \dfrac{11x}{2(x^2+2)}

Now, in the integral we get

\displaystyle\int\frac{x^4+7}{x^3+2x}\,\mathrm dx = \int\left(x+\frac7{2x} - \frac{11x}{2(x^2+2)}\right)\,\mathrm dx

The first two terms are trivial to integrate. For the third, substitute <em>y</em> = <em>x</em> ² + 2 and d<em>y</em> = 2<em>x</em> d<em>x</em> to get

\displaystyle \int x\,\mathrm dx + \frac72\int\frac{\mathrm dx}x - \frac{11}4 \int\frac{\mathrm dy}y \\\\ =\displaystyle \frac{x^2}2+\frac72\ln|x|-\frac{11}4\ln|y| + C \\\\ =\displaystyle \boxed{\frac{x^2}2 + \frac72\ln|x| - \frac{11}4 \ln(x^2+2) + C}

7 0
2 years ago
Find the measure of angle x in the figure below: (1 point) Two triangles are shown such that one triangle is inverted and share
Elena L [17]
75°+75°=150°
angles in a triangle add up to 180°
180°-150°=30°
c) x=30°
5 0
2 years ago
What is the fraction of 35%
Tanzania [10]
Percentage is out of a 100. Therefore, 35/100
Simplify 35/100
Becomes 7/20
Fraction of 35% is 7/20
5 0
3 years ago
Read 2 more answers
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