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a_sh-v [17]
2 years ago
12

A 4-foot tall child walks directly away from a 12-foot tall lamppost at 2 mph. How quickly is the length of her shadow increasin

g when she is 6 feet away from the lamppost (rounded to the nearest tenth of a foot per second)

Mathematics
1 answer:
xz_007 [3.2K]2 years ago
3 0

Answer:

The length of the shadow is increasing with the rate of 1.5 feet per sec

Step-by-step explanation:

Let AB and CD represents the height of the lamppost and child respectively ( shown below )

Also, let E be a point represents the position of child.

In triangles ABE and CDE,

\angle ABE\cong \angle CDE    ( right angles )

\angle AEB\cong \angle CED  ( common angles )

By AA similarity postulate,

\triangle ABE\sim \triangle CDE

∵ Corresponding sides of similar triangles are in same proportion,

\implies \frac{AB}{CD}=\frac{BE}{DE}

We have, AB = 12 ft, CD = 4 ft, BE = BD + DE = 6 + DE,

\implies \frac{12}{4}=\frac{6+DE}{DE}

12DE = 24 + 4DE

8DE = 24

DE=3

Now, the speed of walking = 2 mph = \frac{2\times 5280}{3600}\approx 2.933\text{ ft per sec}

Note: 1 mile = 5280 ft, 1 hour = 3600 sec

Thus, the time taken by child to reach at E  

= \frac{\text{Walked distance}}{\text{Walking speed}}

=\frac{6}{2.933}

= 2.045 hours

Hence, the change rate in the length of shadow

= \frac{\text{Length of shadow}}{\text{Time taken}}

=\frac{3}{2.045}

= 1.5 ft per sec.

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A spherical balloon has a 34-in. diameter when it is fully inflated. Half of the air is let out of the balloon. Assume that the
jeka57 [31]

Answer:

a. 20,579.52 cubic inches

b.10,289.76  cubic inches.

c. 13.49 inches

Step-by-step explanation:

Hi, to answer this question we have to calculate the volume of a sphere:

Volume of a sphere: 4/3 π r³

Since diameter (d) = 2 radius (r)

Replacing with the value given:

34 =2r

34/2=r

r= 17 in

Back with the volume formula:

V = 4/3 π r³

V =4/3 π (17)³

V = 20,579.52 cubic inches

The volume of the half-inflated balloon is equal to the volume of the sphere divided by 2.

20,579.52/2 = 10,289.76  cubic inches.

To find the radius of the half-inflated balloon we have to apply again the volume formula and substitute v=10,289.76

10,289.76= 4/3 π r³

Solving for r

10,289.76/ (4/3 π)= r³

2,456.5 = r³

∛2,456.5 = r

r = 13.49 inches

7 0
3 years ago
Pedro is building a playground in the shape of a right triangle he wants to know the area of the playground to help him decide h
shusha [124]

Answer:

Amount of sand=Area of triangle(ABC)=1/2*AB*BC

Dimension of rectangle as  length=BC and breadth=AB

Step-by-step explanation:

Given:

Pedro building a playground in shape of right angled triangle.

To Find:

How much sand he need to buy

And if playground changed to rectangle what will be the dimensions.

Solution:

<em>Consider a ΔABC be the play ground vertex of playground,</em>

<em>And AB and BC be the sides making right angle.</em>

The sand required to fill ground will be the amount of are covered by the ABC triangle.

So,

Area Of triangle(ABC)=1/2* base* height

Here base will be BC and height =AB

Therefore Area of Triangle(ABC)=1/2*BC*AB

Depending on the lengths of base and height amount of sand will be decided.

Now,

<em>For Rectangle dimensions,</em>

<em>We know that if same sized triangles composes each other forms a rectangle</em>.

It requires two triangle to form one rectangle as follows

(Refer the attachment)

Same sized Triangle ACD is imposed on it  to from rectangle ABCD.

So dimension for rectangle will be same as the triangle

Dimension=length and breadth

i.e. length=base of triangle=BC

Breadth=Height of triangle=AB

i.e Breadth =AB.

5 0
3 years ago
Simplify (7/9a+9/7b)^2-ab
lianna [129]
Ab+49/81a^2+81/49b^2
7 0
2 years ago
Solve for x in simmilar triangles connected
amid [387]

Step-by-step explanation:

You can figure out the missing side length by using proportions because the corresponding side lengths form a proportion. Let's write ratios that form a proportion and find the pattern to figure out the length of the missing side. Looking at this you can see the pattern

6 0
2 years ago
Evaluate the expression below using the properties of operations. Show your steps.−36 ÷ 14 ⋅ (−18) ⋅ (−3) ÷ 6
s2008m [1.1K]

Answer:

(-162)/7 or -23 1/7 as mixed fraction

Step-by-step explanation:

Simplify the following:

(-36)/14 (-18) (-3)/6

Hint: | Express (-36)/14 (-18) (-3)/6 as a single fraction.

(-36)/14 (-18) (-3)/6 = (-36 (-18) (-3))/(14×6):

(-36 (-18) (-3))/(14×6)

Hint: | In (-36 (-18) (-3))/(14×6), divide -18 in the numerator by 6 in the denominator.

(-18)/6 = (6 (-3))/6 = -3:

(-36-3 (-3))/14

Hint: | In (-36 (-3) (-3))/14, the numbers -36 in the numerator and 14 in the denominator have gcd greater than one.

The gcd of -36 and 14 is 2, so (-36 (-3) (-3))/14 = ((2 (-18)) (-3) (-3))/(2×7) = 2/2×(-18 (-3) (-3))/7 = (-18 (-3) (-3))/7:

(-18 (-3) (-3))/7

Hint: | Multiply -18 and -3 together.

-18 (-3) = 54:

(54 (-3))/7

Hint: | Multiply 54 and -3 together.

54 (-3) = -162:

Answer:  (-162)/7

3 0
3 years ago
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