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Art [367]
3 years ago
8

USING SIMILAR TRIANGLES IN INDIRECT MEASUREMENT If the shadow of a tree is 14 m long and the shadow of a person who is 1.8 m tal

l is 4 m long, how tall is the tree? Which of the following proportions could not be used to solve the problem? 14/1.8 = x/4 x/1.8 = 14/4 x/14 = 1.8/4
Mathematics
1 answer:
maw [93]3 years ago
4 0

Answer:

14/1.8 = x/4

Step-by-step explanation:

Using similar triangles,

height of man/length of man's shadow = height of tree/length of tree's shadow

1.8/4 = x/14

x/14 = 1.8/4

If we cross-multiply, we have

1.8 × 14 = x × 4

dividing both sides by 4 and 1.8,we have

14/4 = x/1.8

x/1.8 = 14/4

So, the two expressions we have are

x/14 = 1.8/4 and x/1.8 = 14/4.

So, the answer is 14/1.8 = x/4 since the product 1.8 × 14 = x × 4 cannot be expressed in the given ratio.

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Answer:

A ) The value of x for  the given circle with chords and center is 8.3

B) The circumference of circle with chords 1.2 cm and 0.5 cm is 4.082

Step-by-step explanation:

Given two figures :

<u>For Figure first  </u>

A circle with center y ,  having two chords FM and NM

FM = 5 x

MN = 2 x + 25

Now from theorem of circle ,

Chords equidistant from center of circle are equal in length

I.e distance of chord MN from center y  and distance of FM from center y are equal

So, FM = MN

Or, 5 x = 2 x + 25

Or, 5 x - 2 x = 25

Or, 3 x = 25

∴       x = \frac{25}{3} = 8.33

<u>For figure second</u>

The length of two adjacent chords of circle is 1.2 cm and 0.5 cm

Let the center of circle = O

Length of chord AB = 1.2 cm

Length of chord BC = 0.5 cm

As both chords are at 90° to each other

So The Length of diameter of circle AC = \sqrt{AB^{2}+BC^{2}}

Or, The Length of diameter of circle AC = \sqrt{1.2^{2}+0.5^{2}}

Or, The Length of diameter of circle AC = \sqrt{1.44+0.25}}

Or, The Length of diameter of circle AC = \sqrt{1.69}

∴ The Length of diameter of circle AC = 1.3 cm

So, Circumference of circle = \pi d

Or, Circumference of circle = 3.14 × 1.3

∴ Circumference of circle = 4.082 cm

Hence,

A ) The value of x for  the given circle with chords and center is 8.3

B) The circumference of circle with chords 1.2 cm and 0.5 cm is 4.082 Answer

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If a(x) = 3x + 1 and b(x)= squareroot x-4, what is the domain of (b*a)(x)?
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\boxed{ \ x \geq 1 \ } or can be written as \boxed{ \ [1, \infty) \ }

<h3>Further explanation</h3>

This is a question about the composition of functions and how to get a domain function.

Given \boxed{ \ a(x) = 3x + 1 \ } and \boxed{ \ b(x) = \sqrt{x - 4} \ }.

We will form (b o a)(x) and then determine the domain.

<u>Step-1</u>

\boxed{ \ (b \circ a)(x) = b(a(x)) \ }

Replace each appearance of x in b(x) with \boxed{ \ a(x) = 3x + 1 \ }.

\boxed{ \ (b \circ a)(x) = \sqrt{(3x + 1) - 4} \ }

Thus, \boxed{ \ (b \circ a)(x) = \sqrt{3x - 3} \ }

<u>Step-2</u>

To be defined, the value under the radical sign must not be negative. Therefore, the domain of (b \circ a)(x) = \sqrt{3x - 3} are processed as follows.

\boxed{ \ 3x - 3 \geq 0 \ }

Both sides added by 3.

\boxed{ \ 3x \geq 3 \ }

Both sides divided by 3.

\boxed{ \ x\geq 1 \ }

Thus, the domain of (b \circ a)(x) = \sqrt{3x - 3} is \boxed{ \ x \geq 1 \ } or can be written as \boxed{ \ [1, \infty) \ }

<h3>Learn more</h3>
  1. If f(x) = x² – 2x and g(x) = 6x + 4, for which value of x does (f o g)(x) = 0? brainly.com/question/1774827
  2. Solve for the value of the function composition brainly.com/question/2142762
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