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3 years ago

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A new bridge structure requires triangles that are in a ratio of 1:1. If AC = 2x + 10 and EC = 4x − 18, find the distance betwee

n the top and bottom of the bridge, in feet.

1 answer:

Serjik [45]3 years ago

3 0

Distance between the top and bottom of the bridge is 76 feet

Solution:

The image of the question is attached below.

Ratio of the triangles is 1 : 1.

AC = 2x + 10 and EC = 4x − 18.

Since the two triangles ACB and DCE are in the ratio 1 : 1, so their corresponding sides are also in the ratio 1 : 1.

Therefore sides AC and EC are corresponding to each other.

AC : EC = 1 : 1

$$\Rightarrow \frac{A C}{E C}=\frac{1}{1}$

$\Rightarrow A C=E C$

$\Rightarrow 2 x+10=4 x-18$

Subtract 10 from both sides of the equation.

$\Rightarrow 2 x=4 x-28$

Subtract 4x from both sides of the equation.

$\Rightarrow -2 x=-28$

Divide by -2 on both sides, we get

⇒ x = 14

Distance between the top and bottom of the bridge is EA.

EA = AC + EC

= 2x + 10 + 4x - 18

= 6x - 8

= 6(14) - 8

= 84 - 8

EA = 76 feet

Distance between the top and bottom of the bridge is 76 feet.

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kodGreya [7K]

Answer:

The maximum height of the ball is: 14.0625ft

Step-by-step explanation:

The missing information is:

$h(t) = 30t - 16t^2$

Required

The maximum height the ball attained

First, we calculate the time to reach the maximum height.

For a function: $h(t) = at^2 + bt + c$

The maximum is: $t = \frac{-b}{2a}$

So, the maximum of $h(t) = 30t - 16t^2$ is:

$t = \frac{-b}{2a}$

Where

$a = -16; b = 30$

So:

$t = -\frac{30}{2*-16}$

$t = -\frac{30}{-32}$

$t = \frac{30}{32}$

$t = 0.9375$

The maximum height is then calculated as:

$h(t) = 30t - 16t^2$

$h(0.9375) = 30 * 0.9375- 16 * 0.9375^2$

$h(0.9375) = 28.125- 14.0625$

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8 0

3 years ago

MARKING BRANLIEST!!

grin007 [14]

Area of a triangle is = 0.5bh
if the height (h) is 4 less than base (b) then h = b - 4

48 = 0.5(b)(b - 4)
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b must be either -8 or 12

since a distance can't be negative that means
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3 years ago

Find the smallest positive integer n such that n(n+1)(n+2) is divisible by 247.

Butoxors [25]

Answer:

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Step-by-step explanation:

First we will find the prime factors of 247:

247 = 13 x 19 (which are both prime).

So now we need to find a number (the smallest one) that is of the form (n)(n+1)(n+2) (the product of three consecutive numbers) and that is divisible by both 13 and 19 (and therefore divisible by 247)

Let's take a look at the multiples of 13: 13, 26, 39, 52...

Let's take a look at the multiples of 19: 19, 38, 57...

We can see that the first time we have two multiples close together are the 38 (for 19) and the 39 (for 17).

So, if our number has both 38 and 39 as factors, then it will be divisible by 247.

However, we need not two but three consecutive numbers, and since we want the number to be the smallest positive integer, we will add 37 (since our other choice would be to add 40 and that would make the number bigger) and thus our number is (37)(38)(39) or in other words (37)(37 + 1)(37 + 2) and therefore this is the smallest positive number such that n(n+1)(n+2) is divisible by 247.

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