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8_murik_8 [283]
3 years ago
12

The first side of a triangle is 9 meters shorter than the second side. The third side is 3 times as long as the first side. The

perimeter is 39 meters. Find the length of the longest side.
Mathematics
1 answer:
Alex73 [517]3 years ago
7 0

Answer:

The longest sides is 18 m long.

Step-by-step explanation:

Let x meters be the length of the first side.

The length of the second side = x+9 m.

The length of the third = 3x m.

Perimeter = x + 3x + x + 9 = 39

5x + 9 = 39

5x = 30

x = 6 m.

The other 2 sides are  6+9 = 15 m and 3*6 = 18 m.

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You are a traffic accident investigator. You have arrived at the scene of an accident. Two trucks of equal mass (3,000 kg each)
Kazeer [188]

Answer:

1) Kinetic energy of the truck 1 is 600,000 joules.

Kinetic energy of the truck 2 is 1,837,500 joules.

2 a)Potential energy of truck 1 is 646,800 Joules.

b) Energy lose by the truck 1 just got converted into heat and sound energy during the collision.

Step-by-step explanation:

Mass of the truck 1 and truck 2,m = 3000 kg

Velocity of the truck 1, v_1 = = 20 m./s

Velocity of the truck 2,v_2 = 35 m./s

1. Kinetic energy of the truck 1:\frac{1}{2}mv_{1}^2=\frac{1}{2}\times 3000 kg\times (20 m/s)^=600,000 joules

Kinetic energy of the truck 2:\frac{1}{2}mv_{2}^2=\frac{1}{2}\times 3000 kg\times (35 m/s)^=1,837,500 joules

2.a) Energy loose by the truck 1:

Initial height of the truck on the hill = 22 m

At that height potential energy will be maximum:

Potential energy of truck 1 at that height = mgh=3000\times 9.8 m/s^2\times 22 m=646,800 Joules

b) Energy lose by the truck 1 just got converted into heat and sound energy during the collision.

3 0
3 years ago
What is the volume of a cone with a height of 9.5 inches and a radius of 8 inches? Cone V = 1 3 Bh 1. Rewrite the formula for th
Nesterboy [21]

Answer:

636.4 in³  

Step-by-step explanation:

Volume of a cone is given by:

V = \frac{1}{3}\pi r^2 h

where r is the radius of the base of the cone and h is its height.

It is given that, the radius of the base of the cone is, r = 8 in

The height of the cone is, h = 9.5

\Rightarrow V = \frac{1}{3} \times 3.14 \times (8)^2 (9.5) = 636.4 in^3

Thus, the volume of the cone is 636.4 in³  

6 0
3 years ago
Read 2 more answers
Prove :<br>sin²θ + cos²θ = 1<br><br><br>thankyou ~​
Gnom [1K]

Answer:

See below

Step-by-step explanation:

Here we need to prove that ,

\sf\longrightarrow sin^2\theta + cos^2\theta = 1

Imagine a right angled triangle with one of its acute angle as \theta .

  • The side opposite to this angle will be perpendicular .
  • Also we know that ,

\sf\longrightarrow sin\theta =\dfrac{p}{h} \\

\sf\longrightarrow cos\theta =\dfrac{b}{h}

And by Pythagoras theorem ,

\sf\longrightarrow h^2 = p^2+b^2 \dots (i)

Where the symbols have their usual meaning.

Now , taking LHS ,

\sf\longrightarrow sin^2\theta +cos^2\theta

  • Substituting the respective values,

\sf\longrightarrow \bigg(\dfrac{p}{h}\bigg)^2+\bigg(\dfrac{b}{h}\bigg)^2\\

\sf\longrightarrow \dfrac{p^2}{h^2}+\dfrac{b^2}{h^2}\\

\sf\longrightarrow \dfrac{p^2+b^2}{h^2}

  • From equation (i) ,

\sf\longrightarrow\cancel{ \dfrac{h^2}{h^2}}\\

\sf\longrightarrow \bf 1 = RHS

Since LHS = RHS ,

Hence Proved !

I hope this helps.

5 0
2 years ago
Explain why each of the following studies may fail to yield the desired information. (a) To determine the average annual income
harkovskaia [24]

Answer:

the following studies may fail to yield the desired information because

(a) i. some of the students might have died before 2015.

ii. Some people might lie based on the questionnaire sent.

So based on the two factors above the desired information might be altered or incorrect.

(b) i. individuals may be unwilling to provide accurate answers during the survey.

Step-by-step explanation:

Information may be altered when individuals are asked about their income or spending in other to show off to friends or the person asking the questions.

8 0
3 years ago
Last week, Leon bought 8 pizzas and 13 cakes
romanna [79]
P = pizza and c =cakes

Last week: 8p + 13c = 134
Today: 28p + 4c = 220

Let’s take the formula for today and subtract 28p from each side to isolate the 4c.

4c = 220 - 28p

Now divide each side by 4

c = (220 - 28p)/4
Simplify to c = 55 - 7p

Now go to the formula for last week, substitute the c for 55-7p

8p + 13(55 - 7p) = 134
8p + 715 - 91p = 134

Simplify to 715 - 83p = 134

Let’s add 83p to each side.

715 = 134 + 83p

Subtract 134 from each side

581 = 83p

Divide each side by 83

p = $7
5 0
2 years ago
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