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Veseljchak [2.6K]

3 years ago

15

The perimeter of a triangle is 82 feet. One side of the triangle is 2 times the second side. The third side is 2 feet longer tha

n the second side. Find the length of each side.

1 answer:

andrezito [222]3 years ago

3 0

Answer:

first side=40

second side=20

third side=22

Step-by-step explanation:

LET THE SIDES OF THE TRIANGLES BE y

Perimeter=82

first side=2 x y = 2y

second side=y

third side=2 +y

2y + y + 2 + y=82

4y+2=82

4y= 82-2

4y=80

y=80/4

y=20

first side=2y=2(20)=40

second side=y=20

third side= 2 + y= 2 + 20 = 22

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Order the lengths 1/4 inch, 0.5 inch, and 10/25 inch from least to greatest.

pshichka [43]

Converting everything to decimals:

0.25 inch, 0.5 inch, 0.4 inch

Ordering:

0.25, 0.4, 0.5

Converting the appropriate numbers back to fractions:

1/4,10/25,0.5.

6 0

3 years ago

If 1st and 4tg terms of G.p are 500 and 32 respectively it's second term is ?

bixtya [17]

Answer:

$T_{2} = 200$

Step-by-step explanation:

Given

Geometry Progression

$T_1 = 500$

$T_4 = 32$

Required

Calculate the second term

First, we need to write out the formula to calculate the nth term of a GP

$T_n = ar^{n-1}$

For first term: Tn = 500 and n = 1

$500 = ar^{1-1}$

$500 = ar^{0}$

$500 = a$

$a = 500$

For fought term: Tn = 32 and n = 4

$32 = ar^{4-1}$

$32 = ar^3$

Substitute 500 for a

$32 = 500 * r^3$

Make r^3 the subject

$r^3 = \frac{32}{500}$

$r^3 = 0.064$

Take cube roots

$\sqrt[3]{r^3} = \sqrt[3]{0.064}$

$r = \sqrt[3]{0.064}$

$r = 0.4$

Using: $T_n = ar^{n-1}$

$n = 2$ $r = 0.4$ and $a = 500$

$T_{2} = 500 * 0.4^{2-1}$

$T_{2} = 500 * 0.4^1$

$T_{2} = 500 * 0.4$

$T_{2} = 200$

<em>Hence, the second term is 200</em>

5 0

3 years ago

QUESTIONS IN Picture TYSM Guys

babymother [125]

Option E:

The value of m that makes the inequality true is 5.

Solution:

Given inequality is 3m + 10 < 30.

Let us first simplify the expression.

3m + 10 < 30

Subtract 10 from both side of the equation.

3m < 20 – – – – (1)

<u>To find the value of m that makes the inequality true:</u>

Option A: 20

Substitute m = 20 in (1),

⇒ 3(20) < 20

⇒ 60 < 20

It is not true because 60 is greater than 20.

Option B: 30

Substitute m = 30 in (1),

⇒ 3(30) < 20

⇒ 90 < 20

It is not true because 90 is greater than 20.

Option C: 8

Substitute m = 8 in (1),

⇒ 3(8) < 20

⇒ 24 < 20

It is not true because 24 is greater than 20.

Option D: 10

Substitute m = 10 in (1),

⇒ 3(30) < 20

⇒ 90 < 20

It is not true because 90 is greater than 20.

Option E: 5

Substitute m = 5 in (1),

⇒ 3(5) < 20

⇒ 15 < 20

It is true because 15 is less than 20.

Hence the value of m that makes the inequality true is 5.

Option E is the correct answer.

5 0

3 years ago

PLS TRY TO ANSWER ASAP.

Harrizon [31]

Answer:

<u>0.075 m/min</u>

Explanation:

You need to use derivatives which is an advanced concept used in calculus.

<u>1. Write the equation for the volume of the cone:</u>

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

<u />

<u>2. Find the relation between the radius and the height:</u>

r = diameter/2 = 5m/2 = 2.5m

h = 5.2m

h/r =5.2 / 2.5 = 2.08

<u>3. Filling the tank:</u>

Call y the height of water and x the horizontal distance from the axis of symmetry of the cone to the wall for the surface of water, when the cone is being filled.

The ratio x/y is the same r/h

x/y=r/h

y = x . h / r

The volume of water inside the cone is:

$V=\dfrac{1}{3}\pi x^2y$

$V=\dfrac{1}{3}\pi x^2(2.08)\cdot x\\\\\\V=\dfrac{2.08}{3}\pi x^3$

<u>4. Find the derivative of the volume of water with respect to time:</u>

$\dfrac{dV}{dt}=2.08\pi x^2\dfrac{dx}{dt}$

<u>5. Find x² when the volume of water is 8π m³:</u>

$V=\dfrac{2.08}{3}\pi x^3\\\\\\8\pi=\dfrac{2.08}{3}\pi x^3\\\\\\ 11.53846=x^3\\ \\ \\ x=2.25969\\ \\ \\ x^2=5.1062$ m²

<u>6. Solve for dx/dt:</u>

$1.2m^3/min=2.08\pi(5.1062m^2)\dfrac{dx}{dt}$

$\dfrac{dx}{dt}=0.03596m/min$

<u />

<u>7. Find dh/dt:</u>

From y/x = h/r = 2.08:

$y=2.08x\\\\\\\dfrac{dy}{dx}=2.08\dfrac{dx}{dt}\\\\\\\dfrac{dy}{dt}=2.08(0.035964m/min)=0.0748m/min\approx0.075m/min$

That is the rate at which the water level is rising when there is 8π m³ of water.

4 0

3 years ago

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2 years ago