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3 years ago

Find the equation of the line shown

Mathematics

1 answer:

kupik [55]3 years ago

7 0

Answer:

So Y always the double of x if x is 1 then y is 2 if x is 5 then y is 10 so the equation y=2x

Y= 2x

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A 39-foot ladder is leaning against a vertical wall. If the bottom of the ladder is being pulled away from the wall at the rate

LenaWriter [7]

Answer:

The area of the triangle formed is increasing at a rate of 29.75 square feet per second.

Step-by-step explanation:

A 39-foot ladder is leaning against a vertical wall. We are given that the bottom of the ladder is being pulled away at a rate of two feet per second, and we want to find the rate at which the area of the triangle being formed is is changing when the bottom of the ladder is 15 feet from the wall.

Please refer to the diagram below. x is the distance from the bottom of the ladder to the wall and y is the height of the ladder on the wall.

According to the Pythagorean Theorem:

$\displaystyle x^2+y^2=1521$

Let's take the derivative of both sides with respect to time t. Hence:

$\displaystyle \frac{d}{dt}\left[x^2+y^2\right] = \frac{d}{dt}\left[ 1521\right]$

Implicitly differentiate:

$\displaystyle 2x\frac{dx}{dt} + 2y\frac{dy}{dt} = 0$

Simplify:

$\displaystyle x\frac{dx}{dt} + y \frac{dy}{dt} = 0$

The area of the triangle formed will be given by:

$\displaystyle A = \frac{1}{2} xy$

Again, let's take the derivative of both sides with respect to time t:

$\displaystyle \frac{dA}{dt} = \frac{d}{dt}\left[\frac{1}{2}xy\right]$

From the Product Rule:

$\displaystyle \frac{dA}{dt} = \frac{1}{2}\left(y\frac{dx}{dt} + x\frac{dy}{dt}\right)$

At that instant, the ladder is 15 feet from the base of the wall. So, x = 15. Using this information, find y.

$\displaystyle y = \sqrt{1521-(15)^2}=36$

The bottom of the ladder is being pulled away from the wall at a rate of two feet per second. So, dx/dt = 2. Using this information and the first equation, find dy/dt:

$\displaystyle \frac{dy}{dt} =-\frac{x\dfrac{dx}{dt}}{y}$

Evaluate for dy/dt:

$\displaystyle \frac{dy}{dt} = -\frac{(15)(2)}{(36)}=-\frac{5}{6}$

Finally, using dA/dt, substitute in appropriate values:

$\displaystyle \frac{dA}{dt} = \frac{1}{2}\left((36)(2)+(15)\left(-\frac{5}{6}\right)\right)$

Evaluate. Hence:

$\displaystyle \frac{dA}{dt} = \frac{119\text{ ft}^2}{4\text{ s}} = 29.75\text{ ft$^2$/s}$

The area of the triangle formed is increasing at a rate of 29.75 square feet per second.

8 0

3 years ago

Plssss help fast and give a small explanation

Marrrta [24]

Answer: the area of the triangle is 23.4 cm²

Step-by-step explanation:

The given triangle is not a right angle triangle. Since two sides and one angle are known, we can either apply the Heron's formula or the Sine formula which is expressed as

Area of triangle = 1/2abSinC

Where a and b are the sides of the triangle and C is the given angle. Therefore,

Area = 1/2 × 8.2 × 6.4 × Sin63

Area = 1/2 × 8.2 × 6.4 × 0.8910

Area = 23.4 cm² to the nearest tenth.

6 0

3 years ago

I’ll mark as brainliest!!! Find x and y plz help

Hatshy [7]

Based on the angles, we know this is a 45-45-90 triangle.

In this type of triangle, x and y will be equal. The formula for the sides is x * rad 2 = 8 .

8/ rad 2 = 5.66

Both X and Y are 5.66 units.

6 0

3 years ago

Read 2 more answers

Please help me and this question

lbvjy [14]

Answer: 12 inches cubed

Step-by-step explanation:

volume=length x width x height

volume=1.5 in x 2 in x 4 in

volume=12 in^3

3 0

4 years ago

Find other values of a, b, and c so that log(a) + log(b) + log(c) = log(a + b + c).

yanalaym [24]

Step-by-step explanation:

Given :

log(a) + log(b) + log(c) = log(a + b + c)

We know that by property

log(a) + log(b) + log(c) = log(abc)

Therefore,

log(abc) = log(a + b + c)

Thus,

(abc) = (a + b + c)

Thus when a = b = c = 0,

then (abc) = (a + b + c)

0 = 0

and when a = 1, b = 2, c = 3,

then (abc) = (a + b + c)

(1 x 2 x 3 ) = (1 + 2 + 3)

6 = 6

5 0

3 years ago