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Oksi-84 [34.3K]
3 years ago
5

The altitude of a triangle is increasing at a rate of 1 cm/min while the area of the triangle is increasing at a rate of 2 cm2/m

in. At what rate is the base of the triangle changing when the altitude is 10 cm and the area is 190 cm2? cm/min
Mathematics
1 answer:
Mnenie [13.5K]3 years ago
8 0

Answer:

The base is reducing at a rate of 3.4cm per min.

Step-by-step explanation:

Let The Height of the Triangle, h

Area of the triangle = A

Area of a Triangle, A= \frac{1}{2}bh

When A=190 cm^2, h=10cm

190= \frac{1}{2}*b*10\\b=38cm

\frac{dA}{dt}=\frac{1}{2}h\frac{db}{dt}+ \frac{1}{2}b\frac{dh}{dt}\\\frac{dh}{dt}=1 cm/min, \frac{dA}{dt}=2cm^2/min,

2=\frac{1}{2}*10*\frac{db}{dt}+ \frac{1}{2}*38*1\\2=5\frac{db}{dt}+19\\2-19=5\frac{db}{dt}\\-17=5\frac{db}{dt}\\\frac{db}{dt}=-\frac{17}{5} =-3.4 cm/min

The base is reducing at a rate of 3.4cm per min.

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A delivery of 5 large boxes and 3 small boxes has a total mass of 137 kilograms. A delivery of 2 large boxes and 6 small boxes h
lawyer [7]

Answer:

Large boxes are 18.25 kg

Small boxes are 15.25 kg

Step-by-step explanation:

This is a system of equations. You need to set up each equation first.

I am assigning x to be big boxes and y to be small boxes.

5x + 3y = 137

2x + 6y = 128

To solve, you will need to eliminate a variable. That means you will have to multiply one of the equations by a number to make it so a variable will be eliminated. I will be multiplying the top equation by -2.

-2 ( 5x + 3y = 137)

    2x + 6y = 128

Distribute the -2 to everything in the parentheses in the first equation.

-10x - 6y = -274

2x + 6y = 128

Notice the 6y will go away because -6y + 6y = 0. Now add the equations together. The remaining equation is:

-8x = -146

Solve for x by dividing by -8.

x = 18.25

Now plug that into one of the original equations.

2(18.25) + 6y = 128.

36.5 + 6y = 128                Subtract 36.5 from each side

-36.5            -36.5

6y = 91.5                          Divide by 6 to solve

y = 15.25

7 0
1 year ago
20x+3=17 help please
jeyben [28]
The objective is to get the variable (x) alone. To do this start be subtracting 3. What you do to one side you have to do to the other so you have to subtract three from the other side of the equal sign as well. So now you have:
20x= 17-3 subtract the 3 to get 20x=14
Now because the 20 is attached to the x In order to get the x alone you have to divide by 20:
20x/20. =14/20 divide 14 by 20

X=.7 or x=7/10
5 0
3 years ago
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How do you estimate a length
WARRIOR [948]
A little tip is this 
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Which equation is written in standard form ?
nasty-shy [4]

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3 years ago
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What is the distance, rounded to the nearest tenth, between the points (0,5) and (8,0)?
nekit [7.7K]

Answer:

<h2>The answer is 9.4 units </h2>

Step-by-step explanation:

The distance between two points can be found by using the formula

<h3>d =  \sqrt{( {x1 - x2})^{2} +  ({y1 - y2})^{2}  }</h3>

where

(x1 , y1) and (x2 , y2) are the points

From the question the points are

(0,5) and (8,0)

So the distance between them is

<h3>d =  \sqrt{ ({0 - 8})^{2} +  ({5 - 0})^{2}  }  \\ d =  \sqrt{ ({ - 8})^{2} +  {5}^{2}  }  \\ d =  \sqrt{64 + 25}   \\  \\ d =  \sqrt{89}</h3>

d = 9.4339811

We have the final answer as

<h3>d = 9.4 units</h3>

Hope this helps you

6 0
3 years ago
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