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3 years ago

What is a necessary step for constructing perpendicular lines through a point on a line?

Mathematics

1 answer:

mina [271]3 years ago

8 0

Draw arcs on either side of a given point on the line

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The length of a rectangle is increasing at a rate of 6 cm/s and its width is increasing at a rate of 5 cm/s. When

atroni [7]

Answer:

The area of the rectangle is increasing at a rate of 84 square centimeters per second.

Step-by-step explanation:

The area for a rectangle is given by the formula:

$A=w\ell$

Where w is the width and l is the length.

We are given that the length of the rectangle is increasing at a rate of 6 cm/s and that the width is increasing at a rate of 5 cm/s. In other words, dl/dt = 6 and dw/dt = 5.

First, differentiate the equation with respect to t, where w and l are both functions of t:

$\displaystyle \frac{dA}{dt}=\frac{d}{dt}\left[w\ell]$

By the Product Rule:

$\displaystyle \frac{dA}{dt}=\frac{dw}{dt}\ell +\frac{d\ell}{dt}w$

Since we know that dl/dt = 6 and that dw/dt = 5:

$\displaystyle \frac{dA}{dt}=5\ell + 6w$

We want to find the rate at which the area is increasing when the length is 12 cm and the width is 4 cm. Substitute:

$\displaystyle \frac{dA}{dt}=5(12)+6(4)=84\text{ cm}^2\text{/s}$

The area of the rectangle is increasing at a rate of 84 square centimeters per second.

8 0

3 years ago

Lisa collected leaves from different trees for a science project. Every day for a week (7 days), she collected 7 leaves. How man

tangare [24]

Answer:

49 leaves

Step-by-step explanation:

7 days x 7 leaves per day = 49 leaves in total

6 0

10 months ago

• Packaging of a product can cost a lot of money. Can you design

podryga [215]

The best arrangement can be

3 rows and 4balls each row

Length of one row=1.8(4)=7.2cm
Width=1.8(3)=5.4cm
Height=1.8(2)=3.6cm

TSA

2(LB+BH+LH)
2(5.4(7.2)+(7.2)(3.6)+3.6(5.4))
2(84.24)
168.48cm²

Total cost

168.48(0.01)
1.685€

5 0

1 year ago

The Jones family is landscaping their yard. Their yard is 160 square feet and one side is 10 feet long. What is the length of th

Yuliya22 [10]

The other size is 10 too and there will be enough spaces with 1 foot left!!!! :)

4 0

3 years ago

Geometry: Write a formal proof, ASAP!!!

yulyashka [42]

${\qquad\qquad\huge\underline{{\sf Answer}}}$

Here we go ~

As we can see in the figure, lines m and n are parallel to each other. so we can apply Angle pair properties ~

So,

$\qquad \sf \dashrightarrow \: \angle1 \cong \angle2$

[ they form corresponding angle pair ]

and it's given that :

$\qquad \sf \dashrightarrow \: \angle2 \cong\angle 3$

therefore, by using above information. we can conclude that :

$\qquad \sf \dashrightarrow \: \angle1 \cong \angle3$

7 0

2 years ago