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1 year ago

Which slope is shallower a slope of 3.5 or a slope of 4.6.

Mathematics

1 answer:

suter [353]1 year ago

4 0

Answer:

-> a slope of 3.5

Step-by-step explanation:

The smaller the slope the smaller the incline, here 3.5 > 4.6 so the 3.5 slope is shallower.

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A piece of wire of length 7070 is cut, and the resulting two pieces are formed to make a circle and a square. Where should the

lyudmila [28]

Answer:

a.x=39.2

b.Use whole wire as a circle

Step-by-step explanation:

We are given that

Length of piece of wire=70 units

Let length of wire used to make a square =x units

Length of wire used in circle=70- x

Side of square= $\frac{perimeter\;of\;square}{4}=\frac{x}{4}$

Circumference of circle= $2\pi r$

$70-x=2\pi r$

$r=\frac{70-x}{2\pi}$

Combined area of circle and square,A= $(\frac{x}{4})^2+\pi(\frac{70-x}{2\pi})^2$

Using the formula

Area of circle= $\pi r^2$

Area of square= $(side)^2$

a. $A=\frac{x^2}{16}+\frac{4900+x^2-140x}{4\pi}$

Differentiate w.r.t x

$\frac{dA}{dx}=\frac{x}{8}+\frac{2x-140}{4\pi}$

$\frac{dA}{dx}=0$

$\frac{x}{8}+\frac{2x-140}{4\pi}=0$

$\frac{\pi x+4x-280}{4\pi}=0$

$\pi x+4x-280=0$

$x(\pi+4)=280$

$x=\frac{280}{\pi+4}$

x=39.2

Again differentiate w.r.t x

$\frac{d^2A}{dx^2}=\frac{1}{8}+\frac{1}{2\pi}$ >0

Hence, the combined area of circle and the square is minimum at x=39.2

b.When the wire is not cut and whole wire used as a circle . Then, combined area is maximum.

3 0

2 years ago

Find the slope and reduce.<br> P=(-3, 3) Q=(1, 3)<br> Slope =

Sindrei [870]

Answer:

Slope is 0.

8 0

11 months ago

If a set contains 15 proper subsets then number of elements in that set

Sav [38]

Answer

32,768

Step-by-step explanation:

3 0

2 years ago

Gravel is being dumped from a conveyor belt at a rate of 20 ft3/min, and its coarseness is such that it forms a pile in the shap

11Alexandr11 [23.1K]

Answer:

0.25 feet per minute

Step-by-step explanation:

Gravel is being dumped from a conveyor belt at a rate of 20 ft3/min. Since we are told that the shape formed is a cone, the rate of change of the volume of the cone.

$\dfrac{dV}{dt}=20$ ft^3/min$

$\text{Volume of a cone}=\dfrac{1}{3}\pi r^2 h$

Since base diameter = Height of the Cone

Radius of the Cone = h/2

Therefore,

$\text{Volume of the cone}=\dfrac{\pi h}{3} (\dfrac{h}{2}) ^2 \\V=\dfrac{\pi h^3}{12}$

$\text{Rate of Change of the Volume}, \dfrac{dV}{dt}=\dfrac{3\pi h^2}{12}\dfrac{dh}{dt}$

Therefore: $\dfrac{3\pi h^2}{12}\dfrac{dh}{dt}=20$

We want to determine how fast is the height of the pile is increasing when the pile is 10 feet high.

$h=10$ feet$\\\\\dfrac{3\pi *10^2}{12}\dfrac{dh}{dt}=20\\25\pi \dfrac{dh}{dt}=20\\ \dfrac{dh}{dt}= \dfrac{20}{25\pi}\\ \dfrac{dh}{dt}=0.25$ feet per minute (to two decimal places.)$

When the pile is 10 feet high, the height of the pile is increasing at a rate of 0.25 feet per minute

5 0

2 years ago

Help&EXPLAIN <br> •••••••••••••••••••<br> Help plz

Stolb23 [73]

Answer:

diameter = 2.5 feet

Step-by-step explanation:

Circumference of a circle is given as C = πd

Circumference of the tree trunk = 7.85 ft

π = 3.14

Diameter of the tree trunk = d

Thus:

7.85 = 3.14*d

Divide both sides by 3.14

7.85/3.14 = 3.14*d/3.14

2.5 = d

d = 2.5 ft

3 0

2 years ago