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3 years ago

The limit of tan4x/6x as x approaches 0

1 answer:

5 0

$\displaystyle\lim_{x\to0}\frac{\tan4x}{6x}=\lim_{x\to0}\frac{\sin4x}{4x}\times\frac{4x}{6x\cos4x}=\dfrac23\lim_{x\to0}\sec4x=\dfrac23$

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The cost of 3 pounds of grapes is $6.57. What is the constant of proportionality that relates the cost in dollars, y, to the num

never [62]

Answer:

2.19x=y

Hope this helps!

7 0

2 years ago

A glass paperweight has a composite shape: a square pyramid fitting exacty on top of an 8 centimeter cube. The pyramid has a hei

ArbitrLikvidat [17]

Answer:

Part 1) The volume of the paperweight is $576\ cm^{3}$

Part 2) The total surface area of the paperweight is $400\ cm^{2}$

Step-by-step explanation:

Part 1) what is the volume of the paperweight?

we know that

The volume of the paperweight is equal to the volume of the square pyramid plus the volume of the cube

step 1

Find the volume of the pyramid

The volume of the pyramid is equal to

$V=\frac{1}{3}BH$

where

B is the area of the square base

H is the height of the pyramid

$B=8^{2}=64\ cm^{2}$

$H=3\ cm$

substitute

$V=\frac{1}{3}(64)(3)=64\ cm^{3}$

step 2

Find the volume of the cube

The volume of the cube is equal to

$V=b^{3}$

$V=8^{3}=512\ cm^{3}$

step 3

Find the volume of the paperweight

$64\ cm^{3}+512\ cm^{3}=576\ cm^{3}$

Part 2) what is the total surface area of the paperweight?

we know that

The total surface area of the paperweight is equal to the surface area of 5 faces of the cube plus the lateral area of the pyramid

step 1

Find the surface area of 5 faces of the cube

$SA=5b^{2}$

$SA=5(8^{2})=320\ cm^{2}$

step 2

Find the lateral area of the pyramid

$LA=4[\frac{1}{2}bh]$

$LA=4[\frac{1}{2}(8)(5)]=80\ cm^{2}$

step 3

Find the total surface area of the paperweight

$320\ cm^{2}+80\ cm^{2}=400\ cm^{2}$

8 0

3 years ago

How to do slope intercept form again?!

Anestetic [448]

You intercept by shaping in a volcano form if that's what you mean

8 0

3 years ago

In circle C, r = 32 units.

vlabodo [156]

Probably 2561 but since area equal r^2 I thought it would be 3217

5 0

3 years ago

The greatest integer function, shown below, is defined to be the greatest___ less than or equal to x.

Nataly_w [17]

Answer:

Integer

Step-by-step explanation:

The greatest integer function, F(x)=[[x]], is defined to be the greatest <u>integer that is </u>less than or equal to x.

The Greatest Integer Function is also referred to as the Floor Function.

It is written as F(x)=[[x]]

The value of ⌊x⌋ is the largest or the greatest integer that is less than or equal to x

4 0

3 years ago