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2 years ago

suppose that y=5x+1 and it is required that y be within 0.005 units of 7. for what values of x will this be true

Mathematics

1 answer:

dlinn [17]2 years ago

7 0

Answer:

1.199 ≤ x ≤ 1.201

Step-by-step explanation:

You want ...

|y -7| ≤ 0.005

Substituting the expression for y, you have ...

|5x+1 -7| ≤ 0.005

|x -1.2| ≤ 0.001 . . . . . simplify, divide by 5

-0.0001 ≤ x -1.2 ≤ 0.001 . . . . . "unfold" the absolute value

1.199 ≤ x ≤ 1.201 . . . . . . . . . . . .add 1.2

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Consider this sphere inside the cylinder. Which statements are true? Check all that apply. NEED HELP ASAP

-Dominant- [34]

Option A: The height of the cylinder is equal to the diameter of the sphere.

Option C: The radius of the sphere is half the height of the cylinder.

Option E: The volume of the sphere is two-thirds the volume of the cylinder.

Solution:

The sphere is inside the cylinder.

Let r be the radius of the sphere.

Option A: The height of the cylinder is equal to the diameter of the sphere.

The sphere is fully occupied the cylinder.

If we draw the vertical line through enter of the sphere, which is equal to the height of cylinder.That is h = d. It is true.

Option B: The height of the cylinder is two times the diameter of the sphere.

That is h = 2d. From the above option, we know that h = d.

So, it is not true.

Option C: The radius of the sphere is half the height of the cylinder.

we know that diameter = 2 × radius (d = 2r)

From option A, we have h = d.

Substitute d = 2r, we get

⇒ h = 2r

Divide by 2 on both sides, we get

$$\Rightarrow \frac{h}{2}=r$

Therefore, it is true.

Option D: The diameter of the sphere is equal to the radius of the cylinder.

It is not true, because diameters of both cylinder and sphere are equal.

Option E: The volume of the sphere is two-thirds the volume of the cylinder.

Radius of cylinder and sphere = r

Height of cylinder h = 2r (by option C)

Volume of cylinder = Volume of sphere

$$\Rightarrow \pi r^2 h = \frac{4}{3} \pi r^3$ (formula)

$$\Rightarrow \pi r^2 (2r) = \frac{2\times2}{3} \pi r^3$

$$\Rightarrow 2 \pi r^3= \frac{2}{3} \times 2\pi r^3$

Hence it is true.

Option A, option C and option E are true.

6 0

3 years ago

Read 2 more answers

6x^4 • 5x^3 Pleas help Me on this problem!!

Leto [7]

30x^7

Multiply the coefficients (6•5) to get 30, then add the exponents (4+3) to get 7

Hope this helps!

4 0

2 years ago

Find the area of the circle.

juin [17]

Answer:

See Explanation Below

Step-by-step explanation:

Your question isn't clear; However, I'll solve in two ways

1. Diameter = 14 cm

2. Radius = 14 cm

When Diameter = 14 cm

Given

$Area = \pi r^2$

$Diameter = 14cm$

Required

Calculate the area of the circle

First, the radius has to be solved;

$Radius = \frac{1}{2} Diameter$

$Radius = \frac{1}{2} * 14cm$

$Radius = 7cm$

Using the given formula;

The area is as follows

$Area = \pi r^2$

$Area = 3.14 * 7^2$

$Area = 3.14 * 49$

$Area = 153.86cm^2$

When Radius = 14 cm

Given

$Area = \pi r^2$

$Radius = 14cm$

Required

Calculate the area of the circle

Using the given formula;

The area is as follows

$Area = \pi r^2$

$Area = 3.14 * 14^2$

$Area = 3.14 * 196$

$Area = 615.44cm^2$

7 0

3 years ago

The cost (in dollars) in making b bracelets is represented by 4+5b. The cost (in dollars) of making b necklaces is represented b

ddd [48]

Answer:

$P(b)=3b+2$

Step-by-step explanation:

The cost (in dollars) in making b bracelets is represented is

$B(b)=4+5b$

The cost (in dollars) of making b necklaces is

$N(b)=8b+6$

To find how much more it will cost to make b necklaces than b bracelets, we find the difference,

$P(b)=N(b)-B(b)$

$P(b)=8b+6-(4+5b)$

$P(b)=8b+6-4-5b$

$P(b)=3b+2$

This is a polynomial in descending powers of b, hence it is in standard form;

8 0

3 years ago

Which expression represents the word phrase the product of 3 and 6 more than a number? 3(x+6) 3(6−x) 3x + 6 I don't know.

dezoksy [38]

Answer:

3(6+x)

Step-by-step explanation:

product of 3 and 6 more than a number

6 more than a number = y

y = (6+x)

3(6+x)

PLEASE GIVE BRAINLIEST

4 0

2 years ago