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3 years ago

What is the exact value of x in the exponential equation 4 + e3x = 24?

Mathematics

1 answer:

larisa86 [58]3 years ago

7 0

Answer:

hello : x = (ln(20))/3

Step-by-step explanation:

4 + e3x = 24?

e3x = 24 - 4

e3x = 20

3x = ln(20)

x = (ln(20))/3

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6. In a toy factory, 200 wooden closed cylinders of diameter 35 mm and height 7 cm have to be painted. What is the total surface

Pachacha [2.7K]

Answer:

6) About 19,244.75 square centimeters.

7) About 4895 containers.

Step-by-step explanation:

Question 6)

We need to paint 200 wooden closed cylinders of diameter 35 mm and height 7 cm. And we want to find the total surface area that needs to be painted.

First, since the diameter is 35 mm, this is equivalent to 3.5 cm.

The radius is half the diameter, so the radius of each cylinder is 1.75 cm.

Recall that the surface area of a cylinder is given by the formula:

$\displaystyle \text{SA}=2\pi r^2+ 2\pi rh$

Where r is the radius and h is the height.

Therefore, the surface area of a single cylinder will be:

$\displasytyle \text{SA}=2(3.142)(1.75)^2+2(3.142)(1.75)(7) = 96.22375\text{ cm}^2$

Then the total surface area for 200 cylinders will be:

$\displaystyle \text{SA}_{\text{total}}=200(96.22375)=19244.75\text{ cm}^2$

Question 7)

We know that the tank has a diameter of 2.4 m and a height of 6.4 m.

Since its diamter is 2.4 m, then its radius is 1.2 m.

Find the total volume of the tank. The volume for a cylinder is given by:

$\displaystyle V=\pi r^2h$

Since r = 1.2 and h = 6.4:

$\displaystyle V=(3.142)(1.2)^2(6.4)=28.956672\text{ m}^3$

Each container has a base radius of 8.2 cm and a height of 28 cm.

So, the radius of each container is 0.082 m and the height is 0.28 m.

Then the volume of each container is:

$\displaystyle V=(3.142)(0.082)^2(0.28)=0.005915506\text{ m}^3$

Then to find the number of containers that can be filled by the tank, we can divide the two values. Hence:

$\displaystyle C=\frac{28.956672}{0.005915506}=4895.045466\approx 4895$

Thus, approximately 4895 containers can be filled.

5 0

2 years ago

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Sharon is 18 and would like to buy a house when she is 34. What is the discount factor for today's prices if the housing values

nlexa [21]

If I did the math right it should be A. 12.0%

6 0

2 years ago

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A circle has a radius of 5p6q3 cm. The area of the circle can be found using the formula A = πr2. What is the area of this circl

Tamiku [17]

Answer:

25p^12q^6πcm²

Step-by-step explanation:

Given the area of the circle expressed as;

A = πr^2

Given

r = 5p^6q^3 cm

Substitute into the formula

A = π(5p^6q^3 )²

A = π(25p^12q^6)

A = 25p^12q^6πcm²

hence the area of this circle in square centimeters is 25p^12q^6πcm²

4 0

3 years ago

The sequence 2,6,18,54 shows the number of sit-ups Alan can do each day.

jek_recluse [69]

Step-by-step explanation:

this sequence is geometric not arithmetic

HOw we know that ??

when we get a common difference that must Be equal

d=6-2=4 not equal to d=18-6=12

So it is not arithmetic

but when we get the common ratio that also must be equal

r=6/2=18/6=54/18=3 equal

So it is geometric

By using this equation:

a(n)=a(1)*r^(n-1)

and we have a(1)=2 , r=3

Explicit rule: a(n)=2*(3)^(n-1)

Recursive rule: a(n)= r * a(n-1)

a(n-1) ⇒ priviuse term

SO: a(n)= 3 * a(n-1)

For example:

a(3)= 3 * 6 =18

I really hope this helps <3

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3 years ago

What are the solutions to the equation?

Tems11 [23]

Answer:A

I just took assignment on edge.

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3 years ago

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