MATHEMATICS COLLEGE

Write the expression multiply 0.035 times of a power of 10 so that the product is greater than one by less than 100

Answers

Answer 1

Answer:

Answer:

$0.035* 10^(3)$

$0.035* 10^(2)$

Step-by-step explanation:

Given the number: 0.035 which has three decimal place

Case 1: if we multiply by 10

=> we have: 0.035*10 = 0.35

Hence, the product 0.35 which is smaller than 1 (we do not accept)

Case 2: if we multiply by 1000

=> we have: 0.035*1000 = 35

Hence, the product 35 which is greater than 1 and less than 100

Case 3: if we multiply by 100

=> we have: 0.035*100= 3.5

Hence, the product 3.5 which is greater than 1 and less than 100

Case 4: if we multiply by 10000

=> we have: 0.035*10000= 350

Hence, the product 350 which is greater than 100 (we do not accept)

Therefore, we have two expression:

$0.035* 10^(3)$

$0.035* 10^(2)$

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Guided PracticeFind the balance in the account.

$500 principal earning 4% compounded quarterly, after 6 years.

A.
$632.66

B.
$530.76

C.
$634.87

Answers

Answer:

$634.87

Step-by-step explanation:

A=500×(1+0.04÷4)^(4×6)

A=634.87

$500 shared in ratio 2:3:9

Answers

2:3:9......added together = 14

2/14 (500) = 1000/14 = 71.43
3/14 (500) = 1500/14 = 107.14
9/14 (500) = 4500/14 = 321.43

After school, a student jogged from school to the library. it took the student 35 minutes to get to the library, where he spent 10 minutes browsing and checking out a book. he then walked to the coffee shop, on the same street, in 15 minutes. he spent 40 minutes sitting at a table in the coffee shop and reading the book before heading home. he walked home in 25 minutes and remain there until the next morning.

Answers

Answer:

so what are you asking exactly

Step-by-step explanation:

there are 8 tennis balls in a bag.five of the balls are yellow and the other 3 are green, what's the probability of pulling out a green ball without looking? write your answer as a decimal

Answers

The probability of pulling out a green ball without looking is 3/8 or 0.375 as a decimal of the given problem there are 8 tennis balls in a bag.five of the balls are yellow and the other 3 are green

To find the probability of pulling out a green ball without looking, we need to determine the ratio of green balls to the total number of balls in the bag.

Given that there are 8 tennis balls in total, with 3 of them being green, the probability can be calculated as:

Probability = Number of green balls / Total number of balls

Probability = 3 green balls / 8 total balls

Simplifying this fraction, we have:

Probability = 3/8

Therefore, the probability of pulling out a green ball without looking is 3/8 or 0.375 as a decimal.

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I think
3/8 = 0.375
3 divide by 8 = 0.375

6.2.Find the triangle bounded by the y-axis the line f(x)=9- 6/7x and the line perpendicular to it that passes through the origin

Answers

First.

We need to find the triangle bounded by the y-axis the line $f(x)=9-(6)/(7)x$ and the line perpendicular to it that passes through the origin.

This triangle is illustrated in the First Figure bellow. The triangle has been dotted with black dots. So, let's identify each part of this graph:

The y-axis has been identified by the green line.
The line $f(x)=9-(6)/(7)x$ has been identified by the red line.
To plot the line perpendicular to the previous one that passes through the origin, we need to know that the product of the slopes of two perpendicular lines is $m_(1)m_(2)=-1 \therefore Since \ m_(1)=-(6)/(7) \ then \ m_(2)=(7)/(6)$

Therefore, this line is the blue one and is written as:

$f(x)=(7)/(6)x$

Second.

a.

To find $y(t)$ we need to find the slope and y-intercept. So, taking two points:

$P_(1)(15,150) \ and \ P_(2)(25,450) \n \nm=(450-150)/(25-15)=30$

So:

$Using \ P_(1)(15,150) \n\ny=30t+b\n\n150=30(15)+b \therefore b=-300 \n\n\boxed{y(t)=30t-300}$

Third.

b.

The y-intercept is $b=-300$ and has been calculated above. This value represents the profit in thousands of dollars in 1980, that is, there is no any profit or there is a lost of $300.000.

Fourth.

c.

The x-intercept can be found when y=0 (year 1980), that is:

$y(t)=30t-300 \n\n0=30t-300 \therefore t=10$

This value shows that there is no any profit for the company at the year that represents t=10 (year 1990), because at this point the company starts earning money.

Fifth.

d.

The slope of this function is $m=30$

This value tells you that the profit increases $30.000 each year.

Hello,

Please, see the attached files.

Thanks.

Identify the surface with the given vector equation. r(s, t) = s sin 4t, s2, s cos 4ta. plane
b. hyperbolic paraboloid
c circular paraboloid
d.circular cylinder
e. elliptic cylinder

Answers

Following are the calculation to the given equation:

Given vector equation:

$\to r(s, t)= (s \sin 4t,s^2, s \cos 4t)$

The corresponding parametric equations for the given surface is given by,

$x=s \sin 4t\n\n y =s^2\n\n z=s \cos 4t$

For any point (x,y,z) we have that,

$x^2+z^2 = (s \sin 4t)^2 +(s \cos 4t)^2$

$= s^2 \sin^2 4t +s^2 \cos^2 4t \n\n= s^2 (\sin^2 4t+cos^2 4t) \n\n= s^2 (1) \n\n=s^2\n\n=y \n$

So, after eliminating the parameters, we get, $x^2 +z^2 = y$

Therefore, the answer is "Option c".

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Final answer:

The surface represented by the given vector equation r(s, t) = s sin 4t, s2, s cos 4t is a circular cylinder. This can be inferred from the structure of the equation and the characteristics of the represented shapes.

Explanation:

The surface represented by the given vector equation,

r(s, t) = s sin 4t, s2, s cos 4t

, is a type of cylindrical surface due to the structure of the equation. This can be identified by the s terms being tied to sin/cos functions and an independent s^2 term. This shows that the s variable is acting as a 'driver' of the shape, while t coordinates the rotation. Owing to the periodic sin and cos functions in the vector equation, the surface does not lie in a single plane, ruling out the option of a plane. It also does not exhibit features of a paraboloid or hyperbolic paraboloid. Hence, it's shown that the vector equation represents a

circular cylinder

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