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ICE Princess25 [194]
3 years ago
10

Write the next whole number after 6748nine in the base-nine system.

Mathematics
1 answer:
ale4655 [162]3 years ago
7 0

Answer:

Step-by-step explanation:

6748_9 = 6 *(9^3) + 7 * 9^2 + 4 * 9^1 + 8 * 9 ^ 0 = 4994_{10}

Hence, on base 10, the next whole number is 4995 and if we convert back to base 9, we will have

6* 9^3 + 7*9^2 + 5*9*1 = 4374 + 576+45 = 4995_{10}

Therefore, the number on base 9 will be 6750

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The diagram below shows a triangle with base (x+5) and height 2x inside a shaded rectangle with length (3x+1) and width (3x-5).
Ilya [14]

Answer:

3 for the first one 2ed one is 5

Step-by-step explanation:

6 0
3 years ago
A bucket that weighs 5 lb and a rope of negligible weight are used to draw water from a well that is 60 ft deep. The bucket is f
mestny [16]

Answer:

The value is W= 2640 \  ft \cdot lb

Step-by-step explanation:

From the question we are told that

The weight of the bucket is F =  5 lb

The depth of the well is x_1 =  60 \ ft

The weight of the water is W_w  =  42 lb

The rate at which the bucket with water is pulled is v  = 1.5 \  ft/s

The rate of the leak is r = 0.15 lb/s

Generally the workdone is mathematically represented as

W =  \int\limits^{x_1}_{x_o} {G(x)} \, dx]

Here G(x) is a function defining the weight of the system (water and bucket ) and it is mathematically represented as

G(x) =  F  +  (W_w- Ix)

Here I is the rate of water loss in lb/ft mathematically represented as

I  = \frac{r}{v}

=> I  = \frac{0.15 }{1.5 }

=> I  = 0.1

So

G(x) =  5  +  (42- 0.1x)

=> G(x) =  47- 0.1x)

So

W =  \int\limits^{60}_{0} {47- 0.1x} \, dx]

=> W =  [47x - \frac{0.1x^2}{2} ]|\left 60} \atop {0}} \right.

=> W= [47(60) - 0.05(60)^2]

=> W= 2640 \  ft \cdot lb

7 0
3 years ago
I need help with #12 b
tino4ka555 [31]

Answer:

y = 2x -33

Step-by-step explanation:

The line segment from the center (6, 4) to the given point (16, -1) is a radius of the circle. It is perpendicular to the tangent. Hence you need to write the equation of a line through point (16, -1) that is perpendicular to the line through that point and (6, 4).

The slope of the radius is ...

... ∆y/∆x = (-1-4)/(16-6) = -5/10 = -1/2

The slope of the tangent is the negative reciprocal of that, so is ...

... m = -1/(-1/2) = 2

In point-slope form, the tangent line through (16, -1) is

... y = m(x -h) +k

... y = 2(x -16) +(-1)

Simplifying, this is ...

... y = 2x -33

8 0
3 years ago
How do you rewrite this problem in slope-intercept form
Sergio039 [100]

Solution

-6x - 3y = 9              Add 6x to both sides

-6x + 6x - 3y = 9 + 6x

-3y = 9 + 6x             Or more conventionally

-3y = 6x + 9             Divide by - 3

y = 6x/-3 + 9/-3

y = - 2x - 3  

5 0
3 years ago
the strength of students in a school when increased by 8% becomes 2160. find the original strength of students in the school.
Leni [432]

Answer:

1987.2

Step-by-step explanation:

We can write a proportion to find the total amount in the choir using the information given. A proportion is two equivalent ratios set equal to each other. Since we know the strength of students increased by 8% to 2160 then the original was 92%.

\frac{92}{100}=\frac{y}{2160}

We will cross multiply the numerator of one ratio with denominator of the other. And then solve for y.

92(2160)=100(y)

198720=100y

y=1987.2

There are 1987.2 as the original strength of students.


6 0
3 years ago
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