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4 years ago

____ Solve √3x+4 −2=3

Mathematics

1 answer:

Kryger [21]4 years ago

3 0

Answer:

$\sqrt$ 3x+4=5

Step-by-step explanation:

3x+4=25

3x=21

x=7

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58.(A) (5pts)A certain type of bacteria, given favorable growth medium, quadruples in population every 6 hours. Given that there

Jet001 [13]

Answer:

157286400 bacteria

Step-by-step explanation:

We are given the following in the question:

The bacteria increases 4 times every 6 hours.

Initially there are 150 bacteria.

Thus, we can write the function for number of bacteria after x hours,

$f(x) = 150(4)^{\frac{x}{6}}$

We have to find the number of bacteria in 2.5 days.

1 day = 24 hours

Thus,

$2.5\text{ days} = 24\times 2.5 = 60\text{ hours}$

Putting x = 60 in the above equation, we get,

$f(60) = 150(4)^{\frac{60}{6}} = 150(4)^{10} = 157286400$

Thus, there will be 157286400 bacteria in two and a half days.

5 0

4 years ago

Please answer 1/8 - 1/4 (3 - 1/2) + 2/3 And 2/9 - 1/6 (8- 2/3) + 1/2

Neko [114]

Answer:

1/6, - 1/2_____________

6 0

3 years ago

For the function given below, find a formula for the Riemann sum obtained by dividing the interval (0, 3) into n equal subinterv

Viktor [21]

Splitting up [0, 3] into $n$ equally-spaced subintervals of length $\Delta x=\frac{3-0}n = \frac3n$ gives the partition

$\left[0, \dfrac3n\right] \cup \left[\dfrac3n, \dfrac6n\right] \cup \left[\dfrac6n, \dfrac9n\right] \cup \cdots \cup \left[\dfrac{3(n-1)}n, 3\right]$

where the right endpoint of the $i$ -th subinterval is given by the sequence

$r_i = \dfrac{3i}n$

for $i\in\{1,2,3,\ldots,n\}$ .

Then the definite integral is given by the infinite Riemann sum

$\displaystyle \int_0^3 2x^2 \, dx = \lim_{n\to\infty} \sum_{i=1}^n 2{r_i}^2 \Delta x \\\\ ~~~~~~~~ = \lim_{n\to\infty} \frac6n \sum_{i=1}^n \left(\frac{3i}n\right)^2 \\\\ ~~~~~~~~ = \lim_{n\to\infty} \frac{54}{n^3} \sum_{i=1}^n i^2 \\\\ ~~~~~~~~ = \lim_{n\to\infty} \frac{54}{n^3}\cdot\frac{n(n+1)(2n+1)}6 = \boxed{18}$

8 0

2 years ago

The ratio of boys to girls in a class is 4:2. There are 30 students in class. How many girls and boys are there?

koban [17]

Answer:

20 boys, 10 girls

Step-by-step explanation:

4 + 2 = 6

4:6 ⋅ 5:5 = 20:30

2:6 ⋅ 5:5 = 10:30

3 0

3 years ago

Determine the center and radius of the circle described by the question. (X+2)

LenaWriter [7]

The question is incomplete, I will however explain, with an illustration, how to determine the center and radius of a circle.

Step-by-step explanation:

The standard equation of a circle is given as:

(x - a)² + (y - b)² = r² ........................(1)

Where (a, b) is the center of the circle, and r is the radius.

An expression can be given for us to find the center and the radius of the circle.

Suppose we were given the expression:

x² + y² - 10x + 4y - 7 = 0.....................(2)

To find the center and the radius, it is left for us to rewrite (2) in the form of (1).

Rearranging (2), we have

(x² - 10x) + (y² + 4y) = 7

Completing the squares of each bracket

(x² - 10x + 25 - 25) + (y² + 4y + 4 - 4) = 7

(x² - 10x + 25) + (y² + 4y + 4) - 25 - 4 = 7

(x² - 10x + 25) + (y² + 4y + 4) - 29 = 7

(x - 5)² + (y + 2)² = 7 + 29

(x - 5)² + (y + 2)² = 36

(x - 5)² + (y + 2)² = 6² .....................(3)

Comparing (3) with one, we see that

a = 5, b = -2, and r = 6

Therefore it is a circle centered at (5, -2) with a 6 unit radius.

7 0

4 years ago