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LuckyWell [14K]
3 years ago
11

PLEASE HELP WITH MY MATH. SCIENTIFIC NOTATION PROBLEM.

Mathematics
1 answer:
nasty-shy [4]3 years ago
5 1

Answer:


Step-by-step explanation:

a) 8.23 x 10^5 move the decimal over 5 places, 319000000 is 319 million move the decimal over until there is one number on the left side --> 3.19 x 10^8

b) 3.19 x 10^8 / 8.23 x 10^5 = 387.61 roughly 388 times larger

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This is the pond in a shape of a prism, it is completely full of water. Colin uses a pump to empty the pond. The level goes down
AnnZ [28]

Answer:

150 minutes

Step-by-step explanation:

P.S - The exact question is -

Given - This is the pond in a shape of a prism, it is completely full of

             water. Colin uses a pump to empty the pond. The level goes

             down by 20 cm in the first 30 min.

To find - Work put how many minutes Colin has to wait for the pond

               to completely empty.

Proof -

Given that,

Height of prism = 1 m

Also,

Base of the prism is trapezium and

Sides of the trapezium are 0.6 m and 1.4 m

Height of trapezium is 2 m

We know that,

Area of trapezium = \frac{1}{2}× (sum of sides)× height

                             =  \frac{1}{2}× (0.6 + 1.4)× 2

                             =  \frac{1}{2}× (2)× 2

                             =  2 m²

⇒Area of trapezium = 2 m²

Now,

Volume of prism = Area of trapezium × height of prism

                          = 2 m² × 1 m

                          = 2 m³

⇒Volume of prism = 2 m³

Now,

Given that the level goes down by 20 cm in the first 30 min

We know

100 cm = 1 m

⇒1 cm = \frac{1}{100} m = 0.01 m

⇒20 cm = 20×0.01 m = 0.2 m

⇒The level goes down by 0.2 m in the first 30 min.

Also,

we know that height of water = height of prism = 1 m

So, the remaining water left in the pond = 1 m - 0.2 m = 0.8 m

Also,

Volume of Remaining water = Area of trapezium × height

                                           = 2 m² × 0.8 m

                                           = 1.6 m³

⇒Volume of Remaining water = 1.6 m³

Now,

Volume of emptied water = Total Volume - Volume of Remaining water

                                       = 2 m³ - 1.6 m³

                                       = 0.4 m³

⇒Volume of emptied water = 0.4 m³

Now,

0.4 m³ water will be empty in 30 minutes

⇒ 1 m³ water will be empty in \frac{30}{0.4} = 75 minutes

⇒1.6 m³ water will be empty in 1.6 × 75 = 120 minutes

∴ we get

The remaining water is empty in 120 minutes

So,

Total pond is empty in 120 + 30 minutes

⇒Total pond is empty in 150 minutes

5 0
3 years ago
Solve for XX. Assume XX is a 2×22×2 matrix and II denotes the 2×22×2 identity matrix. Do not use decimal numbers in your answer.
sveticcg [70]

The question is incomplete. The complete question is as follows:

Solve for X. Assume X is a 2x2 matrix and I denotes the 2x2 identity matrix. Do not use decimal numbers in your answer. If there are fractions, leave them unevaluated.

\left[\begin{array}{cc}2&8\\-6&-9\end{array}\right]· X·\left[\begin{array}{ccc}9&-3\\7&-6\end{array}\right] =<em>I</em>.

First, we have to identify the matrix <em>I. </em>As it was said, the matrix is the identiy matrix, which means

<em>I</em> = \left[\begin{array}{ccc}1&0\\0&1\end{array}\right]

So, \left[\begin{array}{cc}2&8\\-6&-9\end{array}\right]· X·\left[\begin{array}{ccc}9&-3\\7&-6\end{array}\right] =  \left[\begin{array}{ccc}1&0\\0&1\end{array}\right]

Isolating the X, we have

X·\left[\begin{array}{ccc}9&-3\\7&-6\end{array}\right]= \left[\begin{array}{cc}2&8\\-6&-9\end{array}\right] -  \left[\begin{array}{ccc}1&0\\0&1\end{array}\right]

Resolving:

X·\left[\begin{array}{ccc}9&-3\\7&-6\end{array}\right]= \left[\begin{array}{ccc}2-1&8-0\\-6-0&-9-1\end{array}\right]

X·\left[\begin{array}{ccc}9&-3\\7&-6\end{array}\right]=\left[\begin{array}{ccc}1&8\\-6&-10\end{array}\right]

Now, we have a problem similar to A.X=B. To solve it and because we don't divide matrices, we do X=A⁻¹·B. In this case,

X=\left[\begin{array}{ccc}9&-3\\7&-6\end{array}\right]⁻¹·\left[\begin{array}{ccc}1&8\\-6&-10\end{array}\right]

Now, a matrix with index -1 is called Inverse Matrix and is calculated as: A . A⁻¹ = I.

So,

\left[\begin{array}{ccc}9&-3\\7&-6\end{array}\right]·\left[\begin{array}{ccc}a&b\\c&d\end{array}\right]=\left[\begin{array}{ccc}1&0\\0&1\end{array}\right]

9a - 3b = 1

7a - 6b = 0

9c - 3d = 0

7c - 6d = 1

Resolving these equations, we have a=\frac{2}{11}; b=\frac{7}{33}; c=\frac{-1}{11} and d=\frac{-3}{11}. Substituting:

X= \left[\begin{array}{ccc}\frac{2}{11} &\frac{-1}{11} \\\frac{7}{33}&\frac{-3}{11}  \end{array}\right]·\left[\begin{array}{ccc}1&8\\-6&-10\end{array}\right]

Multiplying the matrices, we have

X=\left[\begin{array}{ccc}\frac{8}{11} &\frac{26}{11} \\\frac{39}{11}&\frac{198}{11}  \end{array}\right]

6 0
3 years ago
Madison buys supplies so she can make and sell wind chimes. She begins
Studentka2010 [4]
<h3>Explanation:</h3>

In the graph x-coordinate represents the number of wind chimes sold and y-coordinate represents the profit Madison earned. If a point is below the x-axis, means it has negative y-coordinate than it represents loss. Points above x-axis should have x-coordinate more than 6 as stated in the question that she started earning profit after selling her first 6 wind chimes. All the points having x-coordinate less than 6 should lie on or below the x-axis.

By the above statement point B is completely wrong. Point C and Point A are also wrong as they both x-coordinate more than 6 but still they are below x-axis.

Point D is the makes most sense here as it has x-coordinate more than 6 and it is above x-axis. This means that when Madison sold 7 wind chimes she was in a profit of $3.75.

5 0
3 years ago
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goldenfox [79]
It would be great if you added some more details, but for common denominators you try to find the least common number that the 2 or more of the numbers you got have!
For example:
1/2 and 2/3 if you multiply 2 by 3 and 3 by 2, they both are 6, so you would multiply 1/2 both by 3 to make it into 3/6 and 2/3 by 2 to make it into 4/6!
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3 years ago
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snow_lady [41]

Answer:

790

Step-by-step explanation:

You put 5 instead of x and you calculat

6*5^3 +8*5= 750+40=790

6 0
3 years ago
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