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Sonbull [250]
2 years ago
13

Find the indication of the right triangle

Mathematics
2 answers:
olya-2409 [2.1K]2 years ago
7 0
The answer should be 7 on the outside and 3 on the inside
Vinil7 [7]2 years ago
6 0

Answer:

7 \sqrt{3}

tan(60°)=x/7

7tan(60°)=x

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The radius of a sphere is increasing at a rate of 5 mm/s. How fast is the volume increasing (in mm3/s) when the diameter is 40 m
jeka94

9514 1404 393

Answer:

  8000π mm^3/s ≈ 25,133 mm^3/s

Step-by-step explanation:

The rate of change of volume is found by differentiating the volume formula with respect to time.

  V = 4/3πr^3

  V' = 4πr^2·r'

For the given numbers, this is ...

  V' = 4π(20 mm)^2·(5 mm/s) = 8000π mm^3/s ≈ 25,133 mm^3/s

_____

<em>Additional comment</em>

By comparing the derivative to the area formula for a sphere, you see that the rate of change of volume is the product of the area and the rate of change of radius. This sort of relationship will be seen for a number of different shapes.

4 0
3 years ago
Here is a system of equations. (y=x-6 y=-x-2 Graph the system. Then write its solution. Note that you can also answer "No soluti
sladkih [1.3K]

Answer:

Example system with no solution

We're asked to find the number of solutions to this system of equations:

\begin{aligned} y &= -3x+9\\\\ y &= -3x-7 \end{aligned}  

y

y

​  

 

=−3x+9

=−3x−7

​  

 

Without graphing these equations, we can observe that they both have a slope of -3−3minus, 3. This means that the lines must be parallel. And since the yyy-intercepts are different, we know the lines are not on top of each other.

There is no solution to this system of equations.

Example system with infinite solutions

We're asked to find the number of solutions to this system of equations:

\begin{aligned} -6x+4y &= 2\\\\ 3x-2y &= -1 \end{aligned}  

−6x+4y

3x−2y

​  

 

=2

=−1

​  

 

Interestingly, if we multiply the second equation by -2−2minus, 2, we get the first equation:

\begin{aligned} 3x-2y &= -1\\\\ \blueD{-2}(3x-2y)&=\blueD{-2}(-1)\\\\ -6x+4y &= 2 \end{aligned}  

3x−2y

−2(3x−2y)

−6x+4y

​  

 

=−1

=−2(−1)

=2

​  

 

In other words, the equations are equivalent and share the same graph. Any solution that works for one equation will also work for the other equation, so there are infinite solutions to the system.

Step-by-step explanation:

7 0
3 years ago
A rectangular dog park was built with the dimensions shown. The fencing that completely surrounds the park cost $12 a yard. Each
leonid [27]

Answer:

sod- 1662.6

fencing- 807.6

all- 2470.2

Step-by-step explanation:

sod-

25.5 * 8.25 = 207.825

207.825*8= 1662.6

fencing-

8.25+8.25+25.5+25.5= 67.3

67.3*12= 807.6

fencing + sod

1662.6 + 807.6= 2470.2

7 0
2 years ago
Kool-aide is made from flavored powder and water, with the ratio of powder to water 3:2 based on weight. If 120g of flavored pow
MAXImum [283]

The given ratio of powder to water is 3:2 based on weight for Kool-aide. It is also given that 120g of flavored powder is needed for a certain amount of Kool-aide.

Let us assume that the amount of water (by weight) required to maintain the given ratio of 3:2 be represented by the letter x. Thus, from the given information we can conclude that:

\frac{Powder Weight}{Water Weight}=\frac{3}{2}=\frac{120}{x}

\therefore \frac{3}{2}=\frac{120}{x}

Cross-multiplying we get:

3x=240

\therefore x=\frac{240}{3}=80 grams.

Thus, the amount of water in grams in that Kool-aide is 80 grams.

5 0
3 years ago
Read 2 more answers
An arithmetic progression is a sequence of numbers in which the distance (or difference) between any two successive numbers if t
earnstyle [38]

Answer:

Step-by-step explanation:

Solution:

- We are to write a program for evaluating the sum to Nth of an arithmetic sequence such that the sequence starts from positive integer 1, 3 , 5 , 7 , .. n.

- The sum to nth for the arithmetic series is given by two parameters i.e first integer a = 1 and the distance between successive integers d = 2 in our case.

- For any general distance d we can write our sum to nth as:

          Sum to nth = a + (a+d) + (a+2*d) + (a+3*d) .... (a + (n-1)*d)

- From above sequence we can see that every successive number is increased by distance d and added in previous answer.

- We will use an iteration loop for a variable "sum", which is cycled by a "range ( , , )" function.

- The parameters of the range functions corresponds to:

                   range ( first integer , last integer , step size )  

                   range ( a , n + 1 , d )

- Then we can cast the loop as follows:

 " int sum = 0

   int d = 2

   int a = 1

      for i in range ( a , n + 1 , d )

            sum += i

  "

- We see that iteration parameter i starts from a = 1, with step size d = 2 and the sum is previously stored sum value plus i for the current loop.

3 0
3 years ago
Read 2 more answers
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