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Marianna [84]
3 years ago
5

Solve the system: x' = (2 4 -1 6)x

Mathematics
1 answer:
sertanlavr [38]3 years ago
6 0

Answer:

x=e^{8t}+c

Step-by-step explanation:

we have given x'=(24-16)x=8x

x' denotes the differenation

\frac{dx}{dt}=8x  differentiation is performed with respect to t

by variable separable method we can write  

\frac{dx}{x}=8dt

on integrating both side

lnx=8t+c

x=e^{8t}+c (property of log )

so the solution for x will be x=e^{8t}+c

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Jack typed 45 words in 1 minute. how many minutes will it take jack to type 990 words
Wittaler [7]

Answer:

22 minutes

Step-by-step explanation:

990/45=22

8 0
3 years ago
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Any idea ? I need help
trasher [3.6K]
Use the Pythagorean Theorem:
a^2 + b^2= c^2

a= one side= 68 mi
b= second side= 80 mi
c= hypotenuse= Greenville to Columbia mi


a^2 + b^2= c^2

68^2 + 80^2= c^2
square each number

4,624 + 6,400= c^2

11,024= c^2
take square root of both sides

104.995 mi= c


ANSWER: The distance from Greenville to Columbia is 104.995 miles (rounded to 105 miles).

Hope this helps! :)
3 0
3 years ago
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Anna has $430. She wants to buy a phone that costs $275. Anna will also have to pay a sales tax of 7%.
ki77a [65]
19.25 (tax)
294.25 (total price)
135.75 (money left)

REASONING:

In this word problem it says Anna has 430 dollars. The phone costs 275 dollars. It also says that when she buys the phone, she will have to pay a tax of 7%.

To find how much tax she will pay, we must do [275] x [0.07]

After inputting this into a calculator, you will get 19.25 (tax)


To find the total price, all you have to do is add 19.25 to 275. When you do this, you will get 294.25 dollars (total price)


To find how much money she has left,

430-294.25=135.75 (money left)

5 0
3 years ago
Please show work! will mark brainlest!!!!!!!!
GarryVolchara [31]

Answer:

34cm

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A student is trying to calculate the density of a ball. She already knows the mass, but she needs to determine the volume as wel
mario62 [17]
<h2>Answer and Explanation:</h2><h2 />

The density of a substance is defined as its mass per unit volume. In a mathematical language, this can be written as follows:

\rho=\frac{m}{V} \\ \\ \\ Where: \\ \\ \rho: \ density \\ \\ m:mass \\ \\ V:Volume

From the problem, a student is trying to calculate the density of a ball. She already knows the mass, but is facing a problem because she also needs to find the volume. From geometry, we know that the volume of a sphere is:

V=\frac{4}{3} \pi r^{3}

Since a ball is a sphere, then the student can use this formula. She just need to measure the radius of the ball and compute the Volumen, then she have to plug both the value of the mass and the value of the Volume in the equation \rho=\frac{m}{V}. An easy way to find the radius is to take the measure of the diameter of the ball and divide that value by 2.

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