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Ivan
3 years ago
13

(3x+16) ( 5x-54) find the value of the x

Mathematics
1 answer:
devlian [24]3 years ago
5 0

Answer:

15x^2 -82x-864

Step-by-step explanation:

MUse foil method

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The general solution to the second-order differential equation y′′+10y=0 is in the form y(x)=c1cosβx+c2sinβx. Find the value of
allsm [11]

Answer:β=√10 or 3.16 (rounded to 2 decimal places)

Step-by-step explanation:

To find the value of β :

  • we will differentiate the y(x) equation twice to get a second order differential equation.
  • We compare our second order differential equation with the Second order differential equation specified in the problem to get the value of β

y(x)=c1cosβx+c2sinβx

we use the derivative of a sum rule to differentiate since we have an addition sign in our equation.

Also when differentiating Cosβx and Sinβx we should note that this involves function of a function. so we will differentiate  βx in each case and multiply with the differential of c1cosx and c2sinx respectively.

lastly the differential of sinx= cosx and for cosx = -sinx.

Knowing all these we can proceed to solving the problem.

y=c1cosβx+c2sinβx

y'= β×c1×-sinβx+β×c2×cosβx  

y'=-c1βsinβx+c2βcosβx

y''=β×-c1β×cosβx + (β×c2β×-sinβx)

y''= -c1β²cosβx -c2β²sinβx

factorize -β²

y''= -β²(c1cosβx +c2sinβx)

y(x)=c1cosβx+c2sinβx

therefore y'' = -β²y

y''+β²y=0

now we compare this with the second order D.E provided in the question

y''+10y=0

this means that β²y=10y

β²=10

B=√10  or 3.16(2 d.p)

5 0
3 years ago
Find the area of the triangle with the given measurements. Round the solution to the nearest hundredth if necessary. B = 67°, a
kvasek [131]

Among many other formulas, the area of a triangle is


S = \frac 1 2 a c \sin B


where B is the angle between sides a and c.


S=\frac 1 2(10)(20) \sin 67^\circ \approx 92.05 \textrm{ sq cm}



Answer: 92.05 sq cm, first choice


Bonus. Here's a formula for the area S of a triangle your teacher doesn't know:


16S^2 = 4a^2b^2 -(c^2-a^2-b^2)^2=(a^2+b^2+c^2)^2-2(a^4+b^4+c^4)



7 0
3 years ago
What is the center and radius of the circle given by x2 + y2 - 10x - 12y + 24 = 0?​
AveGali [126]

Answer:

centre (5, 6 ) , r = \sqrt{37}

Step-by-step explanation:

the equation of a circle in standard form is

(x - h)² + (y - k)² = r²

where (h, k ) are the coordinates of the centre and r the radius

given

x² + y² - 10x - 12y + 24 = 0 ( collect x and y terms together and subtract 24 from both sides )

x² - 10x + y² - 12y = - 24

using the method of completing the square

add ( half the coefficient of the x / y terms)² to both sides

x² + 2(- 5)x + 25 + y² + 2(- 6)y + 36 = - 24 + 25 + 36

(x - 5)² + (y - 6)² = 37 ← in standard form

with centre (h, k ) = (5, 6 ) and r = \sqrt{37}

3 0
2 years ago
Is 0.23 or 2.3% greater?
Vaselesa [24]

Answer:

0.23

Step-by-step explanation:

If you convert 0.23 into a percent, it becomes 23%, which is more than 2.3%.

<em>Hope that helps!</em>

<em>-Sabrina</em>

5 0
3 years ago
Which of the following shows the polynomial 3x^3 - 5x + x^7 + 9 + 4x^11 written in descending order?
alina1380 [7]

Answer:

4x^11+x^7+3x^3-5x+9

Its highest to lower based on the exponential number

our exponential numbers are: 3, 1, 7,0,11 putting those from highest to lowers would put them: 4x^11+x^7+3x^3-5x+9

7 0
2 years ago
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