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jonny [76]
3 years ago
9

Can someone please help me find the answer to this question please?

Mathematics
1 answer:
spin [16.1K]3 years ago
8 0

Answer:

4x-3

Step-by-step explanation

if im being honest i used photomath

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Factor this polynomial 6x^2 + 19x – 7.
kondaur [170]

Answer:

(3x-1) (2x+7)

8 0
3 years ago
1. Compare 2.01 x 1015 and 2.8 x 1013. Which number is larger?
Leya [2.2K]

Answer:

If these are in exponent form -- the answer would be 2.01 x 10^{15} > 2.8 x 10.3

Step-by-step explanation:

Look at the sheet attached.

6 0
3 years ago
x = c1 cos(t) + c2 sin(t) is a two-parameter family of solutions of the second-order DE x'' + x = 0. Find a solution of the seco
igomit [66]

Answer:

x=-cos(t)+2sin(t)

Step-by-step explanation:

The problem is very simple, since they give us the solution from the start. However I will show you how they came to that solution:

A differential equation of the form:

a_n y^n +a_n_-_1y^{n-1}+...+a_1y'+a_oy=0

Will have a characteristic equation of the form:

a_n r^n +a_n_-_1r^{n-1}+...+a_1r+a_o=0

Where solutions r_1,r_2...,r_n are the roots from which the general solution can be found.

For real roots the solution is given by:

y(t)=c_1e^{r_1t} +c_2e^{r_2t}

For real repeated roots the solution is given by:

y(t)=c_1e^{rt} +c_2te^{rt}

For complex roots the solution is given by:

y(t)=c_1e^{\lambda t} cos(\mu t)+c_2e^{\lambda t} sin(\mu t)

Where:

r_1_,_2=\lambda \pm \mu i

Let's find the solution for x''+x=0 using the previous information:

The characteristic equation is:

r^{2} +1=0

So, the roots are given by:

r_1_,_2=0\pm \sqrt{-1} =\pm i

Therefore, the solution is:

x(t)=c_1cos(t)+c_2sin(t)

As you can see, is the same solution provided by the problem.

Moving on, let's find the derivative of x(t) in order to find the constants c_1 and c_2:

x'(t)=-c_1sin(t)+c_2cos(t)

Evaluating the initial conditions:

x(0)=-1\\\\-1=c_1cos(0)+c_2sin(0)\\\\-1=c_1

And

x'(0)=2\\\\2=-c_1sin(0)+c_2cos(0)\\\\2=c_2

Now we have found the value of the constants, the solution of the second-order IVP is:

x=-cos(t)+2sin(t)

3 0
3 years ago
Find the volume of a cone with a diameter of 12 m and a height of 6 m.
castortr0y [4]

Answer: D. 72 m

Step-by-step explanation:

The formula for the volume of a cone is Volume = pi times radius squared and then times the height, and then divided by 3.

Since the diameter is 12, the radius is 6. Applying the formula, 6 squared is 36, times pi is 36 pi. The height is 6 so 36 * 6 = 216.

But be careful, we're not done yet... We still have to divide by 3

216 / 3 = 72

we can be sure this answer is correct because the other answers are clearly too big

here's your answer, hope this helps :)

3 0
2 years ago
The manager of a furniture factory finds that it costs $2400 to manufacture 60 chairs in one day and $4800 to produce 260 chairs
tamaranim1 [39]

Answer:

C(x) = 12x + 1680

Slope = 12

Intercept = 1680

Step-by-step explanation:

Given that:

X1 = 60 chairs ; y1 = 2400

X2 = 260 chairs ; y2 = 4800

Obtain the slope ; m

m = y2 - y1 / x2 - x1

m = 4800 - 2400 / 260 - 60

m = 2400 / 200

m = 12

Using the point slope relation:

y - y1 = m(x - x1)

y - 2400 = 12(x - 60)

y - 2400 = 12x - 720

y = 12x - 720 + 2400

y = 12x + 1680

C(x) = 12x + 1680

From the general slope intercept equation :

y = mx + c

m = slope ; c = intercept

Hence,

C(x) = 12x + 1680

Slope = 12

Intercept = 1680

5 0
2 years ago
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