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3 years ago

Use the discriminant to determine the number of real solutions to the equation. −4x^2=−8−10x

Mathematics

2 answers:

ICE Princess25 [194]3 years ago

6 0

Answer:

Step-by-step explanation:

Len [333]3 years ago

6 0

Answer:

Step-by-step explanation:

You don't get a free answer. I am, after all, a high school math teacher, so there has to be a lesson in with this.

The discriminant is part of the quadratic formula. It is:

$b^2-4ac$ . If this value is found to be > 0 and a perfect square, there are 2 real roots; if this value is found to >0 and not a perfect square, there are 2 complex roots; if this value is found to be = 0, then there is 1 real root with a multiplicity of 2; and finally, if this value is found to be < 0, then there are 2 imaginary roots. Also, it would help to know that, because we are dealing with the discriminant, which comes from the quadratic formula, and quadratics, by definition, have 2 solutions, you must have 2 solutions listed as the possible roots for the equation. Our equation is:

$-4x^2=-8-10x$ but in order to determine the a, b, and c for the discriminant, that equation has to be in standard form, set equal to 0:

$-4x^2+10x+8=0$

From this we can see that a = -4, b = 10, and c = 8. Filling in the discriminant:

$10^2-4(-4)(8)$ which gives us a value of

100 - [4(-4)(8)] (don't forget orders of operation here!)

100 - (-128) = 100 + 128 = 228

This value is greater than 0 but is not a perfect square, so there are 2 complex roots. That means that there will be radicals in the solutions.

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Find the average value of f(x)=e2x over the interval [2, 4].

shusha [124]

<h2>Option B is the correct answer.</h2>

Step-by-step explanation:

We need to find average value of $e^{2x}$ in [2,4]

Area of $e^{2x}$ in [2,4] is given by

$\int_{2}^{4}e^{2x}dx=\frac{1}{2}\times \left [ e^{2x}\right ]^4_2\\\\\int_{2}^{4}e^{2x}dx=\frac{1}{2}\times(e^8-e^4)=1463.18$

Area of $e^{2x}$ in [2,4] = 1463.18

Difference = 4 - 2 = 2

Average value = Area of $e^{2x}$ in [2,4] ÷ Difference

Average value = 1463.18 ÷ 2

Average value = 731.59

Option B is the correct answer.

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3 years ago

Your class was asked to design a scooter for less than $30. What are some possible

JulijaS [17]

Answer:

$30 is not a lot of Capita so every $ needs to count!

Step-by-step explanation:

Budget well.

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4 years ago

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Find the balance in the account after the given period. $2000 principal earning 6% compounded annually, for 8 years. The bala

Harman [31]

Do 2000 divided by 8 than divided that by 6%

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3 years ago

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You stand a known distance from the base of the tree, measure the angle of elevation the top of the tree to be 15â—¦ , and then

gogolik [260]

Answer:

The maximum possible error of in measurement of the angle is $d\theta_1 =(14.36p)^o$

Step-by-step explanation:

From the question we are told that

The angle of elevation is $\theta_1 = 15 ^o = \frac{\pi}{12}$

The height of the tree is h

The distance from the base is D

h is mathematically represented as

$h = D tan \theta$ Note : this evaluated using SOHCAHTOA i,e

$tan\theta = \frac{h}{D}$

Generally for small angles the series approximation of $tan \theta \ is$

$tan \theta = \theta + \frac{\theta ^3 }{3}$

So given that $\theta = 15 \ which \ is \ small$

$h = D (\theta + \frac{\theta^3}{3} )$

$dh = D (1 + \theta^2) d\theta$

=> $\frac{dh}{h} = \frac{1 + \theta ^2}{\theta + \frac{\theta^3}{3} } d \theta$

Now from the question the relative error of height should be at most

$\pm p$ %

=> $\frac{dh}{h} = \pm p$

=> $\frac{1 + \theta ^2}{\theta + \frac{\theta^3}{3} } d \theta = \pm p$

=> $d\theta = \pm \frac{\theta + \frac{\theta^3}{3} }{1+ \theta ^2} * \ p$

So for $\theta_1$

$d\theta_1 = \pm \frac{\theta_1 + \frac{\theta^3_1 }{3} }{1+ \theta_1 ^2} * \ p$

substituting values

$d [\frac{\pi}{12} ] = \pm \frac{[\frac{\pi}{12} ] + \frac{[\frac{\pi}{12} ]^3 }{3} }{1+ [\frac{\pi}{12} ] ^2} * \ p$

=> $d\theta_1 = 0.25 p$

Converting to degree

$d\theta_1 = (0.25* 57.29) p$

$d\theta_1 =(14.36p)^o$

4 0

3 years ago

Bryce has heard that gas appliances are cheaper to use and can lower utility costs. He is interested in purchasing a new gas sto

Bond [772]

Answer:

C. $29.20

Step-by-step explanation:

The difference between using an electric stove and a gas stove everyday is 13 cents - 5 cents= 8 cents.

Saving 8 cents everyday.

Therefore for a year, Bryce will save 8 cents × 365days = 2920 cents

Then 2920 cents = $(2920÷100)

=$29.20

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3 years ago