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3 years ago

Please please help me

Mathematics

1 answer:

Alex73 [517]3 years ago

6 0

Answer:

x = 5.5

Step-by-step explanation:

Given 2 secants intersecting the circle from a point outside the circle then

The product of the external part and the entire part of one secant is equal to the product of the external part and the entire part of the other secant, that is

x(x + 14) = 6(6 + 12)

x² + 14x = 6 × 18 = 108 ( subtract 108 from both sides )

x² + 14x - 108 = 0 ← in standard form

with a = 1, b = 14 and c = - 108

Using the quadratic formula to solve for x

x = ( - b ± $\sqrt{b^2-4ac}$ ) / 2a

= ( - 14 ± $\sqrt{14^2-(4(1)(-108)}$ ) / 2

= ( - 14 ± $\sqrt{196+432}$ ) / 2

= ( - 14 ± $\sqrt{628}$ ) / 2

x = $\frac{-14-\sqrt{628} }{2}$ or x = $\frac{-14+\sqrt{628} }{2}$

x = - 19.5 or x = 5.5 ( to 1 dec. place )

However x > 0 ⇒ x = 5.5

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Please help me!!!!!!!!!!!!

Aloiza [94]

Answer:

16.03

Step-by-step explanation:

3 0

3 years ago

For 0 ≤ ϴ < 2π, how many solutions are there to tan(StartFraction theta Over 2 EndFraction) = sin(ϴ)? Note: Do not include va

Black_prince [1.1K]

Answer:

3 solutions:

$\theta={0, \frac{\pi}{2}, \frac{3\pi}{2}}$

Step-by-step explanation:

So, first of all, we need to figure the angles that cannot be included in our answers out. The only function in the equation that isn't defined for some angles is $tan(\frac{\theta}{2})$ so let's focus on that part of the equation first.

We know that:

$tan(\frac{\theta}{2})=\frac{sin(\frac{\theta}{2})}{cos(\frac{\theta}{2})}$

therefore:

$cos(\frac{\theta}{2})\neq0$

so we need to find the angles that will make the cos function equal to zero. So we get:

$cos(\frac{\theta}{2})=0$

$\frac{\theta}{2}=cos^{-1}(0)$

$\frac{\theta}{2}=\frac{\pi}{2}+\pi n$

$\theta=\pi+2\pi n$

we can now start plugging values in for n:

$\theta=\pi+2\pi (0)=\pi$

if we plugged any value greater than 0, we would end up with an angle that is greater than $2\pi$ so, that's the only angle we cannot include in our answer set, so:

$\theta\neq \pi$

having said this, we can now start solving the equation:

$tan(\frac{\theta}{2})=sin(\theta)$

we can start solving this equation by using the half angle formula, such a formula tells us the following:

$tan(\frac{\theta}{2})=\frac{1-cos(\theta)}{sin(\theta)}$

so we can substitute it into our equation:

$\frac{1-cos(\theta)}{sin(\theta)}=sin(\theta)$

we can now multiply both sides of the equation by $sin(\theta)$

so we get:

$1-cos(\theta)=sin^{2}(\theta)$

we can use the pythagorean identity to rewrite $sin^{2}(\theta)$ in terms of cos:

$sin^{2}(\theta)=1-cos^{2}(\theta)$

so we get:

$1-cos(\theta)=1-cos^{2}(\theta)$

we can subtract a 1 from both sides of the equation so we end up with:

$-cos(\theta)=-cos^{2}(\theta)$

and we can now add $cos^{2}(\theta)$

to both sides of the equation so we get:

$cos^{2}(\theta)-cos(\theta)=0$

and we can solve this equation by factoring. We can factor $cos(\theta)$ to get:

$cos(\theta)(cos(\theta)-1)=0$

and we can use the zero product property to solve this, so we get two equations:

Equation 1:

$cos(\theta)=0$

$\theta=cos^{-1}(0)$

$\theta={\frac{\pi}{2}, \frac{3\pi}{2}}$

Equation 2:

$cos(\theta)-1=0$

we add a 1 to both sides of the equation so we get:

$cos(\theta)=1$

$\theta=cos^{-1}(1)$

$\theta=0$

so we end up with three answers to this equation:

$\theta={0, \frac{\pi}{2}, \frac{3\pi}{2}}$

7 0

3 years ago

Please help I really need help a sister out I just wanna finish this please thank you!

scZoUnD [109]

Answer:

5 rolls

Step-by-step explanation:

The perimeter lengths are the same because it's a square. So 12 times 4 is 48. You would need a minimum of 5 rolls because each roll as a length of paper of 10 feet. So 40 feet plus 8 would round to 50. That's why it would be 5 rolls.

5 0

3 years ago

(18)-(4-2)x 2<br><br> Plz help

Verdich [7]

Answer:

so first u do (4-2) which is 2

then minus 18 from 2 which is 16

then u multiply by 2 which is 32

therefore the answer is 32

5 0

3 years ago

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Paha777 [63]

Answer:

Step-by-step explanation:

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