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3 years ago

Simplest radical form of square root 11x

Mathematics

1 answer:

grin007 [14]3 years ago

6 0

Answer:

Step-by-step explanation:

Radical form means an answer with the √

$\sqrt{11x}$ Should already be in the simplest radical form.

Since 11 only has the factors 1 and 11, it cannot be simplified further.

EXAMPLE

$\sqrt{4x}$ can be simplified. 4 has the factors 2 and 2.

$\sqrt{4x}$ = $\sqrt{(2*2)x}$ = $2\sqrt{x}$

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Please help me <br><br>If 180°<α<270°, cos⁡ α=−8/17, what is sin -α?

rewona [7]

Starting from the fundamental trigonometric equation, we have

$\cos^2(\alpha)+\sin^2(\alpha)=1 \iff \sin(\alpha)=\pm\sqrt{1-\cos^2(\alpha)}$

Since $180$ , we know that the angle lies in the third quadrant, where both sine and cosine are negative. So, in this specific case, we have

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

Plugging the numbers, we have

$\sin(\alpha)=-\sqrt{1-\dfrac{64}{289}}=-\sqrt{\dfrac{225}{289}}=-\dfrac{15}{17}$

Now, just recall that

$\sin(-\alpha)=-\sin(\alpha)$

to deduce

$\sin(-\alpha)=-\sin(\alpha)=-\left(-\dfrac{15}{17}\right)=\dfrac{15}{17}$

6 0

3 years ago

Read 2 more answers

A 10-foot ladder leans against a wall so that it is 6 feet high at the top. The ladder is moved so that the base of the ladder t

konstantin123 [22]

Answer:

The top of the ladder is now at 10 ft.

Step-by-step explanation:

At the start, we have a height H=6, a length L=10 and a base B, that has to be calculated by the Pythagorean theorem:

$B^2=L^2-H^2=10^2-6^2=100-36=64\\\\B=\sqrt{64}=8$

The base is moved twice the distance the height moves up.

We called this distance x, so we have:

$L^2=(H+x)^2+(B-2x)^2=H^2+2Hx+x^2+B^2-4Bx+4x^2\\\\L^2=(H^2+B^2)+5x^2+(2H-4B)x\\\\L^2=L^2+5x^2+(2H-4B)x\\\\0=5x^2+(2H-4B)x\\\\5x+(2H-4B)=0\\\\x=\dfrac{4B-2H}{5}=\dfrac{4*8-2*6}{5}=\dfrac{32-12}{5}=\dfrac{20}{5}=4$

The new height (H+x) is

$H'=H+x=6+4=10$

The base travels 2x=8, so the new base B' is 0.

This means that the ladder is all against the wall (L=H').

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3 years ago

A ball is thrown vertically upward. After t seconds, its height h (in feet) is given by the function =ht−64t16t2. What is the ma

ryzh [129]

This is the concept of applications of polynomial equations. Given that the height of the ball is modeled by the function:
h(t)=16t^2-64t
the maximum height will be calculated as follows;
h(t)=16t(t-4)
therefore:
t=0 or t=4
h(4)=-64(4)+16(4^2)
=0

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4 years ago

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Oksanka [162]

Answer:

Step-by-step explanation:

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3 years ago

You just took out a $200,000 mortgage. You must make equal monthly payments over 30 years, and your interest rate is 6% APR. Wha

Vesnalui [34]

Answer:

a) $1199.10

b) interest: $1000.00

c) principal: $199.10

Step-by-step explanation:

a) The monthly payment can be found using a financial calculator or using the amortization formula:

A = P(r/12)/(1 -(1+r/12)^(-12t))

for Principal P, annual interest rate r, and time t years.

Filling in the given values and doing the arithmetic yields ...

A = $200,000(0.06/12)/(1 -(1+0.06/12)^(-12·30)) = 1000/(1 -1.005^-360)

A ≈ $1199.10

b) The first month's interest is the monthly interest rate times the initial loan balance:

= (0.06/12)·(200,000) = 1000.00 . . . . dollars in interest

c) The first month's payment to principal is the difference between the payment amount and the amount to interest:

$1199.10 -1000 = $199.10 . . . . . first month's payment on principal

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3 years ago