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3 years ago

How to simply the radical

Mathematics

1 answer:

zlopas [31]3 years ago

3 0

6√2 + 4 √32
try to get the same number "2" remaining under the root sign by finding what # times 2 gives 32
6√2 + 4√2×√16
since 16 is a perfect Square √16 gives 4
therefore.
6√2 + 4 ×4 √2
6√2 +16√2
these are Like terms so add them
which would give u
22√2
hoped i helped, feel free to ask any question XOX

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A radio transmission tower is feet tall. How long should a guy wire be if it is to be attached feet from the top and is tomake a

Bond [772]

Answer:

<em> Length of guy wire is 590.6 ft</em>

Step-by-step explanation:

The complete question is

A radio transmission tower is 210 feet tall. How long should a guy wire be if it is to be attached 8 feet from the top and is to make an angle of 20° with the ground. Give your answer to the nearest tenth of a foot.

height of tower = 210 ft

8 ft fro the top leaves 210 - 8 = 202 ft to the ground

This is an angle of elevation problem

the opposite is 202 ft

hypotenuse = ?

angle is 20°

using sin ∅ = opp/hyp

sin 20° = 202/hyp

0.342 = 202/hyp

hyp = 202/0.342 = <em>590.6 ft this is the length of the guy wire</em>

3 0

2 years ago

Posting a screenshot. please help.

Alinara [238K]

X^2 + 10x + 11 = 0
x^2 + 10x = -11
x^2 + 10x + 25 = -11 + 25
(x + 5)^2 = 14 <===
x + 5 = (+-) sqrt 14
x = -5 (+-) 3.74

x = -5 + 3.74 = -1.26 <== solution
x = -5 - 3.74 = - 8.74 <== solution

7 0

3 years ago

Suppose that each time Giannis Antetokounmpo shoots a free throw, he has a 3/4 probability of success. If Giannis shoots three f

GREYUIT [131]

Answer:

84.38% probability that he succeeds on at least two of them

Step-by-step explanation:

For each free throw, there are only two possible outcomes. Either Giannis makes it, or he does not. The free throws are independent. So we use the binomial probability distribution to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

In which $C_{n,x}$ is the number of different combinations of x objects from a set of n elements, given by the following formula.

$C_{n,x} = \frac{n!}{x!(n-x)!}$

And p is the probability of X happening.

He has a 3/4 probability of success.

This means that $p = \frac{3}{4} = 0.75$

Giannis shoots three free throws

This means that $n = 3$

What is the probability that he succeeds on at least two of them

$P(X \geq 2) = P(X = 2) + P(X = 3)$

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

$P(X = 2) = C_{3,2}.(0.75)^{2}.(0.25)^{1} = 0.4219$

$P(X = 3) = C_{3,3}.(0.75)^{3}.(0.25)^{0} = 0.4219$

$P(X \geq 2) = P(X = 2) + P(X = 3) = 0.4219 + 0.4219 = 0.8438$

84.38% probability that he succeeds on at least two of them

6 0

2 years ago

A spinner has 4 equal-sized sections labeled A, B, C, and D. It is spun and a fair coin is tossed. What is the probability of sp

allsm [11]

Probability of spinning a C =1/4
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8 0

2 years ago

Save me the headache

maxonik [38]

$(9\sin2x+9\cos2x)^2=81$

Taking the square root of both sides gives two possible cases,

$9\sin2x+9\cos2x=9\implies\sin2x+\cos2x=1$

$9\sin2x+9\cos2x=-9\implies\sin2x+\cos2x=-1$

Recall that

$\sin(\alpha\pm\beta)=\sin\alpha\cos\beta\pm\cos\alpha\sin\beta$

If $\alpha=2x$ and $\beta=\dfrac\pi4$ , we have

$\sin\left(2x+\dfrac\pi4\right)=\dfrac{\sin2x+\cos2x}{\sqrt2}$

so in the equations above, we can write

$\sin2x+\cos2x=\sqrt2\sin\left(2x+\dfrac\pi4\right)=\pm1$

Then in the first case,

$\sqrt2\sin\left(2x+\dfrac\pi4\right)=1\implies\sin\left(2x+\dfrac\pi4\right)=\dfrac1{\sqrt2}$

$\implies2x+\dfrac\pi4=\dfrac\pi4+2n\pi\text{ or }\dfrac{3\pi}4+2n\pi$

(where $n$ is any integer)

$\implies2x=2n\pi\text{ or }\dfrac\pi2+2n\pi$

$\implies x=n\pi\text{ or }\dfrac\pi4+n\pi$

and in the second,

$\sqrt2\sin\left(2x+\dfrac\pi4\right)=-1\implies\sin\left(2x+\dfrac\pi4\right)=-\dfrac1{\sqrt2}$

$\implies2x+\dfrac\pi4=-\dfrac\pi4+2n\pi\text{ or }-\dfrac{3\pi}4+2n\pi$

$\implies2x=-\dfrac\pi2+2n\pi\text{ or }-\pi+2n\pi$

$\implies x=-\dfrac\pi4+n\pi\text{ or }-\dfrac\pi2+n\pi$

Then the solutions that fall in the interval $[0,2\pi)$ are

$x=0,\dfrac\pi4,\dfrac\pi2,\dfrac{3\pi}4,\pi,\dfrac{5\pi}4,\dfrac{3\pi}2,\dfrac{7\pi}4$

5 0

3 years ago

Read 2 more answers