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Fudgin [204]
3 years ago
7

The expression (x-5)^2 is equivalent to...

Mathematics
1 answer:
liq [111]3 years ago
5 0

Answer:

option a x²-25

Step-by-step explanation:

(x-5)²

x²-25

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£35 X 12(months) = £420 per year he saves.
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The results of a poll show that the percent of people who want a new restaurant is in the interval (24%, 38%) . There are 112,48
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Change the percents to decimals (by moving the decimal 2places to the left)
(.24, .38)

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Find all points on the curve x=4cos(t),y=4sin(t) that have the slope of 12.
Marianna [84]

Answer:

\left (-\dfrac{4}{\sqrt{5}},\dfrac{8}{\sqrt{5}}\right )\text{ and }\left (\dfrac{4}{\sqrt{5}},-\dfrac{8}{\sqrt{5}}\right ).

Step-by-step explanation:

We need to find all the points on the curve x=4cos(t),y=4sin(t) that have the slope of 1/2.

x=4cos (t)

\dfrac{dx}{dt}=-4sin (t)

y=4sin (t)

\dfrac{dy}{dt}=4cos (t)

Now,

\dfrac{dy}{dx}=\dfrac{dy}{dt}\times \dfrac{dt}{dx}

\dfrac{dy}{dx}=4cos (t)\times \dfrac{1}{-4sin (t)}

\dfrac{dy}{dx}=-\cot t

So, slope of the curve is -\cot t.

-\cot t=\dfrac{1}{2}

-\tan t=2

\tan t=-2            ...(1)

Using \sec^2t=1+\tan^2t, we get

\sec^2t=1+(-2)^2

\sec^2t=1+4

\sec t=\pm \sqrt{5}

\cos t=\pm \dfrac{1}{\sqrt{5}}

Now,

\sin^2t=1-cos^2t

\sin t=\pm \sqrt{1-\dfrac{1}{5}}

\sin t=\pm \sqrt{\dfrac{4}{5}}

\sin t=\pm \dfrac{2}{\sqrt{5}}

It equation (1), tan(t) is negative. So, sin and cos have different signs.

If \sin t= \dfrac{2}{\sqrt{5}}, then \cos t=- \dfrac{1}{\sqrt{5}}.

x=4cos (t)=-\dfrac{4}{\sqrt{5}}

y=4sin (t)=\dfrac{8}{\sqrt{5}}

If \sin t=- \dfrac{2}{\sqrt{5}}, then \cos t= \dfrac{1}{\sqrt{5}}.

x=4cos (t)=\dfrac{4}{\sqrt{5}}

y=4sin (t)=-\dfrac{8}{\sqrt{5}}

Therefore, the two points are \left (-\dfrac{4}{\sqrt{5}},\dfrac{8}{\sqrt{5}}\right )\text{ and }\left (\dfrac{4}{\sqrt{5}},-\dfrac{8}{\sqrt{5}}\right ).

5 0
3 years ago
Help on thishwwhejjddjhdhddhdhdj
QveST [7]
The answer is D.
The first one says you add -4 each time in the sequence.
The second says you add -2 each time in the sequence.
The third says you multiply by -2 each time in the sequence.
The fourth says you multiply by -4 each time in the sequence.
-2*-4=8
8*-4=-32
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What is b2*b5*b3 simplified?
Valentin [98]

Answer:

B10

Step-by-step explanation:

8 0
3 years ago
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