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3 years ago

Help me please increase £660 by 5%

Mathematics

1 answer:

GalinKa [24]3 years ago

7 0

Answer:

Step-by-step explanation:

I am from America therefore I am a butt human being and have no idea what that symbol is

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DUE 10:00 PM HELP ASAP. When Sarah left your house this morning her cell phone was 80% charged and then it started to lose 8% ch

Nataly_w [17]

Answer:

The answer would be B=-8>80

Step-by-step explanation:

6 0

3 years ago

Read 2 more answers

Sin(x)^4+ cos(x)^4=1/2

posledela

I'll assume that what was meant was $\sin ^4 x + \cos ^4 x = \dfrac{1}{2}$ .

The exponent in the funny place is just an abbreviation: $\sin ^4 x = (\sin x)^4$ .

I hope that's what you meant. Let me know if I'm wrong.

Let's start from the old saw

$\cos^2 x + \sin ^2x = 1$

Squaring both sides,

$(\cos^2 x + \sin ^2x)^2 = 1^2$

$\cos^4 x + 2 \cos ^2 x \sin ^2x +\sin ^4x = 1$

$\cos^4 x + \sin ^4x = 1 - 2 \cos ^2 x \sin ^2x$

So now the original question

$\sin ^4 x + \cos ^4 x = \dfrac{1}{2}$

becomes
$1 - 2 \cos ^2 x \sin ^2x = \dfrac{1}{2}$

$4 \cos ^2 x \sin ^2x = 1$

Now we use the sine double angle formula

$\sin 2x = 2 \sin x \cos x$

We square it to see

$\sin^2 2x = 4\sin^2 x \cos^2 x = 1$

Taking the square root,

$\sin 2x = \pm 1$

Not sure how you want it; we'll do it in degrees.

When we know the sine of an angle, there's usually two angles on the unit circle that have that sine. They're supplementary angles which add to $180^\circ$ . But when the sine is 1 or -1 like it is here, we're looking at $90^\circ$ and $-90^\circ$ , which are essentially their own supplements, slightly less messy.

That means we have two equations:

$\sin 2x = 1 = \sin 90^\circ$

$2x = 90^\circ + 360^\circ k \quad$ integer $k$

$x = 45^\circ + 180^\circ k$

or

$\sin 2x = -1 = \sin -90^\circ$

$2x = -90^\circ+ 360^\circ k$

$x = - 45^\circ + 180^\circ k$

We can combine those for a final answer,

$x = \pm 45^\circ + 180^\circ k \quad$ integer $k$

Check. Let's just check one, how about

$x=-45^\circ + 180^\circ = 135^\circ$

$\sin(135)= 1/\sqrt{2}$

$\sin ^4(135)=(1/\sqrt{2})^4 = 1/4$

$\cos ^4(135)=(-1/\sqrt{2})^4 = 1/4$

$\sin ^4(135^\circ) +\cos ^4(135^\circ) = 1/2 \quad\checkmark$

6 0

3 years ago

Calculate the surface area?<br><br> Please help

marissa [1.9K]

Answer:

0.0846153846 when divided

6 0

3 years ago

Read 2 more answers

An investigator claims, with 95 percent confidence, that the interval between 10 and 16 miles includes the mean commute distance

RideAnS [48]

Answer:

Hello the options to your question is missing below are the options

A) if sample means were obtained for a long series of samples, approximately 95 percent of all sample means would be between 10 and 16 miles

B.the unknown population mean is definitely between 10 and 16 miles

C.if these intervals were constructed for a long series of samples, approximately 95 percent would include the unknown mean commute distance for all Californians

D.the unknown population mean is between 10 and 16 miles with probability .95

Answer : if these intervals were constructed for a long series of samples, approximately 95 percent would include the unknown mean commute distance for all Californians ( c )

Step-by-step explanation:

95% confidence

interval = 10 to 16 miles

To have 95% confidence signifies that if these intervals were constructed for a long series of samples, approximately 95 percent would include the unknown mean commute distance for all Californians

confidence interval covers a range of samples/values in the interval and the higher the % of the confidence interval the more precise the interval is,

7 0

3 years ago

Javier designs leather shoes at his workshop. He charges $45 for women's shoes and $50 for men's shoes. He needs to make $2,500

Reil [10]

45x + 50y = 2500

45(0) + 50y = 2500

50y = 2500

y = 50

4 0

3 years ago

Read 2 more answers