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3 years ago

What is £56 divided in a ratio of 3:5?

1 answer:

7 0

First, add the ratio together to get the denominator of the fraction you will use to determine the share. 3+5= 8. Now, you have two fractions: 3/8 and 5/8. Next, just find 3/8 and 5/8 of 56 to get your answers:
(56÷8)×3= <span>£21
</span>and
(56÷8)×5= <span>£35</span>

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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

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a family is staying in a hotel and the total bill for 4 nights is $400. there is a one-time $60 tax fee. what was the nightly ra

Natasha2012 [34]

Answer:

Yes. For example, a hotel advertises, “Buy 4 nights, get the 5th night free.” Taking advantage of the deal, a customer purchases 5 nights for $400. Each night of the customer’s 5-night stay is subject to the fee.

Step-by-step explanation:

8 0

2 years ago

Stan has made a $125.30 monthly deposit into an account that pays 1.5% interest, compounded monthly, for 35 years. he would now

Andrew [12]

The annuity of the monthly deposit into an account that pays 1.5% interest, compounded monthly, for 35 years is $333.71

<h3>What is annuity?</h3>

An annuity is a series of payments made at equal period of time.

future value = annuity x [(1 + i)ⁿ - 1] / i

annuity = $125.30

i = 1.5% / 12 = 0.00125

n = 35 years x 12 months = 420

future value = $125.30 x [(1 + 0.00125)⁴²⁰ - 1] / 0.00125

future value = $69,156.049 ≈ $69,156.05

annuity = [i x (present value)] / [1 - (1 + i)⁻ⁿ]

i = 1.5% / 12 = 0.00125

n = 20 years x 12 months = 240

present value = $69,156.05

annuity = (0.00125 x $69,156.05) / [1 - (1 + 0.00125)⁻²⁴⁰]

annuity = $86.45 / 0.25904

= $333.71

Learn more about annuity;

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1 year ago

Is 60.43 an irrational number

zhuklara [117]

Answer:

No, It is rational

Step-by-step explanation:

An number with a finite number of decimal point/numbers can be rational unlike numbers that repeat on forever like the number pi

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2 years ago

PLEASE HELP me!! will give brainliest!! (:

Cloud [144]

Answer:

The answer to your question is: Yes, x - 5 is a factor of the polynomial.

Step-by-step explanation:

To answer this question you need to divide the polynomial by the factor and if there is nothing left, they are factor.

x -5

x² + x -2

x-5 x³ -4x² -7x +10

-x³ + 5x²

x² - 7x

-x² + 5x

-2x + 10

+2x -10

0 0 These zeros tell us that the linear

expression is a factor of the polynomial

5 0

3 years ago

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