3 years ago

Cot^2 x- 6cotx - 5=0

Mathematics

1 answer:

viva [34]3 years ago

3 0

Step-by-step explanation:

cotx=t

t^2-6t-5=0

t=cotx=1or5

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Ms. Steven creates a drawing in her kitchen. Her drawing is 7cm in length and 4cm in width. The scale on the drawing is 1cm = 3f

marysya [2.9K]

Answer:

7cm=7×3ft=21ft

4cm=4×3ft=12ft

here

length=21ft

breadth=12ft

now

area= l×b

=21ft×12ft

=252ft^2

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3 years ago

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Solve the equation <br> y-x=17<br> y=4x+2

gogolik [260]

Y-x =17
y = -x + 17

substitute this into the second equation

y = 4x + 2
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3 years ago

Two angles are supplementary. The measure

BlackZzzverrR [31]

Answer:

57°

Step-by-step explanation:

Let's assume the measurement of the second angle is x.

so, following the problem

(2x + 9) + x = 180

2x + x = 3x

=> 3x + 9 = 180

=> 3x = 180 - 9

3x = 171

x = 171/3

x = 57°

57° is the smallest angle

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3 years ago

The rate of change of revenue (in dollars per calculator) from the sale of x calculators is R′(x)=(x+1)ln(x+1)R ′ (x)=(x+1)ln(x+

jekas [21]

Answer:

Total revenue = $\frac{169}{2}\ln(13)-\frac{169}{4}$ dollars

Step-by-step explanation:

$R'(x)=(x+1)\ln(x+1)$

Integrate with respect to $x$ .

$R(x)=$ ∫ $(x+1)\ln(x+1)$ dx

Take $x+1=u$

Differentiate with respect to $x$

$dx=du$

So,

$R(x)=$ ∫ $u\ln(u)\,du$

Use integration by parts: ∫f g dx = f∫ g dx-∫(∫g dx)f' dx

Therefore,

$R(x)=$ $\frac{u^2}{2}\ln(u)$ $-$ ∫ $\frac{u^2}{2}\frac{1}{u}\,du$

= $\frac{u^2}{2}\ln(u)$ $-$ ∫ $\frac{u}{2}\,du$

Put $u=x+1$

$R(x)= \frac{(x+1)^2}{2}\ln(x+1)-\frac{(x+1)^2}{4}$

To find total revenue from the sale of the first 12 calculators, put $x=12$

$R(x)= \frac{(12+1)^2}{2}\ln(12+1)-\frac{(12+1)^2}{4}\\\\= \frac{(13)^2}{2}\ln(13)-\frac{(13)^2}{4}\\\\=\frac{169}{2}\ln(13)-\frac{169}{4}$

Total revenue = $\frac{169}{2}\ln(13)-\frac{169}{4}$ dollars

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3 years ago

A spinner is numbered 1-10. What is the probability of the spinner landing on the number 5 on the first spin and an even number

Deffense [45]

Answer:

10% and 50%

Step-by-step explanation:

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3 years ago