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4 years ago

Solve: X+14.91=59.67

1 answer:

7 0

Hihi!

The answer to X+14.91=59.67 would be X= 44.76! This is because you would take 14.91 ÷ X = 59.67

I hope I helped!
-Jailbaitasmr

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A sin^3theta+b cos^3theta=sintheta costheta and a sintheta-b costheta=0 then prove a^2+b^2=1

frozen [14]

Answer:

Proof in explanation

Step-by-step explanation:

Trigonometric Identities

The basic trigonometric identity is:

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

We'll use it and some basic algebra to prove that, given:

$a sin^3\theta+b cos^3\theta=sin\theta cos\theta$

And

$a\sin\theta-b\cos\theta=0$

Then

$a^2+b^2=1$

From the equation:

$a\sin\theta-b\cos\theta=0$

We have:

$a\sin\theta=b\cos\theta\qquad [1]$

The equation

$a sin^3\theta+b cos^3\theta=sin\theta cos\theta$

Can be rewritten as

$a\sin\theta \sin^2\theta+b \cos^3\theta=\sin\theta \cos\theta$

Replacing [1]:

$b\cos\theta \sin^2\theta+b \cos^3\theta=\sin\theta \cos\theta$

Taking the common factor:

$b\cos\theta (\sin^2\theta+ \cos^2\theta)=\sin\theta \cos\theta$

The expression in parentheses is 1, thus:

$b\cos\theta =\sin\theta \cos\theta$

Dividing by $\cos\theta$

$b=\sin\theta$

Replacing in

$a\sin\theta=b\cos\theta$

We have

$a\sin\theta=\sin\theta\cos\theta$

Dividing by $\sin\theta$

$a=\cos\theta$

Now:

$a^2+b^2=(\cos\theta)^2+(\sin\theta)^2$

This expression is 1, thus it's proven:

$\boxed{a^2+b^2=1}$

6 0

3 years ago

Hi. I need help wih this question (see image). Please show workings.

Kipish [7]

Answer:

$\frac{dy}{dx}$ = 12x³ - 6x² - 7

Step-by-step explanation:

Differentiate each term using the power rule

$\frac{d}{dx}$ (a $x^{n}$ ) = na $x^{n-1}$

Given

y = 3 $x^{4}$ - 2x³ - 7x + 5, then

$\frac{dy}{dx}$ = 4.3 $x^{4-1}$ - 3.2 $x^{3-1}$ - 7 $x^{1-1}$ + 0

= 12x³ - 6x² - 7

4 0

3 years ago

Give the number that is 2 less than its own absolute value

nexus9112 [7]

Answer:

-1

Step-by-step explanation:

l -1 l = 1

1 - -1 = 2

i HOPE U UNDERSTOOD!! :)

4 0

3 years ago

Solve by completing the square: x2+4x-5=0

Sidana [21]

Answer:

The solutions are {-5, 1}

Step-by-step explanation:

Next time, please use the symbol " ^ " to denote exponentiation:

x^2+4x-5=0

Start by identifying the coefficient of the x term (it is 4 here). Divide this by 2, resulting in 2. Square this result (square 2), obtaining 4.

Now add this 4 after the 4x term, and then subtract this 4:

x^2+4x +4 - 4 -5=0

Rewrite x^2+4x + 4 as (x + 2)²:

(x + 2)² - 9 = 0

Add 9 to both sides, to isolate (x + 2):

(x + 2)² = 9

Take the square root of both sides:

x + 2 = ±3

Solve for x: x = -2 + 3, or 1

x = -2 - 3, or -5

The solutions are {-5, 1}

3 0

4 years ago

Joint-Serve Prosthetics spends 43% of its total expenses for payroll. It increased its total expenses when it spent $250,000 for

Leni [432]

Answer: $2,150,000

Explanation: Let

T = Total expenses of Joint-Serve

Then, before the company acquired robotic assemblers, the expenses allocated for payroll is given by

Expenses for Payroll = 43% of Total Expenses
Expenses for Payroll = 0.43T (1)
(Because 43% = 0.43)

Because the total expenses increased by $250,000 after spending for robotic assemblers, the total expenses = T + 250,000

So, the payroll expense is now calculated as

Expenses for Payroll = 38% of Total Expenses
Expenses for Payroll = 0.38(T + 250,000) (2)
(Because 38% = 0.38 and total expenses = T + 250,000)

By comparing equations (1) and (2),

$0.43T = 0.38(T + 250,000)
\\ 0.43T = 0.38T + 0.38(250,000)
\\ 0.43T = 0.38T + 95,000
\\ 0.43T - 0.38T = 95,000
\\ \frac{0.05T}{0.05} = \frac{95,000}{0.05} 
\\ \boxed{T = \$ 1,900,000}$

Thus, the total expense before the purchase of robotic assemblers is T = $ 1,900,000. Therefore, the total expense after purchasing the robotic assemblers is T + 250,000 = 1,900,000 + 250,000 = $2,150,000

6 0

3 years ago