(1-cos^2x)csc^2x=1 Please verify

geniusboy [140]

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4 0

2 years ago

The area of rectangular is 64m the length of the pool is 12 m less that the width .The situation can be represented by the equat

beks73 [17]

Answer:

Width = 16 m

Length = 4 m

Step-by-step explanation:

The area of rectangular is 64m² the length of the pool is 12 m less that the width . The situation can be represented by the equation x

Area of a rectangle = Length × Width

L = W - 12

Hence:

64 = (W - 12) × W

64 = W² - 12W

W² - 12W - 64 = 0

Factor using

(W + 4)(W - 16) = 0

Width = 16m

Length = W - 12

Length = 16 m - 12 m

= 4 m

6 0

2 years ago

Marcela is registering for her college classes, which cost $105 per unit. How many units can she take to have a maximum cost of

OverLord2011 [107]

Answer:

Marcela can take up to 13 units.

Step-by-step explanation:

In order to find the number of units that Marcela can take for her college classes, we can set up an inequality and solve for the variable. Since each unit costs $105, we can say that 105u ≤ 1365 where u = the number of units. The number of units multiplied by the cost per unit, must be less than or equal to $1,365. In order to solve for 'u', we can use inverse (opposite) operations and get rid of the coefficient by dividing both sides of the inequality by 105. 1365÷105 = 13. So, the number of units that Marcela can take must be less than or equal to 13 units.

6 0

2 years ago

Read 2 more answers

Si 4x= 5/6y entonces 5y=

Hunter-Best [27]

Answer:

$5y=24x$

Step-by-step explanation:

The question in English is

If 4x= 5/6y then 5y=

we have

$4x=\frac{5}{6}y$

Solve for 5y

Multiply both sides by 6

$6*4x=(6)*\frac{5}{6}y$

Simplify

$24x=5y$

Rewrite

$5y=24x$

8 0

2 years ago

Given that −4i is a zero, factor the following polynomial function completely. Use the Conjugate Roots Theorem, if applicable. f

GalinKa [24]

Answer:

$\large \boxed{\sf \bf \ \ f(x)=(x-4i)(x+4i)(x+3)(x-5) \ \ }$

Step-by-step explanation:

Hello, the Conjugate Roots Theorem states that if a complex number is a zero of real polynomial its conjugate is a zero too. It means that (x-4i)(x+4i) are factors of f(x).

$\text{Meaning that } (x-4i)(x+4i) =x^2-(4i)^2=x^2+16 \text{ is a factor of f(x).}$

The coefficient of the leading term is 1 and the constant term is -240 = 16 * (-15), so we a re looking for a real number such that.

$f(x)=x^4-2x^3+x^2-32x-240\\\\ =(x^2+16)(x^2+ax-15)\\\\ =x^4+ax^3-15x^2+16x^2+16ax-240$

We identify the coefficients for the like terms, it comes

a = -2 and 16a = -32 (which is equivalent). So, we can write in $\mathbb{R}$ .

$\\f(x)=(x^2+16)(x^2-2x-15)$

The sum of the zeroes is 2=5-3 and their product is -15=-3*5, so we can factorise by (x-5)(x+3), which gives.

$f(x)=(x^2+16)(x^2-2x-15)\\\\=(x^2+16)(x^2+3x-5x-15)\\\\=(x^2+16)(x(x+3)-5(x+3))\\\\=\boxed{(x^2+16)(x+3)(x-5)}$

And we can write in $\mathbb{C}$

$f(x)=\boxed{(x-4i)(x+4i)(x+3)(x-5)}$

Hope this helps.

Do not hesitate if you need further explanation.

Thank you

7 0

2 years ago