All categories

2 years ago

What is the value of f^-1 (-3)

Mathematics

1 answer:

maxonik [38]2 years ago

7 0

According to the plot of $f(x)$ , whose curve passes through the point (-5, -3), we have

$f(-5) = -3 \implies f^{-1}(-3) = \boxed{-5}$

You might be interested in

-6 + -8 10 points plz help

satela [25.4K]

Answer

The answer is negative 14.

Step-by-step explanation:

When you add a negative by a negative it equals a negative. Like if you add 1 + 1 it's going to equal 2 which is a positive, not a negative. So the answer is technically 8 + 6 which is 14 and all you have to do is add a negative sign.

4 0

3 years ago

A rectangular box is to have a square base and a volume of 12 ft3. If the material for the base costs $0.17/ft2, the material fo

katen-ka-za [31]

Answer:

(a)Length =2 feet

(b)Width =2 feet

(c)Height=3 feet

Step-by-step explanation:

Let the dimensions of the box be x, y and z

The rectangular box has a square base.

Therefore, Volume of the box $V=x^2z$

Volume of the box $=12 ft^3\\$

$Therefore, x^2z=12\\z=\frac{12}{x^2}$

The material for the base costs $\$0.17/ft^2$ , the material for the sides costs $\$0.10/ft^2$ , and the material for the top costs $\$0.13/ft^2$ .

Area of the base $=x^2$

Cost of the Base $=\$0.17x^2$

Area of the sides $=4xz$

Cost of the sides= $=\$0.10(4xz)$

Area of the Top $=x^2$

Cost of the Base $=\$0.13x^2$

Total Cost, $C(x,z) =0.17x^2+0.13x^2+0.10(4xz)$

Substituting $z=\frac{12}{x^2}$

$C(x) =0.17x^2+0.13x^2+0.10(4x)(\frac{12}{x^2})\\C(x)=0.3x^2+\frac{4.8}{x} \\C(x)=\dfrac{0.3x^3+4.8}{x}$

To minimize C(x), we solve for the derivative and obtain its critical point

$C'(x)=\dfrac{0.6x^3-4.8}{x^2}\\Setting \:C'(x)=0\\0.6x^3-4.8=0\\0.6x^3=4.8\\x^3=4.8\div 0.6\\x^3=8\\x=\sqrt[3]{8}=2$

Recall: $z=\frac{12}{x^2}=\frac{12}{2^2}=3\\$

Therefore, the dimensions that minimizes the cost of the box are:

(a)Length =2 feet

(b)Width =2 feet

(c)Height=3 feet

7 0

3 years ago

Perform the division and leave the result in trigonometric form.

Anettt [7]

Answer:

$\frac{1}{2}$ ( cos40° + isin40°)

Step-by-step explanation:

To divide

$\frac{r_{1(cosx_{1}+isinx_{1}) } }{r_{2}(cosx_{2}+isinx_{2}) }$

= $\frac{r_{1} }{r_{2} }$ [ cos(x₁ - x₂) + isin(x₁ - x₂)

Given

$\frac{2(cos90+isin90}{4(cos50+isin50)}$

= $\frac{2}{4}$ ( cos(90 - 50)° + isin(90 - 50)°

= $\frac{1}{2}$ ( cos40° + isin40° )

8 0

3 years ago

PLSSSSSSSSSSS HELPPP>> Show work solve the sysytem- y=1/2x^2+4x+4 y=-4x+12 1/2

Mrac [35]

Answer:

(1, 8.5 ) and ( - 17, 80.5 )

Step-by-step explanation:

Given the 2 equations

y = $\frac{1}{2}$ x² + 4x + 4 → (1)

y = - 4x + 12 $\frac{1}{2}$ → (2)

Substitute (1) into (2), that is

$\frac{1}{2}$ x² + 4x + 4 = - 4x + 12 $\frac{1}{2}$ ( multiply through by 2 to clear the fractions )

x² + 8x + 8 = - 8x + 25 ( add 8x to both sides )

x² + 16x + 8 = 25 ( subtract 25 from both sides )

x² + 16x - 17 = 0 ← in standard form

(x + 17)(x - 1) = 0 ← in factored form

Equate each factor to zero and solve for x

x + 17 = 0 ⇒ x = - 17

x - 1 = 0 ⇒ x = 1

Substitute these values into either of the 2 equations and evaluate for y

Substituting into (2 )

x = 1 : y = - 4(1) + 12.5 = - 4 + 12.5 = 8.5 ⇒ (1, 8.5 )

x = - 17 : y = - 4(- 17) + 12.5 = 68 + 12.5 = 80.5 ⇒ (- 17, 80.5 )

5 0

3 years ago

A pizza has a diameter of 5 inches. what is the area of the pizza? what is the circumference of the pizza

lesantik [10]

Answer:

2.5 is circumvented the area is 7.5

7 0

2 years ago