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3 years ago

What is the radian measure of the smaller angle formed by the hands of a clock at 4 pm?

Mathematics

1 answer:

never [62]3 years ago

4 0

On a clock, every 5 minutes is just another 30° angle deviation away from the 12th hour, hence 30° × 4 = 120°

Converting this value into radians..

$\frac{120\pi}{180}$
Simplifying this value should get you, 2π/3 rad, which is the radian measure of the clock hands at 4pm.

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PLEASE HELP

postnew [5]

Answer:

Below

Step-by-step explanation:

Substituting the given values:

f(6) = 6(2/3) - 2 = cube root of 6^2 - 2 = cube root 36 - 2

f(-6)= (-6)(2/3) - 2 = cube root of(-6)^2 - 2 = cube root 36 - 2

So This is true,

f(6) = cube root of 6^2 - 2 = cube root 36 - 2 = 1.3019

2 * f(3) = 2 * (cube root of 3^2 - 2 ) = 2 * (cube root of 9 - 2) = 0.1602

So False,

4 0

3 years ago

Do you agree with the statement that " cubic functions must have at least 1 x-intercept but not more than 3, whereas quadratic f

vladimir2022 [97]

Answer:

Yes, I agree

Step-by-step explanation:

For the cubic function

A cubic function is represented as:

$f(x)=ax^3+bx^2+cx+d$

A cubic function may have 1, 2 or 3 x intercepts. This is shown below

For 3 x intercepts

$y = x^3 - x$

Equate y to 0

$x^3 - x = 0$

Expand

$x(x^2 - 1) = 0$

Express $x^2 - 1$ as difference of two squares

$x(x - 1)(x +1 ) = 0$

x = 0 or 1 or -1

For 2 x intercepts

$y = x^3 - x$

$y =(x-5)^2)(x+7)$

Equate y to 0

$(x-5)^2(x+7) = 0$

Expand

$(x-5)(x-5)(x+7) = 0$

x= 5 or x = -7

For 1 x intercept

$y = x^3$

Equate y to 0

$x^3 = 0$

Take cube roots of both sides

$x = 0$

It has been shown above that a cubic function may have 1, 2 or 3.

So, I agree to the statement

For the quadratic function

A quadratic function will not have any x intercept when the function can not be factorized;

E.g.

$y = x^2 + x + 17$

The above function has no x intercept.

A quadratic function will have at least 1 x intercept when the function can be factorized;

E.g.

$y = x^2- 6x + 9$

Equate y to 0

$x^2- 6x + 9 = 0$

Expand

$x^2 - 3x - 3x + 9 = 0$

$(x - 3)(x-3) = 0$

$x = 3$

We've shown that a quadratic may have no x intercept, and it may also have x intercept(s)

Hence, I agree to both statement

3 0

2 years ago

An ice cube is melting, and the lengths of its sides are decreasing at a rate of 0.8 millimeters per minute At what rate is the

julia-pushkina [17]

Answer:

The rate of decrease is: $43.2mm^3/min$

Step-by-step explanation:

Given

$l = 18mm$

$\frac{dl}{dt} = -0.8mm/min$ ---- We used minus because the rate is decreasing

Required

Rate of decrease when: $l = 18mm$

The volume of the cube is:

$V = l^3$

Differentiate

$\frac{dV}{dl} = 3l^2$

Make dV the subject

$dV = 3l^2 \cdot dl$

Divide both sides by dt

$\frac{dV}{dt} = 3l^2 \cdot \frac{dl}{dt}$

Given that: $l = 18mm$ and $\frac{dl}{dt} = -0.8mm/min$

$\frac{dV}{dt} = 3 * (18mm)^2 * (-0.8mm/min)$

$\frac{dV}{dt} = 3 * 18 *-0.8mm^3/min$

$\frac{dV}{dt} = -43.2mm^3/min$

Hence, the rate of decrease is: 43.2mm^3/min

8 0

3 years ago

I NEED HELP IN MATH!!! It’s due tonight and I’ve tried to do it and it don’t fully understand please help if u can!!!

Katyanochek1 [597]

Answer:

1. 42

2. 77

3. 87.75

4. 117

5. 119

6. 89.25

7. 39

8. 58.5

9. 218.75

Good Luck!

6 0

3 years ago

Read 2 more answers

Solve for y. –5(y − 3) − 10 = –6y y =

Naya [18.7K]

Answer:

$y = - 5$

Step-by-step explanation:

$- 5(y - 3) - 10 = - 6y$

➡️ $- 5y + 15 - 10 = - 6y$

➡️ $- 5y + 5 = - 6y$

➡️ $- 5y + 6y = - 5$

➡️ $y = - 5$

7 0

3 years ago