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3 years ago

HELP! 20 POINTS!

Mathematics

1 answer:

adell [148]3 years ago

4 0

Answer:

Small tire, 9in ----> 127 rotations

Big tire, 30in ------> 38 rotations

Step-by-step explanation:

First, we convert the values of feet to inches

600 feet = 7200 in

Each rotation of a tire is equivalent to a traveled distance equal to the perimeter

P = 2*pi*radius

This means that if we divide the traveled distance by the perimeter of each tire, we can find out the number of rotations.

Small tire, 9in

7200 in / 2*pi*9in = 127 rotations

Big tire, 30in

7200 in / 2*pi*30in = 38 rotations

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Find the extreme values of the function f(x, y) = 4x2 + 6y2 on the circle x2 + y2 = 1.

julia-pushkina [17]

Answer with Step-by-step explanation:

We are given that

$f(x,y)=4x^2+6y^2$

Let g(x,y)= $x^2+y^2=1$

We have to find the extreme values of the given function

$\nabla f(x,y)$

$\nabla g(x,y)=$

Using Lagrange multipliers

$\nabla f(x,y)=\lambda \nabla g(x,y)$

$f_x=\lambda g_x$

$8x=\lambda 2x$

Possible value x=0 or $\lambda=4$

If x=0 then substitute the value in g(x,y)

Then, we get $y=\pm 1$

$f_y=\lambda g_y$

$12y=\lambda 2y$

If $\lambda=4$ and substitute in the equation

Then , we get possible value of y=0

When y=0 substitute in g(x,y) then we get

$x=\pm 1$

Hence, function has possible extreme values at points (0,1),(0,-1), (1,0) and (-1,0).

$f(0,1)=6$

$f(0,-1)=6$

$f(1,0)=4$

$f(-1,0)=4$

Therefore, the maximum value of f on the circle $x^2+y^2=1$ is $f(0,\pm1)=6$ and minimum value of $f(\pm1,0)=4$

7 0

3 years ago

A large totem pole near Kalama, Washington, is 100 feet tall. On a particular day at noon it casts a 219-foot shadow. What is th

zhenek [66]

Answer: Angle of elevation of sun at that time is 24.51° .

Step-by-step explanation:

Since we have given that

Height of a large totem pole near Kalama, Washington = 100 feet

Length of a shadow at noon = 219 foot

We need to find the angle of elevation of sun at that time .

As we know the formula for "Tangent ":

$\tan\theta=\frac{AB}{BC}\\\\\tan\theta=\frac{100}{219}\\\\\tan\theta=0.456\\\\\theta=\tan^{-1}(0.456)\\\\\theta=24.51\textdegree$

Hence, Angle of elevation of sun at that time is 24.51° .

7 0

3 years ago

There are 32 volunteers to donate blood. Unfortunately, n of the volunteers did not meet the heath requirements, so they couldn'

Daniel [21]

Answer:

The volunteers donated $470(32-n)$ millimeters of blood.

Step-by-step explanation:

Given:

Total Number of Volunteers = 32

number of Volunteers failed to donate = n

Amount of blood donated by each volunteer = 470 mm

We need to find the Total amount of blood donated by the Volunteers.

Solution:

First we will find the number of volunteers donated blood.

the number of volunteers donated blood is equal to Total Number of Volunteers minus number of Volunteers failed to donate.

framing in equation form we get;

the number of volunteers donated blood = $(32-n)$

Now we will find Total amount of blood donated by the Volunteers.

Total amount of blood donated by the Volunteers is equal to Amount of blood donated by each volunteer multiplied by the number of volunteers donated blood.

framing in equation form we get;

Total amount of blood donated by the Volunteers = $470(32-n)$

Hence The volunteers donated $470(32-n)$ millimeters of blood.

5 0

3 years ago

How do I solve the factor expression using the GCF for 2+8

Talja [164]

The correct answer is 10

8 0

3 years ago

Let m = 3. Enter > , < , or = to compare the expressions. 4m−1 ? 5m−4

bazaltina [42]

= because 4 times 3 minus 1 equals 11 and 5 times 3 minus 4 equals 11

4 0

3 years ago

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