3,9,7,21,19,57.55,165 what is the last number?

Can you help me find t value in this problem?

Eduardwww [97]

we have a maximum at t = 0, where the maximum is y = 30.

We have a minimum at t = -1 and t = 1, where the minimum is y = 20.

<h3>How to find the maximums and minimums?</h3>

These are given by the zeros of the first derivation.

In this case, the function is:

w(t) = 10t^4 - 20t^2 + 30.

The first derivation is:

w'(t) = 4*10t^3 - 2*20t

w'(t) = 40t^3 - 40t

The zeros are:

0 = 40t^3 - 40t

We can rewrite this as:

0 = t*(40t^2 - 40)

So one zero is at t = 0, the other two are given by:

0 = 40t^2 - 40

40/40 = t^2

±√1 = ±1 = t

So we have 3 roots:

t = -1, 0, 1

We can just evaluate the function in these 3 values to see which ones are maximums and minimums.

w(-1) = 10*(-1)^4 - 20*(-1)^2 + 30 = 10 - 20 + 30 = 20

w(0) = 10*0^4 - 20*0^2 + 30 = 30

w(1) = 10*(1)^4 - 20*(1)^2 + 30 = 20

So we have a maximum at x = 0, where the maximum is y = 30.

We have a minimum at x = -1 and x = 1, where the minimum is y = 20.

If you want to learn more about maximization, you can read:

brainly.com/question/19819849

6 0

2 years ago

Hunter is 4.52 feet tall. His sister is 0.75 times his height. How tall is Hunter's sister

Dominik [7]

Answer:

Hunter's sister is 4.53 feet tall.

Step-by-step explanation:

4.52 x 0.75 = 3.39 feet

4 0

3 years ago

The diagram below gives the dimensions of a swimming pool. 18 ft , 20ft, 36ft (c) What is the total area of the swimming pool? E

WARRIOR [948]

The picture in the attached figure

Part 1) What is the total area of the swimming pool?

we know that
area of the swimming pool=area rectangle-area semi circle

area rectangle=20*36-----> 720 ft²

area semicircle=pi*r²/2
r=18/2----> 9 ft
area semicircle=pi*9²/2----> 127.17 ft²

area of the swimming pool=720 ft²-127.17 ft²----> 592.83 ft²

the answer Part 1) is
The area of the swimming pool is 592.83 ft²

Part 2) What is the perimeter of the swimming pool?

perimeter of the swimming pool=perimeter of rectangle-18 ft+perimeter semi circle
perimeter of rectangle=2*[20+36]---> 112 ft

perimeter semi circle=2*pi*r/2----> pi*r
r=9 ft
perimeter semi circle=pi*9----> 28.26 ft
so
perimeter of the swimming pool=112 ft-18 ft+28.26 ft----> 122.26 ft

the answer Part 2) is
122.26 ft

6 0

3 years ago

Solving for an Unknown Using the Distributive Property

ArbitrLikvidat [17]

Complete Question:

The equation a= 180(n-2)/n represents the angle measures, a, in a regular n-sided polygon. When the equation is solved for n, n is equal to a fraction with a denominator of a – 180. What is the numerator of the fraction?

Answer:

The numerator of fraction is -360

Solution:

Given that,

The equation represents the angle measures, a, in a regular n-sided polygon is:

$a = \frac{180(n - 2)}{n}$

We have to solve the equation for "n"

Rearrange the equation

$a \times n = 180(n - 2)\\\\a \times n = 180n - 360\\\\an - 180 n = -360\\\\Take\ n\ as\ common\ factor\\\\n(a-180) = -360\\\\n = \frac{-360}{a - 180}$

Thus the numerator of the fraction is -360

4 0

2 years ago

Alex has a grid in the shape of a rectangle. he has right triangles. each right triangle has an area of 25 square millimeters an

Maurinko [17]

First you have to find the area of the rectangular grid. The area of a rectangle is length•width.
So:
A= 20•12
A= 240cm
Then you need to convert 240cm into mm.
240cm is 2400mm.

Then you need to figure out how many triangles can fit into the rectangle if all the triangles have an area of 25mm. So you divide 2400 by 25.
2400:25= 96

So Alex can fit 96 triangles into the grid.

4 0

3 years ago