Please help me with these questions!!! I really need help :)

Answers

Answer 1

Answer: Rectangular prism
V = 12*8*4 = 384 in^3

Triangular prism
V = 0.5*3*15*16 = 360 ft^3

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Let f(x)=x^2 - 16. find f^-1(x).

Answers

$f(x)=x^2-16\n\ny=x^2-16\n\nx^2=y+16\n\nx=√(y+16)\n\nf^(-1)(x)=√(x+16)$

A quadratic function doesn't have inverse function. But you can find inverse function for each of its "arms".

$f(x)=x^2-16 \Rightarrow x_(vertex)=0\n y=x^2-16\n x^2=y+16\n x=-√(y+16) \vee x=√(y+16)\n f^(-1)(x)=-√(x+16) \hbox{ for } x<0\hbox{ (left arm)}\n f^(-1)(x)=√(x+16) \hbox{ for } x>0\hbox{ (right arm)}$

20. The temperature of a pot of water is 62*F. The temperature increasesby 20*F per minute when being heated. Write an equation to represent

the linear relationship. *

Answers

Given :

The temperature of a pot of water is 62 F .

The temperature increases by 20 F per minute when being heated .

To Find :

Write an equation to represent the linear relationship.

Solution :

Here , the temperature is increasing directly with the time .

Therefore , it is a linear equation .

Let temperature varies with as :

T = at+b .... equation 1 .

( Here , a and b are constants )

Now , at t= 0 min .

$T = 62 =a* 0 + b$

$b=62$

Now , after 1 min temperature will be , T = 62 +20 =82 F

$T = 82 = a* 1+62\na=20$

Putting value of a ans b in equation 1 , we get :

$T=20t+62\ F$

Hence , this is the required relation .

A balloon is 30 yards above the ground. It starts to float upwards, and the altitude increases at a rate of 5 yards per minute. Enter the altitude, in yards, of the balloon after 20 minutes.

Answers

a=20(5)+30

20*5=100

100+30=130

Altitude: 130 yards.

Final answer:

The balloon's altitude increases by 5 yards each minute. So, after 20 minutes, the balloon has ascended 100 additional yards. If it was initially 30 yards above the ground, it is now at an altitude of 130 yards.

Explanation:

Based on the provided information, the altitude of the balloon changes at a rate of 5 yards per minute. At the beginning, the balloon is 30 yards above the ground. This initial altitude is increased by the amount of change happening every minute. Therefore, after 20 minutes of continuous upward movement, the change in altitude is 20 minutes * 5 yards/minute = 100 yards. Thus, the final altitude of the balloon becomes the sum of its initial altitude and the change, which is 30 yards + 100 yards = 130 yards.

Learn more about Linear Motion here:

brainly.com/question/32294697

#SPJ11

Please help me with this question please is so hard

Answers

Answer:

1) $101,400

2) $27,000

Step-by-step explanation:

1) For this, we can first find how much she makes in a year from her salary alone:

$2,200×12= $26400.

Now, she also received a commission of 2.5%, so we can take this percentage from 3 million to find the total from commission:

3,000,000×0.025= $75,000

Adding these two gives us a total of $101400.

2) We can use the Simple Interest Formula to solve this (I= Prt). Plug in the values given to give us:

I= 5000(1.08)(5)

I= $27000

How many roots does the function have?f(x)= x^6 + 2x^5 - 2x^4 + 3x^3 + 4x^2 - 5x +7

A. 21

B. 2

C. 6

D. 7

Answers

Answer:

C. 6

Step-by-step explanation:

The degree of the polynomial function is 6. The "fundamental theorem of algebra" tells you the number of roots is equal to the degree of the polynomial.

f(x) has 6 roots.

Zero product property to solve equations1. a^2+8a=0
2. (3h-6)(2h-8)=0
3. 6m^2+17m+5=0
4. y^2-36=0
5. (3g+4)^2=0

Answers

1. a² + 8a = 0
a(a) + (8) = 0
a(a + 8) = 0
a = 0 or a + 8 = 0
- 8 - 8
a = -8

2.   (3h - 6)(2h - 8) = 0
(3(h) - 3(2))(2(h) - 2(4)) = 0
(3(h - 2))(2(h - 4)) = 0
6(h - 2)(h - 4) = 0
6 6
(h - 2)(h - 4) = 0
h - 2 = 0 or h - 4 = 0
+ 2 + 2 + 4 + 4
h = 2 h = 4

3. 6m² + 17m + 5 = 0
6m² + 15m + 2m + 5 = 0
3m(2m) + 3m(5) + 1(2m) + 1(5) = 0
3m(2m + 5) + 1(2m + 5) = 0
(3m + 1)(2m + 5) = 0
3m + 1 = 0 or 2m + 5 = 0
  - 1 - 1    - 5 - 5
3m = -1 2m = -5
3 3 3   3
m = ⁻¹/₃   m = -1²/₃

4. y² - 36 = 0
y² - 6y + 6y - 36 = 0
y(y) - y(6) + 6(y) - 6(6) = 0
y(y - 6) + 6(y - 6) = 0
  (y + 6)(y - 6) = 0
y + 6 = 0 or y - 6 = 0
- 6 - 6 + 6 + 6
y = -6 y = 6

5. (3g + 4)² = 0
(√(3g + 4))² = √(0)
  3g + 4 = 0
  - 4 - 4
3g = -4
3 3
g = -1¹/₃