What is the approximate volume of the sphere?
What is the approximate volume of the sphere? - 1

Answers

Answer 1
Answer:

Volume of sphere with radius

r= (4/3)Pi(r)^3

I hope that's help ! Please if you have question(s) fell free to let know !

Thanks :)


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Use angle difference identity to find the exact value.1. tan 15 degrees

2. tan -105 degrees

Answers

Hello,

1)
tan (a-b)=(tan a - tan b)/(1+tan a tan b)

15=45-30
tan 45°= (√2/2)/(√2/2)=1
tan 30°=(1/2)/(√3/2)=√3/3
tan (45°-30°)= (1-√3/3)/(1+1*√3/3)=(3-√3)/(3+√3)=(3-√3)²/6=2-√3

tan (-105°)=tan (75°)= tan (60°+15°)=(tan 60+tan15°)/(1-tan 60°*tan 15°)

tan 15°=2-√3
tan 60°=√3°
tan (-105°)=(√3+2-√3)/(1-√3*(2-√3))=2/(1-2√3+3)=1/(2-√3)=2+√3

A mathematical formula designed to predict population fluctuations in a community could be called a(an)

Answers

It would be called an ecological model.

Mike and Kate plan to save money for their wedding over a 20 month period. They will need to save $8,000 to help pay for the wedding. They set aside the same amount each month. After a year they saved $4,000. Mike and Kate know they must adjust their plan in order to meet their goal, so they came up with the following options:Option A: Stay with saving the same amount they've been saving each month but postpone the wedding 2 months.
Option B: Increase the amount of money they save each month by $80 from what they've been saving.
Which of the following is a true statement?
a.
Only option A will allow them to meet their goal.
b.
Only option B will allow them to meet their goal.
c.
Both options A and B will allow them to meet their goal.
d.
Neither option A nor option B will allow them to meet their goal.



Please select the best answer from the choices provided


A
B
C
D

Answers

D is the correct answer. Mike and Kate require $8000 for their wedding and have saved $4000 already, so they need a further $4000. They have saved the money over 12 months, which means they have been saving $333.33 every month (4000/12). In Option A they have 10 months to save money - the original 8 months, plus the 2 months the wedding is postponed. This will give them the chance to save $3333.33 (333.33 x 10). In Option B, they can increase their monthly savings by $80, giving them total monthly savings of $413.33 (333.33 + 80). In the remaining 8 months before the wedding, they will be able to save $3306.66 (413.33 x 8). However, neither of these options give them the $4000 required to make their $8000 budget.

Answer:

d

Step-by-step explanation:

What is the vertex of the parabola whose equation is y = (x + 1)2 + 3? (-1, -3) (-1, 3) (1, 3)

Answers

Algebra:
A standard parabola is y = x^2. Its vertex is at (0,0)
You can change the position (or vertex) of the parabola.
To move a parabola across the x-axis, you can add or subtract a number from x WITHIN brackets of the ^2
eg. (x + 1)^2 will move the parabola across the x-axis. It will move is one unit to the LEFT (as the sign is opposite to the direction it moves ie. The sign it + but you move the whole parabola in the -ve direction).
Adding or subtracting a number from x OUTSIDE of the ^2 moves the parabola up or down the y-axis
eg. x^2 + 3 will move the parabola UP 3 units (the sign is the same as the direction it moves when the added/subtracted number is outside of the ^2 ie. the sign is positive so the parabola moves up in the positive direction)

From this, we can conclude that because (x + 1)^2 + 3, the vertex will be where x = -1 and where y = 3

Vertex : (-1,3)



Calculus:
f(x) = (x + 1)^2 + 3 = x^2 + 2x + 1 + 3 = x^2 + 2x + 4
Expanding the formular to make it easier to differentiate

f'(x) = 2x + 2
Differentiating (finding the formular the the gradiet of the parabola)

0 = 2x + 2
When the gradient is equal to zero, it must be the vertex

-2 = 2x
-2/2 = x
x = -1
Solve to give the x value at the vertex

f(x) = (x + 1)^2 + 3
= (-1 + 1)^2 + 3
Substitute x = -1 into original equatiom to find y value at the vertex

= (0)^2 + 3
= 0 + 3
= 3
Solve for y

Vertex : (-1,3)


Answer:

Vertex : (-1,3) is the answer

Hope this helped!!!!

Step-by-step explanation:

When I started here, there were 500 employees. Since then, we have added 35% more employees, so we now have a total of __________ employees.

Answers

Number of employees when i initially started = 500
Percentage increase in the number of employees = 35%
Then
Increase in the number of employees = (35/100) * 500
                                                             = 35 * 5
                                                             = 175
So the total number of employees = 500 + 175
                                                       = 675
So now we have a total of 675 employees. I hope the procedure is not that complicated for you to understand. You can generally use this method for solving similar type of problems in future without requiring any help from anyone.

The Drama club is showing a video of their recent play. The first showing begins at 2:30 p.m. The second showing is scheduled at 5:25 P.m. With a 1/2-hour break between the showings

Answers

Answer is 2 hours 25 minutes 2:30+30=3:00 5:25 and 3:00= 2 hours 25 mins inbetween