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3 years ago

There are (4^9)^5 •4^0 books are the library. What is the total number of books at the library?

Mathematics

1 answer:

VladimirAG [237]3 years ago

8 0

4^45

When you have exponents like that, you have to multiply them together. So, 9*5 =45

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9. Two points in the plane, A(−3,8) and ????(17,8), represent the endpoints of the diameter of a circle.

kherson [118]

Answer:

a) (7,8)

b) r = 10

c) $(x-7)^2+(y-8)^2=100$

Step-by-step explanation:

a) Given the endpoints the diameter of the circle as A(-3,8) and B(17,8)

we should realize that the center of the circle lies exactly at the midpoint of these two points. let's denote the midpoint as $(x_m,y_m)$

$(x_m, y_m) = \left(\dfrac{x_1+x_2}{2},\dfrac{y_1+y_2}{2}\right)$

$(x_m, y_m) = \left(\dfrac{-3+17}{2},\dfrac{8+8}{2}\right)$

$(x_m, y_m) = (7,8)$

this is the coordinate of the center of the circle.

b) The radius of the circle can be easily found by using the distance formula between the center point and either of the two endpoints of the diameter.

the general distance formula is:

$r = \sqrt{(x_1-x_2)^2+(y_1-y_2)^2}$

in our case the equation changes to: (selecting the centre and point B)

$r = \sqrt{(x_m-x_2)^2+(y_m-y_2)^2}$

$r = \sqrt{(7-17)^2+(8-8)^2}$

$r = 10$

side note: there are more alternate ways to find the radius for e.g (you can use the distance formula between the points A and B and that'll give you the length of the diameter which you can divide by 2 to get the radius) OR (you don't need to use the distance formula at all <u>since in this particular case</u> all the coordinates lie on the same horizontal line, so by simply subtracting the two x-coordinates of the center and either of A or B)

c) the ingredients needed to make the equation of the circle are the

coordinates of the center: $(x_m,y_m) = (7,8)$
radius of the circle: $r = 10$

we can put this in the formula of the circle:

$(x-a)^2+(y-b)^2=r^2$

in our case the equation changes to:

$(x-x_m)^2+(y-y_m)^2=r^2$

$(x-7)^2+(y-8)^2=(10)^2$

$(x-7)^2+(y-8)^2=100$

this is the equation of the circle!

6 0

3 years ago

Item 7 You run for 2 hours at a speed no faster than 6.3 miles per hour.Question 1 Write an inequality that represents the possi

aalyn [17]

The formula which relates Distance, av.Speed and Time is
$Distance=Speed\cdot Time$

The maximal Distance would be covered if the average speed was 6.3 miles per hour.

In that case D=6.3 (mi/h) * 2 h = 12.6 mi

thus, if x represents the number of miles, x≤12.6 mi

Answer: x≤12.6 mi

3 0

4 years ago

P = {x:x is a multiple of 4, x ≤ 20} and Q = (x:x is a multiple of 5, x ≤ 20 }

ioda

Answer:

Hope it will help you.....

Step-by-step explanation:

my answer is

P=(4,8,12,16,20)

Q=(5,10,15,20)

5 0

3 years ago

Simplify 6s^5t x s^4t^2. 6 points on the line please help me

Ghella [55]

Answer:

6s9t3

—————

Step-by-step explanation:

Step 1 :

Simplify —

Equation at the end of step 1 :

(((6 • (s5)) • —) • s4) • t2

Step 2 :

Equation at the end of step 2 :

(((2•3s5) • —) • s4) • t2

Step 3 :

Multiplying exponential expressions :

3.1 s5 multiplied by s4 = s(5 + 4) = s9

Equation at the end of step 3 :

6s9t

———— • t2

Step 4 :

Multiplying exponential expressions :

4.1 t1 multiplied by t2 = t(1 + 2) = t3

3 0

3 years ago

Please fill in the blanks for problem #10

Ugo [173]

Answer:

1) $55

2) less than

7 0

4 years ago