Use the position function s(t) = –4.9t2 + 500, which gives the height (in meters) of an object that has fallen for t seconds from a height of 500 meters. The velocity at time t = a seconds is given by the following.
lim t->a: (s(a) - s(t)) / (a - t)
Find the velocity of the object when t = 3. (Round your answer to two decimal places.)

Answer:

40%

Step-by-step explanation:

[tex]\frac{8}{20} X 100%[/tex][tex]=40%[/tex]%

Answer:

The answer is

Step-by-step explanation:

Equation of a line is y = mx + c

where

m is the slope

c is the y intercept

To find the equation of the perpendicular line we must first find the slope of the original line

From the question the original line is

2x - 3y = 3

Write the equation in the general form above

That's

3y = 2x - 3

y = 2/3x - 1

Comparing with the general equation above

Slope = 2/3

Since the lines are perpendicular to each other the slope of the perpendicular line is the negative inverse of the original line

Slope of perpendicular line = - 3/2

So the Equation of the line using point

( 1 , 2) and slope - 3/2 is

[tex]y -2 = - \frac{3}{2} ( x - 1) \\ 2y - 4 = - 3(x - 1) \\ 2y - 4 = - 3x + 3 \\ 3x + 2y - 4 - 3 = 0[/tex]

We have the final answer as

[tex]3x + 2y = 7[/tex]

Hope this helps you

Answer: $35.75

Step-by-step explanation: 6.5x5.5=35.75

Answer:

the answer is drum rollll

Step-by-step explanation:

7.58

Step-by-step explanation:

Here hope this helps........

Answer:

[tex]f^{-1}(x)=\sqrt[5]{\frac{x+11}{6}}[/tex]

Step-by-step explanation:

So we have the function:

[tex]f(x)=6x^5-11[/tex]

To find the inverse of a function, switch f(x) and x, change f(x) to f⁻¹(x), and solve for f⁻¹(x). So:

[tex]f(x)=6x^5-11\\x=6(f^{-1}(x))^5-11[/tex]

Add 11 to both sides:

[tex]x+11=6(f^{-1}(x))^5[/tex]

Divide both sides by 6:

[tex]\frac{x+11}{6}=f^{-1}(x)^5[/tex]

Take the fifth root of each side:

[tex]f^{-1}(x)=\sqrt[5]{\frac{x+11}{6}}[/tex]

And we're done :)

Answer:

Step-by-step explanation:

[tex]f(x)=6x^5-11\\[/tex]

Let y equal the equation

[tex]y =6x^5-11\\y+11=6x^5\\\\Divide\:both\:sides\:of\:the\:equation\:by \: 6\\\frac{y+11}{6} = \frac{6x^5}{6} \\\\\frac{y+11}{6} = x^5\\ \\Quatric\:root\:both\:sides\\\sqrt[5]{\frac{y+11}{6} } = \sqrt[5]{x^5} \\\\\sqrt[5]{\frac{y+11}{6} } = x\\\\f^-^1(x) = \sqrt[5]{\frac{x+11}{6} }[/tex]

Answer:

the measure of angle DCF is 75° + 54° = 129°

Answer:

x=36

only 1 solution

Answer:

2,844 ft, 713 ft, 481 ft, 55ft.

Step-by-step explanation:

New Mexico has the highest of the lowest land elevations of the given states, at 2,844 feet. It is followed by Idaho, at 713 feet, which is followed by Nevada, at 481 feet. Arkansas has the lowest land elevation at 55 feet. The elevations in order from highest to lowest are thus 2,844 feet, 713 feet, 481 feet, and 55 feet.

Answer:

2x + 8y + 2z

Step-by-step explanation:

Answer:

Just use the 2 to multiply the numbers in the bracket.

which is

2x+8y+2z.

Answer:

m=-8

Step-by-step explanation:

im assuming the equation is: [tex]\frac{9}{8} m-\frac{1}{6} m=-4-\frac{11}{3}[/tex]

find common denominators i choose 24

9/8 = 27/24

1/6 = 4/24

11/3 = 88/24

4 = 96/24

now start solving:

(Note that because denominators are the same you can just ignore them and focus on the numerator)

simplify (27/24)m - (4/24)m to (23/24)m

simplify -(96/24) - (88/24) to -184/24

now you are left with 23/24 m = -184/24

get rid of denominators 23m=-184

Divide -184 by 23 to get m= -8

Answer:

41/24

Step-by-step explanation:

Answer:

41/24

Step-by-step explanation:

transform the expression

add the numbers

alternate form

Answer:

i think it might be D

Answer:

The confidence Interval = (0.329, 0.391)

Step-by-step explanation:

Formula for the Confidence Interval for proportion =

p ± z × √p(1 - p)/n

where

p = x/n

From the question

n = 900 people

x = 36% of 900 people

= 36/100 × 900

= 324

z = z score of 95% confidence Interval

z = 1.98

p = x/n

= 324/900

= 0.36

Confidence Interval = p ± z × √p(1 - p)/n

= 0.36 ± 1.96 × √0.36 (1 - 0.36)/900

= 0.36 ± 1.96 ×√0.36 (0.64)/900

= 0.36 ± 1.96 × √0.000256

= 0.36 ± 1.96 × 0.016

= 0.36 ± 0.03136

Confidence Interval = 0.36 ± 0.03136

= 0.36 - 0.03136

= 0.32864

Approximately to 3 decimal places = 0.329

= 0.36 + 0.03136

= 0.39136

Approximately to 3 decimal places = 0.391

Therefore, the 95% confidence interval for the population proportion of people who believe the governor broke campaign financing laws = (0.329, 0.391)

Answer:

You cant solve this question without knowing how many rows there are, and also without knowing how many seats there are per row.

Answer:

72 and 90 gcf

Step-by-step explanation:

Answer:

Answer is h(0)=1

Step-by-step explanation:

All you have to do is substitute x with 0 in the original equation.

Answer:

21

Step-by-step explanation:

3 + 3 = 6

6 + 4 = 10

10 + 5 = 15

so...

15 + 6 = 21

Answer:

(11, 12)

Step-by-step explanation:

Mid point coordinates:

Since midpoint and one endpoint given (10, 4) and (9, -4), the other endpoint:

So the other endpoint is: (11, 12)

Answer:

3 numbers

Step-by-step explanation:

Answer:

infinite rational numbers

Step-by-step explanation:

There are infinite rational numbers between 0 and 4. Now,single decimal value change like 2.34 and 2.35 can change the total value of a rational number. And there are infinite combinations of this decimal value between just two numbers.

Answer:

[tex]Y = 441[/tex]

Step-by-step explanation:

Given

M = 27 when Y = 16 and X = 9

Required

Find Y when M = 7 and X = 2

We start by getting the algebraic representation of the given statement

[tex]X^2 \alpha \frac{1}{\sqrt Y} \alpha M[/tex]

Convert the variation to an equation; we have

[tex]X^2 = \frac{KM}{\sqrt Y}[/tex]

Where K is the constant of variation;

When M = 27; Y = 16; X = 9, the expression becomes

[tex]9^2 = \frac{K * 27}{\sqrt{16}}[/tex]

This gives

[tex]81 = \frac{k * 27}{4}[/tex]

Make K the subject of formula

[tex]K = \frac{81* 4}{27}[/tex]

[tex]K = \frac{324}{27}[/tex]

[tex]K = 12[/tex]

Solving for Y when M = 7 and X = 2

Recall that [tex]X^2 = \frac{KM}{\sqrt Y}[/tex]

Substitute values for K, M and X

[tex]2^2 = \frac{12 * 7}{\sqrt{Y}}[/tex]

[tex]4 = \frac{84}{\sqrt{Y}}[/tex]

Take square of both sides

[tex]4^2 = (\frac{84}{\sqrt{Y}})^2[/tex]

[tex]16 = \frac{7056}{Y}[/tex]

Make  Y the subject of formula

[tex]Y = \frac{7056}{16}[/tex]

[tex]Y = 441[/tex]

Answer:

[tex]\displaystyle \lim_{x \to 3^-} f(x) = -1[/tex]

General Formulas and Concepts:

Calculus

Limits

Graphical Limits

Step-by-step explanation:

As we approach 3 from the left according to the graph (follow the left graphed line), we see that we approach -1.

∴  [tex]\displaystyle \lim_{x \to 3^-} f(x) = -1[/tex]

Topic: AP Calculus AB/BC (Calculus I/I + II)

Unit: Limits

Answer:

Step-by-step explanation:

(x²+4)²-11(x²+4)+24=0

put x²+4=y

y²-11y+24=0

y²-3y-8y+24=0

y(y-3)-8(y-3)=0

(y-3)(y-8)=0

y=3,8

so x²+4=3

x²=-1=i²

x=±i

or x²+4=8

x²=4

x=±2

Answer:

B) (2/3, 3 2/3)

Step-by-step explanation:

I think whoever write this problem thought the distance from A to C was 10.  It’s not.  It’s 10.77. (See below). But following what they did, the answer must be B) (2/3, 3 2/3)

First, find the distance from A to C.

4²+10²=c²

16+100=c²

116=c²

c=√116

10=10.77

The coordinates of point B on AC such that the ratio of AB to AC is 1:3 is (2/3, 3 2/3) option (B) is correct.

A segment bisector is a line, ray, line segment, or point that divides a line segment into two equal halves at its center.

It is given that:

The line segment shown in the picture is in the ratio of AB to AC is 1:3

AB : AC = 1 : 3

m : n = 1 : 3

The coordinate of point A is (2, 7)

The coordinate of point C is (-2, -3)

Let the coordinate of the point B is (x, y)

m = 1

n = 2

x1 = 2

x2 = -2

y1 = 7

y2 = -3

x = (-2+4)/3

x = 2/3

y = (-3+14)/3

y =11/3

y = 3 2/3

B = (x, y) = (2/3, 3 2/3)

Thus, the coordinates of point B on AC such that the ratio of AB to AC is 1:3 is (2/3, 3 2/3) option (B) is correct.

The options are:

A. (1/3, 2 5/6)

B. (2/3, 3 2/3)

C. (-2/3, 1 1/6)

D. (-2/3, 1/3)

Learn more about the segment bisector here:

brainly.com/question/4137998

#SPJ2

Answer:

22

Step-by-step explanation:

Marissa has $4.40 quarter and dimes

she has 5 more quarters than dimes

that means she times

$4.40×5=22

Answer:

Dimes = 9 dimes.

Quarters = 14 quarters.

Step-by-step explanation:

Q = D + 5 (1)

25×Q + 10×D = 440. (2)

From eq(1) substitute the expression for Q into equation (2)

25×(D+5) + 10D = 440

25D + 125 + 10D = 440

35D = 440 - 125

35D = 315

D = 315/35

D = 9

so,

Dimes = 9 dimes.

and,

Quarters = 9+5

= 14 quarters.

25×Q + 10×D = 440

25×14 + 10×9 = 440

350 + 90 = 440

440 = 440

Answer:

46 degree

Step-by-step explanation:

180-134=46

=>46 degrees

Answer:

(0,0) and (7,10)

Step-by-step explanation:

recall that the slope - intercept  form of a linear equation can be given as

y = mx + b

where m = slope and b = y intercept

in our case, we are given that slope, m = 10/7, hence our equation becomes

y = (10/7) x + b

since we are not given any information about the y-intercept, we can simply pick a value for b that is most convenient for us.

We pick b = 0, hence the equation simplifies to:

y = (10/7) x  ----- eq 1

we can see immediately that if x = 0, y must also = 0

proof if x = 0:

y = (10/7)(0) =0

since 0 is an integer, then (0,0) must be the first point.

we can also observe that for y to be an integer, we must get rid of the denominator 7. We can do this by multiply the right side by 7. Hence we let x = 7:

y = (10/7) x 7

y = 10

hence (7,10) is the second point.

Answer:

1,250

Step-by-step explanation:

5 to the 4 power is 50,and 5 to the 2 power is 25 and then Multiply them and that should be your answer

Answer:

4483.1

Step-by-step explanation:

Helix shape of the metal fitting parameterized :

C(t) = (cos(t), sin(t), t )

This shows that:  x = cos(t), y = sin(t), z = t

density of the metal can be represented as

f (x(t), y(t), z(t) = 2z = 2t

To calculate the mass of the fitting an integral is generated below ( attached below is remaining part of the solution )

Answer:

12.

Explanation:

Use the distance formula to determine the distance between two points.