A baseball diamond is a square with sides 90 ft long. A batter is at bat, with runners at first and second base. At the moment the ball is hit, the runner at first base runs to second base at 25 ft/s. Simultaneously, the runner on second base runs to third base at 15 ft/s. How fast is the distance between these two runners changing 2 s after the ball is hit?

Use the quotient rule:

[tex]\dfrac{\mathrm dy}{\mathrm dx}=\dfrac{(x^3-5)\frac{\mathrm d(x^2+4x)}{\mathrm dx}-(x^2+4x)\frac{\mathrm d(x^3-5)}{\mathrm dx}}{(x^3-5)^2}[/tex]

[tex]\dfrac{\mathrm dy}{\mathrm dx}=\dfrac{(2x+4)(x^3-5)-3x^2(x^2-4x)}{(x^3-5)^2}[/tex]

[tex]\dfrac{\mathrm dy}{\mathrm dx}=-\dfrac{x^4 - 16 x^3 + 10 x + 20}{(x^3-5)^2}[/tex]

Step-by-step explanation:

7 is the coeffiecient

3 is the constant

Answer:

3 + 3.75x=18

subtract 3 from both sides

3.75x=15

divide by 3.75 on both sides

x=4

Step-by-step explanation:

Answer:

Written in Python

print("Enter three sides of a triangle: ")

length = []

for i in range(0,3):

    inp = int(input(""))

    length.append(inp)    

length.sort()

if length[1]+length[2] > length[0] and length[0] + length[2] > length[1] and length[0] + length[1] > length[2]:

    print("Triangle")

    if length[2]**2 == length[0]**2 + length[1] **2:

         print("Right Angled")

    else:

         print("Not Right Angled")

else:

    print("Not Triangle")

Step-by-step explanation:

This line prompts user for sides of triangle

print("Enter three sides of a triangle: ")

This line declares an empty list

length = []

The following iteration gets user input

for i in range(0,3):

    inp = int(input(""))

    length.append(inp)    

This line sorts user input

length.sort()

The following if condition checks if user input is triangle

if length[1]+length[2] > length[0] and length[0] + length[2] > length[1] and length[0] + length[1] > length[2]:

The following is executed is the if condition is true

    print("Triangle")

The following if condition checks if user input forms a right angled triangle

    if length[2]**2 == length[0]**2 + length[1] **2:

         print("Right Angled")

    else:

         print("Not Right Angled")

This is executed if user input is not a triangle

else:

    print("Not Triangle")

Answer:

7.2

Step-by-step explanation:

Answer:

the answer is 0.4 The reason is because 0.4 x8=0.32

Step-by-step explanation:

Answer:

2 1/4

Step-by-step explanation:

3/4 ÷ 1/3 = ?

(to divide fractions faster you flip the second fraction so:)

3/4 x 3/1 = 2 1/4

Answer:

30.25

Step-by-step explanation:

121 divided by 4 is 30.25

Answer:

37

Step-by-step explanation:

just add the two numbers like they are not negative.

Answer:

Point 1: (6.4, 117)

Point 2: (6.6, 120)

Step-by-step explanation:

Answer:

Point 1: (6.4, 117)

Point 2: (6.6, 120)

Step-by-step explanation:

Answer:

√23 = a

Step-by-step explanation:

/ab/²= /ac/²+/bc/² (Pythagoras theorem)

12² = a² +11²

144 = a² + 121

144 - 121 = a²

23 = a²

√23 = a

Answer:

C. no solution

Step-by-step explanation:

3x – 4 = 3x + 4

3x-3x=4+4

0=8

which is not possible.

So, it has no solutions.

Answer:

got u homie

Step-by-step explanation:

Answer:

l +c _> 12

Step-by-step explanation:

[tex]\mathfrak{\huge{\pink{\underline{\underline{AnSwEr:-}}}}}[/tex]

Actually Welcome to the Concept of the Statistics,

If we see here, The Andrew is working for 20 hours and his pay for 20hours is, $175

so for 1 hour, he gets = 175÷20 => $8.75 per hour

, so now after 1 year, his pay increases by $1.05 per hour, then we have to add this new amount of pay in his old amount, so that we can show that his pay is actually INCREASED, so the new pay is given as,

$8.75 + $1.05 (per hour)= $9.80

so now his total pay is given as,

E= 9.80h

Option D.) is correct

Answer:

Yes it appropriate to use the normal approximation to find the probability that more than 43% of the people in the sample have high blood pressure

Step-by-step explanation:

From the question we are told that

The population proportion is  p=0.4

  The sample size is  n =  39

  The sample proportion is  [tex]\^ p = 0.43[/tex]

Generally for normal approximation to be used

       [tex]np > 10[/tex]

so np  =  39 * 0.4 =  15.6 > 10

   and [tex]n(1- p) > 10[/tex]

so   n(1-p ) = 39(1-0.4) = 23.4 >10

Given that the both condition is meet it mean that  it appropriate to use the normal approximation to find the probability that more than 43% of the people in the sample have high blood pressure

The answer fam is..... 14

Answer:

A. Response Variable is POUND SOLD Explanatory variable is PRICE PER POUND

B. ii. -4.681

Step-by-step explanation:

A. Based on the statistics that was shown in the given information above the:

Response Variable is POUND SOLD Explanatory variable is PRICE PER POUND

B. Calculation to determine slope of the estimated regression line that relates the response variable to the predictor variable

Using this formula

Slope =r*Sy/Sx

Let plug in the formula

Slope=-0.927*18.33/3.63

Slope=-16.99191/3.63

Slope=-4.681

Therefore , the slope of the estimated regression line that relates the response variable to the predictor variable is: -4.681

Answer: 0=0

Step-by-step explanation: Simplify

Answer:

It's the first one

Its A

PLEASE MARK ME AS THE BRAINLIEST!!!!!!!!!!!!!!!!!!!!

Answer:

B slope = 1 and y intercept is 3

Step-by-step explanation:

The y intercept is where the line crosses the y axis (x is zero).

The slope can be figured by how far the line rises and runs to the next intersection of lines. In this case it goes up 1 and to the right 1. The slope would be 1/1 or 1

Answer:

Slope =1 ; Y-intercept=3

Step-by-step explanation:

The y intercept would be the point on the vertical line that touches the graph which in this case is three.

then to get to the next point that's on the line would have to move over 1 once to the right and one time up. so the slope is 1 over 1 which would equal 1.

Answer: C

Step-by-step explanation:

I just took the quiz and I got it right

Statement describes how to geometrically divide a complex number z by a second complex number w is Option (C) Scale z by the reciprocal of the modulus of w, then rotate clockwise by the argument of w.

In mathematics, a complex number is an element of a number system that contains the real numbers and a specific element denoted i, called the imaginary unit

Modulus of the complex number is the distance of the point on the argand plane representing the complex number z from the origin

Given,

Complex number z divides by a second complex number w

To divide a complex number a complex number then multiply the conjugate with the numerator and the denominator of the complex fraction

From the given statements Scale of z by the reciprocal of the modulus of w, then rotate clockwise by the argument of w

Hence, Statement describes how to geometrically divide a complex number z by a second complex number w is Option (C) Scale z by the reciprocal of the modulus of w, then rotate clockwise by the argument of w.

Learn more about Complex number and Modulus of a complex number here

https://brainly.com/question/19554199

#SPJ2

Answer:

-4√10 / 5 or -8√10 / 5

Step-by-step explanation:

See attachment for calculation

Answer:

28

Step-by-step explanation:

28/1 = 28

Answer:

Step-by-step explanation:

1)

A. 2 meters to centimeters

1 m = 100 cm

[tex]2 m = 2 \times 100 \\2 m = 200 cm = 2 \times 10^2[/tex]

B)108 centimeters to meters

100 cm =1 m

[tex]1 cm = \frac{1}{100} m \\108 cm = \frac{108}{100}=108 \times 10^{-2} m[/tex]

C)2.49 meters to centimeters

1 m = 100 cm

[tex]2.49 m = 2.49 \times 100 = \frac{249}{100} \times 100 = 249 cm[/tex]

D)50 centimeters to meters

100 cm = 1m

[tex]1 cm = \frac{1}{100} m \\50 cm = \frac{50}{100}= 5 \times 10^{-1} m[/tex]

E)6.3 meters to centimeters

1 m = 100 cm

[tex]6.3 m = 6.3 \times 100=\frac{63}{10} \times 100 = 630 cm[/tex]

F)7 centimeters to meters

100 cm = 1 m

[tex]1 cm = \frac{1}{100} m\\\\7 cm = \frac{7}{100} = 7 \times 10^{-2} m[/tex]

2)

a)4 meters to millimeters

1 m = 1000 mm

[tex]4 m = 4000 = 4 \times 10^3 mm[/tex]

b)1.7 meters to millimeters

1 m = 1000 mm

[tex]1.7 m = 1.7 \times 1000= \frac{17}{10} \times 1000=17 \times 10^2 mm[/tex]

Given:

You are given $893 in one, five, and ten dollar bills.

There are 165 bills.

There are twice as many five dollar bills as there are ones and tens combined.

To find:

How many bills of each type are there?

Solution:

Consider the number of bills of one dollars, five dollars and ten dollars are x, y and z respectively.

According to the question,

Number of bills : [tex]x+y+z=165[/tex]         ...(1)

Total amount : [tex]1x+5y+10z=893[/tex]         ...(2)

Condition : [tex]y=2(x+z)[/tex]     ...(3)

Equation (3) can be written as

[tex]\dfrac{y}{2}=x+z[/tex]       ...(4)

Substituting [tex]x+z=\dfrac{y}{2}[/tex] in (1), we get

[tex]\dfrac{y}{2}+y=165[/tex]

[tex]\dfrac{3y}{2}=165[/tex]

[tex]3y=330[/tex]

[tex]y=110[/tex]

Substituting y=110 in (4), we get

[tex]x+z=\dfrac{165}{2}[/tex]

[tex]x+z=55[/tex]

[tex]x=55-z[/tex]       ...(5)

Substituting y=110 and x=55-z in (2), we get

[tex](55-z)+5(110)+10z=893[/tex]

[tex]55-z+550+10z=893[/tex]

[tex]9z+605=893[/tex]

[tex]9z=893-605[/tex]

[tex]9z=288[/tex]

Dividing both sides by 9, we get

[tex]z=32[/tex]

Substituting z=32 in (5), we get

[tex]x=55-32[/tex]

[tex]x=23[/tex]

Therefore,

One dollar bills = 23

Five dollars bills= 110

Ten dollars bills = 32

Answer:

yes

Step-by-step explanation:

Answer:

yes? That's right. ummmm lol