Round 32.697 to the nearest hundredths

Answers

Answer 1

Answer: 32.697 is rounded to (32.7)because the hundreths place is 7 when the number is 5 and up you round up you round the tenths place up to 7

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if its length is 2x-3 feet and its width is 5x+1 feet, what is the actual length and width of the rectangle ? ( a rectangle has an area of 1281 square feet.)

Answers

( 2x - 3) X ( 5x +1) = 1281

*it's a quadratic

10x² -13x -3 = 1281 * move 1281 to the left side to equal zero

10x² -13x - 1284= 0

and solve to look for the zeros....

Do you know how to?

10+6x = 15+9x-3xis this one solution, no solution, or multiple solution if one of 2 please tell me what is x

Answers

Simplifying
10 + 6x = 15 + 9x + -3x

Combine like terms: 9x + -3x = 6x
10 + 6x = 15 + 6x

Add '-6x' to each side of the equation.
10 + 6x + -6x = 15 + 6x + -6x

Combine like terms: 6x + -6x = 0
10 + 0 = 15 + 6x + -6x
10 = 15 + 6x + -6x

Combine like terms: 6x + -6x = 0
10 = 15 + 0
10 = 15

Solving
10 = 15

Couldn't find a variable to solve for.

This equation is invalid, the left and right sides are not equal, therefore there is no solution.

Answer:

No solution

Step-by-step explanation:

Let's solve this equation to see if there are any solutions.

First we need to simplify it;

10 + 6x = 15 + 9x - 3x

Combine like terms:

6x - 9x + 3x = 15 - 10

0x = 5

0 = 5

Zero cannot be equal to 5, so there is no solution

A ladder 39 ft long leans against a vertical wall. If the lower end is being moved away from the wall at the rate of 4 ft/sec, how fast is the height of the top changing (this will be a negative rate) when the lower end is 15 feet from the wall?

Answers

Answer:

-5/3 ft/sec

Step-by-step explanation:

In this question, we are asked to calculate the rate at which the height of the top of a ladder is changing given that the lower end is being dragged at a particular rate.

Please check attachment for complete solution and step by step explanation.

Answer:

The rate of change of height, dy / dt = -1.667 ft/s

Step-by-step explanation:

Solution:-

- The length of the ladder, L = 39 ft

- The foot of the ladder is moved away from wall at a rate, dx/dt = 4ft/s

Find:-

how fast is the height of the top changing (this will be a negative rate) when the lower end is 15 feet from the wall?

Solution:-

- We will first draw a right angle triangle, with vertical height of the ladder to be"y" and distance of the foot of the ladder and the wall to be "x".

- Then express the length "L" in terms of x and y using pythagorean theorem:

L^2 = x^2 + y^2

y^2 = 39^2 - x^2

- Taking height of the ladder as the dependent variable and distance of the foot of the ladder from wall as independent variable.

- Formulate a differential equation from the given expression above in terms of "dy/dt" and "dx/dt". Perform implicit differential of the computed expression "d/dt":

2y*dy/dt = -2x*dx/dt

dy / dt = -(x/y)*dx/dt

- Where, dy / dt : The change in height of the ladder.

- The height of the ladder at x = 15 ft is:

$y = √(39^2 - x^2) = √(39^2 - 15^2) = 36$

- Then evaluate dy/dt:

dy / dt = -(15/36)*4

dy / dt = -1.667 ft/s

Evaluate the following expression: 7.0 x 10⁴ + 6.0 x 10³

A) 13 x 10⁷
B) 42 x 10⁷
C) 67 x 10³
D) 76 x 10³

Answers

$7.0 \cdot 10^4 + 6.0 \cdot 10^3=10^3\cdot (7.0 \cdot 10+6.0)= (70.0 +6.0)\cdot10^3= 76 \cdot10^3\n \n Answer: \ D) \ \ 76 \cdot 10^3$

What whole numbers lie in between the square root of 600

Answers

Answer:

$√(600)$ is between 24 and 25.

Step-by-step explanation:

The perfect squares closest to 600 are 576 and 625. Then $√(600)$ is between the square roots of 576 and 625.

Square root of 576 is 24.

$√(576) =24$

Square root of 625 is 25.

$√(625) =25\n$

An airplane flies in a straight line for 5 hours & then takes a turn 12 degrees to the right & flies 3 hours in the new direction. The plane maintained a constant speed of 550 miles per hour throughout the flight. How far is the plane from the starting point in the air at the end of this time? (could someone pls explain this lol -3-)

Answers

we have triangle with side 5*550 = 2750 and side 3*550=1650 and angle 180-12 = 168 between them
Now we use the cosine theorem to get third side

$d = √(2750 ^2+1650^2-2*1650*2750*cos(168)) = 4 377.40670603041$

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