PLEASE HELPP MEEEEE

A satellite camera takes a rectangular-shaped picture. The smallest region that can be photographed is a 4-km by 8-km rectangle. As the camera zooms out, the length l and width w of the . rectangle increase at a rate of 3 km/sec. How long does it take for the area A to be at least 5 times its original size?

Answers

Answer 1
The smallest region that can be photographed is
5*7 = 35 square km
so we want to know how long it takes to zoom out to an area of
35 * 5 = 175 square km.

Notice that the length and width increase at the same rate, 2 km/sec, and they start out with a difference of two, so when the width has increased from 5 to x, the length will have increased from 7 to x+2. At the desired coverage area, then,
x(x+2) = 175
x^2 + 2x = 175
x^2 + 2x + 1 = 176 [completing the square]
(x+1)^2 = 176
x+1 = ±4√11
x = -1 ±4√11

Since a negative value for x is meaningless here, x must be
-1 + 4√11 = about 12.27 km
and the time it took to increast to that value was
(12.27 - 5) km / (2 km/sec) = about 3.63 seconds
Answer 2
Final answer:

To find the time it takes for the area to be at least 5 times its original size, we need to solve an equation involving the rates of increase for the length and width of the rectangle. The original area is 32 km² and the rates of increase are both 3 km/sec. By substituting these values into the equation and solving for time, we can determine the answer.

Explanation:

To determine how long it takes for the area A to be at least 5 times its original size, we first need to find the original area and then solve for the time it takes for the area to reach 5 times that value.

The original area is equal to the length multiplied by the width, so it is A = 4 km * 8 km = 32 km².

Let's denote the rate at which the length and width increase as dl/dt and dw/dt respectively. We know that dl/dt = dw/dt = 3 km/sec.

To find the time it takes for the area to be 5 times its original size, we need to solve the equation 32 + 3l(t) * 3w(t) = 5 * 32, where l(t) and w(t) are the length and width at time t.

Simplifying the equation, we get 9lw - 160 = 0.

Since we're given the rates at which l and w increase, we can substitute l and w with their formulas: l(t) = 4 + 3t and w(t) = 8 + 3t.

Substituting these formulas into the equation, we get 9(4 + 3t)(8 + 3t) - 160 = 0.

Solving this equation will give us the value of t, which represents the time it takes for the area to be at least 5 times its original size.

Learn more about Finding time for an area to increase here:

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Related Questions

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the answer is 5k^2+6k+1

Which two units of measure below are longer than a meter?

centimeter

kilometer

millimeter

heptometer

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The two measurements that are longer than a meter are
Kilometer and hectometer.

Good luck!

What is the value of f(3) when f(x) = 4x + 1

Answers

Here is the equation:

[tex]f(x)=4x+1[/tex]

You need to find f(3). To do that, substitute all the x's with 3:

[tex]f(x)=4x+1 \rightarrow f(3)=4\times3 + 1[/tex]

The first thing you need to do is multiply 4 by 3. Multiply:

[tex]4 \times 3 = 12[/tex]

Here is your new equation:

[tex]f(3)=12+1[/tex]

To get your answer, you need to add 12 and 1. Add:

[tex]12+1 = 13[/tex]

That means:

[tex]\bf f(3)=13[/tex]

If you have any questions, feel free to ask in the comments! :)

F(x)= 4x+1

To find f(3) you substitute it into x.

F(3)= 4(3)+1

F(3)=12+1

F(3)=13

Find the x-coordinate where the graph of the function f(x) = e(–sinx) has a slope of 0

pie
pie/4
pie/2
none of these

Answers

[tex]y = e^{-sin(x)}[/tex]

[tex]y' = -e^{-sin(x)}(cos(x))[/tex]

[tex]0 = -e^{-sin(x)}(cos(x))[/tex]

When is cos (x) = 0?  at 90° (aka π/2)

Answer: [tex]\frac{\pi}{2}[/tex]

Answer: Hello there!

We have the function f(x) = exp(-sin(x)) and we want to see in wich point the slope is 0.

This is equivalent to see when f'(x) = 0

where f'(x) is the derivative of f(x)

Then the first step is derivate the function f(x)

if we have a function of the form g(h(x)), his derivate is:

g'(h(x))*h'(x)

In our case, g(x) = exp(x) and h(x) = - sin(x)

then f'(x) = exp(-sin(x))*(-cos(x))

Now we know that exp(-sin(x)) is never equal to 0, then we need to se when the cosine is equal to zero.

cos(90°) = 0, and 90° is equivalent to pi/2

Then f'(pi/2) = exp(-sin(pi/2))*(-cos(pi/2)) = 0

this means that the function f(x) has a slope of 0 in the point x = pi/2

There were 70 birds in a tree. One year later, the number oIn 2013, there were 70 birds in a tree. One year later, the number of birds decreased by 30%. How many birds were in the tree in 2014?F birds decreased by 30%. How many birds were in the tree in 2014?

Answers

70 times 30% is 21, 70 subract 21 is 49, there are 49 birds in year 2014.

What is the subset of 0, -3, and 8!! 

Answers

the subset of -3 and 8 is: { }, {-3}, {8}, {-3,8}, {8,-3}

math question, any help is appreciated <3

Answers

Since you already know the solution, you need to substitute every occurrence of x and y with those values: the first equation checks out, because it becomes

[tex] 3\cdot 4 - 2 \cdot 2 = 12-4 = 8 [/tex]

The second becomes

[tex] 2 \cdot 4 + 3 \cdot 2 = Q \iff 8+6 = Q \iff Q = 14 [/tex]

Julio cubes a number and then takes the cube root of the result.He ends up with 20.What number did julio start with

Answers

Cube rooting a number that is the result of cubing a number means you will end up with the original number again.

for example, if you do 3 cubed you get 27, and the cube root of 27 is 3. This means Julio started with the number 20

Julio initially started with the number 20, because cubing the number and then taking the cube root returns the original number.

If Julio cubes a number and then takes the cube root of the result, and ends up with 20, then the number he started with is also 20. This is because the cube of a number n is n
to the power of 3 (n³), and the cube root of a number is the inverse operation, which will return the original number. In symbolic form, if n is cubed to get n³, then taking the cube root of n³ will return n. Since Julio ends up with 20, the number he started with must have been 20.

you are biking at a speed of 18 miles per hour you are 3 miles behind your friends who is biking at a speed of 12 miles per hour how amount of time it catch up to your friend

Answers

you put them in fractions then cross multiple.
18/12 and 3/x so that's 36 equals 18x then you divide 36 by 18 which is 2.

Erin has $45,688 in sales. If her commission rate Is 2.9% , what is the amount of her commission?

Answers

Answer:

The amount of her commission is $1,324.952

Step-by-step explanation:

1. You have the following information given in the problem above:

- Erin has $45,688 in sales.

- Erin's commission rate is 2.9% (0.029).

2. Therefore, to solve this exercise you must multiply the commission rate by her sales, as following:

[tex](45,688)(0.029)=1,324.952[/tex] dollars


Please help me with this question

Answers

For this question, you simply take the x value from the given chart and plug it into the equation, then if the outcome makes sense based on the chart then you use another value of x and plug the second value in and if that also makes sense then you continue plugging in all the x values from the chart until all of them match. There is only one chart which contain the correct table of values.

To start of, let’s plug in the x values from graph 1, the first two values seems to be correct. However, in the third value, it does not match, therefore the first option is in correct.

Moving on to the second option, we could already determine that this table of values is incorrect because the very first x value does not match.

Moving onto the third table of values, we determine that all of the x values are in accordance with the y-values, therefore this option is correct.

Answer: Third option


to answer this question you need to solve for the y values

to solve for the y values you plug in the x on the right side of the table and into the equation: -4x+3 and see if the y value given is the correct value

so lets start with the first option:
1. plug in your x value: -4(-1)+3
2. multiply: 4+3
3. add: 7
4. does the y value match? no

second option:
1. plug in your x value: -4(-3)+3
2. multiply: 12+3
3. add: 13
4. does the y value match? no

third option:
1. plug in your x value: -4(0)+3
2. multiply: 0+3
3. add: 3
4. does the y value match? yes

fourth option:
1. plug in your x value: -4(2)+3
2. multiply: -8+3
3. add: -5
4. does the y value match? no

so your answer has to be the third option!

if you need any help or want me to check any problems please let me know:)




Select the multiplication sentence that applies the commutative property of multiplication to the example.

Example: 6 × 8 = 48
A.
8 × 6 = 48
B.
24 × 2 = 48
C.
12 × 4 = 48

Answers

we are given

6 × 8 = 48

we know that

commutative property of multiplication:

[tex]a \times b =b \times a[/tex]

now, we will verify each options

option-A:

we have

6 × 8 = 48

now, we can find it's commutative

so, we get

8 × 6 = 48

so, this is TRUE

option-B:

we have

6 × 8 = 48

now, we can find it's commutative

so, we get

8 × 6 = 48

so, this is FALSE

option-C:

we have

6 × 8 = 48

now, we can find it's commutative

so, we get

8 × 6 = 48

so, this is FALSE



GEOMETRY HELP , thank you doe helping me , the question is in the below

Answers

The answer to your problem is Substitution (A) due to y being 4.

How can u solve this by graphing ?

Answers

*(Answer)*= (2,1)

*(Information)*= There is an attachment of the graph


Write a variable expressi on for *10 divided by the sum of y and 4

Answers

Answer:

x = 10 / (y + 4)

Step-by-step explanation:


Nola hiked down a trail at a steady rate for 10 minutes. Her change in elevation was −170 feet. Then she continued to hike down for another 20 minutes at a different rate. Her change in elevation for this part of the hike was −220 feet. During which portion of the hike was her rate of change in elevation greater? Complete the explanation

Answers

Answer: First portion is greater than second portion.

Step-by-step explanation:

Time taken to hiked down a trail = 10 minutes

Change in elevation = (-) 170 feet

Speed is given by

[tex]Speed=\frac{Distance}{Time}\\\\Speed=\frac{170}{10}\\\\Speed=17\text{ feet per minute}[/tex]

Similarly,

Time taken to hiked down a trail = 20 minutes

Change in elevation = (-)220 feet

Speed is given by

[tex]Speed=\frac{Distance}{Time}[/tex]

[tex]Speed=\frac{220}{20}\\\\Speed=11\text{ feet per minutes}[/tex]

So, we can see that first portion of the hike where he hiked down a trail at a steady rate for 10 minutes and her change in elevation was (-) 170 feet, was her rate of change in elevation greater.

As 17 feet per minutes is greater than 11 feet per minutes.


Is the following equation true, false, or open?

8x + 7 = 16

[] Open, there is a variable
[] True, the expressions are the same for all the values of the variables.
[] False, the expressions are never the same.

Answers

its false or open because 17-8 = 9 and you cannot divide 8 by 9 so you will not find x

What is the answer to − 4/7 = 5/2t ( its a one step equation)

Answers

the answer to this equation would be -8/35

what is y=8/5(x-9)+16 in slope intercept form

Answers

y = 8/5( x - 9 ) + 16

8/5 = 1.6

y = 1.6x - 14.4 + 16

y = 1.6x + 1.6

The slope is therefore 1.6 and

The y-intercept is 1.6


Myra is evaluating the expression –31.7 + 4.5x, when x = 2.1.
    –31.7 + 4.5(2.1)
    –27.2(2.1)
    –57.12
What was Myra’s error?
Myra should have multiplied -31.7 and 2.1 first.
Myra should have multiplied 4.5 and 2.1 first.
Myra should have subtracted -27.2 and 2.1 first.
Myra should have added -31.7 and 2.1 first.

Answers

–31.7 + 4.5x, when x = 2.1.

-31.7 + 4.5(2.1)

-31.7 + 9.45

Myra should have multiplied 4.5 and 2.1 first.

Answer:

B.Myra should have multiplied 4.5 and 2.1 first.

Step-by-step explanation:

We are given that Myra is evaluating the expression

-31.7+4.5 x when x=21.

We have to find the error in Myra's calculation

When x=2.1

-31.7+4.5(2.1)

-31.7+9.45

=-22.25

By using DMAS rule

D=Divide

M=Multiply

A=Addition

S=Subtraction

But Myra first add  -3.7 to 4.5 then multiply

Hence, Myra should have multiplied 4.5 and 2.1 first instead of add.

Answer:B.Myra should have multiplied 4.5 and 2.1 first.

What is the inverse of the following conditional statement?
"If an angle measures ninety degrees then it is a right angle."

A. If an angle measures ninety degrees then it is a right angle.
B. If an angle does not measure ninety degrees then it is a right angle.
C. If an angle measures ninety degrees then it is not a right angle.
D. If an angle does not measure ninety degrees then it is not a right angle.

Answers

The answer is D. You essentially just put "not" in front of the true statements.

Answer:  D. If an angle does not measure ninety degrees then it is not a right angle.

Step-by-step explanation:

Hi, to obtain the inverse of a conditional statement we have to negate the hypothesis and the conclusion of the conditional statement.

In this case, the hypothesis is "If an angle measures ninety degrees"

The negative form is  "If an angle does not measure ninety degrees" .

The conclusion of the statement is, "then it is a right angle."

The negative form is  "then it is not a right angle."

In conclusion, the correct option is option  D. If an angle does not measure ninety degrees then it is not a right angle.

Feel free to ask for more if it´s necessary or if you did not understand something.

What is the value of x?



Enter your answer in the box.

x =

Answers

Keep in mind both of these angles are equal to each other meaning the equation will have a = So...

4x+7=5(x-4)

Now multiply 5 to x and 4

4x+7=5x-20

Now subtract 4x from 5x

7=1x-20

Now add  20 to both sides

27=x

So x=27

Distance between 2 airports = 1,450 miles. Average speed of airplane = 350 mph. Travel time by bus after arrival at airport = 20 minutes. Total travel time = hours.

Answers

Divide total miles between airports by the airplane's speed to find the time it took to travel by plane:


1450 miles / 350 mph = 4.142 hours = 4 hours 9 minutes

Then add the time the bus traveled:

4 hours 9 minutes  + 20 minutes = 4 hours 29 minutes

Answer:

4 hours and 29 mins

Step-by-step explanation:

One number is 4 more than another. The difference between their squares is 56. What are the numbers?

Answers

Final answer:

To solve the given problem, we set up an equation based on the information that one number is 4 more than the other and the difference between their squares is 56. After simplifying the equation, we find that the numbers in question are 5 and 9.

Explanation:

Let's denote the two numbers as n and n+4.

According to the problem, one number is 4 more than the other, and the difference between their squares is 56.

We can create an equation based on this information:

(n+4)^2 - n^2 = 56

Expanding the equation:

n^2 + 8n + 16 - n^2 = 56

The n^2 terms cancel out:

8n + 16 = 56

Subtracting 16 from both sides gives us:

8n = 40

Dividing by 8:

n = 5

The other number would be:

n+4 = 5+4

n+4 = 9

So, the two numbers are 5 and 9.

Final answer:

To find the numbers, set up an equation using variables. Solve for the variables to find the values of the numbers.

Explanation:

To solve this problem, let's assign variables to the numbers. Let the first number be x. Since the other number is 4 more than the first number, we can represent it as x + 4. The difference between their squares is 56, so we can set up the equation (x + 4)² - x² = 56.

Expanding the equation, we get x² + 8x + 16 - x² = 56. Simplifying further, we have 8x + 16 = 56. Subtracting 16 from both sides, we get 8x = 40. Dividing both sides by 8, we find x = 5.

So, the numbers are 5 and (5 + 4) = 9.

The expression below represents the number of bacteria in a petri dish after t hours. Interpret the meaning of the expression.

Answers

The answer is B) The initial number of bacteria is 57, and the growth rate is 31% per hour.


The expression shown is an exponential expression.  An exponential expression usually takes the form [tex]ab^{x}[/tex], as this one does.  A represents the initial value, in this case-the initial number of bacteria.  B represents the growth rate.  When it is an increasing growth rate, it will begin with 1, because it will have everything it had before, plus the percent increase, the decimal portion.  In this case, a=57, and b=0.31.


Hope this makes sense!

1. Find the diameter of a circle whose circumference is 18.85 m. A. 3.46 m B. 12 m C. 6 m D. 2.45 m

Answers

18.85 = 3.14d

Divide both sides by 3.14

x=6

The answer is C. 6m

For this case we have to:


The circumference or perimeter of a circle is given by:


[tex]c = \pi d\\[/tex]

where d is the diameter of the circle.


Substituting the given value of c, [tex]c = 18.85m[/tex], we have:


[tex]18.85 = \pi d\\[/tex]

[tex]d = \frac{18.85}{\pi } \\\\d = 6\\[/tex]

Therefore, the diameter of the circle is 6m.


Answer:


Option C

The equation y-2 is equal to -3 parentheses X minus one is written in point slope or slope intercept form

Answers

Answer: Point-Slope

Step-by-step explanation:

Point-Slope: y - y₁ = m(x - x₁)  ; where m is the slope and (x₁ , y₁) is the point

Slope-Intercept: y = mx + b  ; where m is the slope and b is the y-intercept

************************************************************************************************

y - 2 = -3(x - 1) is in Point-Slope form where -3 is the slope and (1, 2) is the point

Which of the following illustrates the truth value of the given statements? Sugar is sour, and lemons are sweet.

F F → F

T F → F

F T → F

T T → T


Which of the following illustrates the truth value of the given statements?


A triangle has four sides, and a rectangle has three sides.


T F → F

F T → F

T T → T

F F → F

Answers

Sugar is actually sweet and lemons are sour, both those statements are false so the answer is: F F → F


A triangle has 3 sides, a rectangle has 4, both those statements are also false, so the answer would be: F F → F

Answer:

        F F → F         F F → F

Step-by-step explanation:

1)

We are given first statement as:

           Sugar is sour, and lemons are sweet.

This is a false statement since both the statements are opposite.

Sugar is sweet while lemons are sour.

Hence, the truth value of the given statements is:

              F  F → F

2)

The statement is given as:

A triangle has four sides, and a rectangle has three sides.

It is again a false statement since a triangle is a polygon with three sides and a rectangle is a polygon with four sides.

Hence, both the statements given in it are false.

Hence, the answer is:

                 F  F → F

What is the value of 9y-9 given that -2y+6=2

Answers

First we use the quation given to solve for y.

-2y + 6 = 2 ------> Subtract 6 from both sides. (-6+2=-4)
-2y = - 4 ------> Divide both sides by -2 (-4/-2=2)
y = 2

Now you substitute the value of y or 2 into the first expression.

9(2)-9----> Multiply
18-9------->Subtract
9

Given f(x) = ax – b, what is f-1(x)?

A) x+b/a

B) 1/ax-b

C) 1/ax+b

Answers

ANSWER

The correct answer is A

[tex]f^{-1}(x)=\frac{x+b}{a}[/tex]

EXPLANATION


Given [tex]f(x)=ax-b[/tex].


We can find the inverse by taking the steps.


1. Let  [tex]y=ax-b[/tex]


2. Interchange x and y

[tex]x=ay-b[/tex]


3. Make y the subject


[tex]x+b=ay[/tex]


[tex]\frac{x+b}{a}=y[/tex]


The new function we got now is the inverse of f(x)


[tex]f^{-1}(x)=\frac{x+b}{a}[/tex]




x + b/a Replace f(x) with y, interchange x and y and solve for y.

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