Graph question
f(x)=3/5x-5
two points of function

The water level will be dropping at the rate of [tex]0.64 cm/sec[/tex] when the height of the water reaches [tex]3cm[/tex]

We are give a cone with dimensions as seen in the diagram in the attached image.

The volume changes at the rate

[tex]\frac{dV}{dt}=-2cm^2/sec[/tex]

the negative sign is used because the volume of water is reducing.

what we need to know is the rate the height is changing when [tex]h=3cm[/tex]. That is, we need to evaluate

[tex]\frac{dh}{dt}|_{h=3cm}[/tex]

The relationship between the volume and the height is given by

[tex]V=\frac{1}{3}\pi r^2h[/tex]

but both [tex]h[/tex] and [tex]r[/tex] are changing when [tex]V[/tex] changes. So we need to eliminate [tex]r[/tex] somehow. From the diagram, we can use the similar triangle property to accomplish this

[tex]\frac{r}{2}=\frac{h}{6}\\\\\implies r=\frac{h}{3}[/tex]

substitute into the volume formula to eliminate [tex]r[/tex]

[tex]V=\frac{\pi h^3}{27}[/tex]

differentiate both sides with respect to time, [tex]t[/tex], since both the volume and height are functions of time. They will both be differentiated implicitly

[tex]\frac{dV}{dt}=\frac{\pi h^2}{9}\frac{dh}{dt}[/tex]

to find [tex]\frac{dh}{dt}|_{h=3cm}[/tex], substitute the values for [tex]\frac{dV}{dt}[/tex] and [tex]h[/tex]

[tex]-2=\frac{\pi 3^2}{9}\frac{dh}{dt}\\\\\frac{dh}{dt}=-\frac{2}{\pi}\\\\\approx -0.64 cm/sec[/tex]

So the rate at which the height is reducing when it reaches [tex]3cm[/tex] is [tex]0.64cm/sec[/tex]

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Answer:

14.5 ≥ g(1.5)

g = The number of trips to the grocery store.

You will have 11.5 gallons left.

Answer:

Perimeter = 2(l+w) = 2*(5+8) = 26ft

Area = wl = 8*5 = 40

Step-by-step explanation:

pretty sure :)

Answer:

Second and fourth

Step-by-step explanation:

A line is in point-slope form when you write down as [tex]y-y_0=m(x-x_0)[/tex] - do not be distracted by the signs, +1 and +5 can both be written as -(-1) or -(-5) rispectively.

Answer:

option C

Step-by-step explanation:

x + 5 ≤ 13

x + 5 - 5 ≤ 13 - 5

x = ≤ 8

Answer:

x  ≤  8

Step-by-step explanation:

Move all terms not containing  x to the right side of the inequality. Then solve for x. :)

Step-by-step explanation:

Option A is the correct answer

Answer:

A is correct

Step-by-step explanation:

[tex]\frac{1}{8}[/tex] is 0.125

[tex]\frac{2}{3}[/tex] is 0.667

[tex]\frac{9}{10}[/tex] is 0.9

[tex]\frac{7}{6}[/tex] is 1.167

which from this you can see that A represents the order from smallest to largest

Answer:

61

Step-by-step explanation:

he read first 74 and need to

= 74-30

=44

Answer:

Step-by-step explanation:

When divide f(x)=ax³+bx²+cx+d by (x+3), the remainder is 4:

Then 2f(x) - 6 is:

As we see the remainder is 2

Answer:

  see attached

Step-by-step explanation:

The one that matches the triangle shown in the attachment has the given vertices.

Answer:

46,206

Step-by-step explanation:

simple math

Answer:

the answer is 46,206

Step-by-step explanation:

Good luck!!!!

The equation m(x + n) = n​ si solved for x will be given as x = n / m (1 - m).

A linear system is one in which the parameter in the equation has a degree of one. It might have one, two, or even more variables.

The equation is given below.

m(x + n) = n​

By simplifying for x, then we have

x + n = n / m

     x = n / m - n

     x = (n - mn) / m

     x = n / m (1 - m)

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Answer:

2+(-6)

Step-by-step explanation:

hope this helps

Answer:

$0.03

Step-by-step explanation:

chips: 7.84/16=0.49

pretzels: 12.48/24=0.52

0.52=0.49=0.03

The point (4,6) means it took Ziah 4 minutes to run 6 blocks.

This is because any point is of the form (x,y) where in this case

x = number of minutes

y = number of blocks

Answer:

5

Step-by-step explanation:

=========================================================

Explanation:

We have 6 slots to fill A,B,C,D,E,F

There are 6 choices for choice A, then 5 choices for slot B, 4 for C, and so on until we reach one choice for slot F. Count down by 1 each time a slot is filled.

Multiply out those values to get: 6*5*4*3*2*1 = 720

For more information, check out the concept of factorials.

---------

Another approach is to use the nPr permutation formula which is

[tex]_nP_r = \frac{n!}{(n-r)!}[/tex]

where in this case n = 6 and r = 6.

Answer:

Length=8 m,Breadth=6 m,Height=3 m

We know,

LSA=2(l+b)×h

LSA=2×14×3=84 m

2

Therefore, cost of painting = 84×60=Rs.5040.

Answer:

Given that 15coffee stops=100,000people

then: x= 1,602,000

100,000×x= 15×1,602,000

100,000x= 24,030,000

100,000x÷100,000= 24,030,000÷100,000

x= 240.3

so therefore there are 240.3 coffee stops if there are 1,602,000

Manhattan has approximately 1,602,000 people. Then the number of coffee shops will be 241.

A ratio is a collection of ordered integers a and b represented as a/b, with b never equaling zero. A proportionate expression is one in which two items are equal.

In Manhattan, there are 15 CoffeeStops per 100,000 people.

Then the number of coffee shops per person will be

⇒ 15 / 100,000

⇒ 1.5 × 10⁻⁴ coffee shops per person

Manhattan has approximately 1,602,000 people.

Then the number of coffee shops will be

⇒ 1,602,000 × 1.5 × 10⁻⁴

⇒240.3 or 241 coffee shops

Manhattan has approximately 1,602,000 people. Then the number of coffee shops will be 241.

More about the ratio and the proportion link is given below.

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Answer:

11+ 200% = 33 pounds

The percent increase is 200%

Step-by-step explanation:

The equation of the line perpendicular to y = 8 - 5z is 5x+8y=16.

8y=-5x+16

y=-5/8x+2.

To be perpendicular, the slope has to be 8/5.

The slope-intercept form is y=mx+c

Where m is the slope and c is the y-intercept.

So y=8/5x+b.

We can plug in the given coordinates to get

7=8/5*-5+b

7=-8+b

b=15.

So eqn is y=8/5x+15 or in point-slope form, y=8/5x+15

5y=8x+75

5y-8x=75

The equation of the line perpendicular to y = 8 - 5z is 5x+8y=16.

To learn more about the slope-intercept form visit:

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Answer:

It's a graph, see the image.

Step-by-step explanation:

Use the equation to find the slope. Use the slope and the point to graph the line.

Answer:

answer is in an image here

imageshare.best/image.php?id=JS9NDO

Explanation:

copy n paste in browser

not a bot btw

Answer:

it is c I think if not sorry

[tex]~\hspace{10em}\textit{function transformations} \\\\\\ \begin{array}{llll} f(x)= A( Bx+ C)^2+ D \\\\ f(x)= A\sqrt{ Bx+ C}+ D \\\\ f(x)= A(\mathbb{R})^{ Bx+ C}+ D \end{array}\qquad \qquad \begin{array}{llll} f(x)=\cfrac{1}{A(Bx+C)}+D \\\\\\ f(x)= A sin\left( B x+ C \right)+ D \end{array} \\\\[-0.35em] ~\dotfill[/tex]

[tex]\bullet \textit{ stretches or shrinks horizontally by } A\cdot B\\\\ \bullet \textit{ flips it upside-down if } A\textit{ is negative}\\ ~~~~~~\textit{reflection over the x-axis} \\\\ \bullet \textit{ flips it sideways if } B\textit{ is negative}\\ ~~~~~~\textit{reflection over the y-axis}[/tex]

[tex]\bullet \textit{ horizontal shift by }\frac{ C}{ B}\\ ~~~~~~if\ \frac{ C}{ B}\textit{ is negative, to the right}\\\\ ~~~~~~if\ \frac{ C}{ B}\textit{ is positive, to the left}\\\\ \bullet \textit{ vertical shift by } D\\ ~~~~~~if\ D\textit{ is negative, downwards}\\\\ ~~~~~~if\ D\textit{ is positive, upwards}\\\\ \bullet \textit{ period of }\frac{2\pi }{ B}[/tex]

now keeping that template for transformations above in mind, let's take a look at this one

[tex]\stackrel{\textit{original}}{f(x) = |x|}\implies f(x)=\stackrel{A}{1}|\stackrel{B}{1}x+\stackrel{C}{0}|+\stackrel{D}{0}[/tex]

now, the vertex of this type, or original that'll be the origin at (0,0), and its' graph looks like a V.

now let's take a peek at the graph, hmmm from the original V-shape it moved to the left by 2 units, with a horizontal shift of C/B = 2, we can say that +2/1 gives B = 1 and  C = +2, and moved upwards by 3 units, namely D = +3.

we can also see that it flipped upside-down over the horizontal(x-axis), namely A is negative, on all choices the only value we see for A is "4", so it must be that A = -4

let's plug all those in

[tex]\begin{cases} A=-4\\ B=1\\ C=+2\\ D=+3 \end{cases}\qquad f(x)=\stackrel{A}{-4}|\stackrel{B}{1}x+\stackrel{C}{2}|+\stackrel{D}{3}\implies f(x)=-4|x+2|+3[/tex]

Answer: C. 95 is a composite number.

Step-by-step explanation:

You can look at the ones place of each number to see if any end in 0, 2, 5, or any other digit that indicates that the number is not prime. Since 95 ends in a 5, it can be divided by 5, making it have more factors than 1 and itself. Therefore, 95 is the composite number of the list of numbers.

Answer:95

Step-by-step explanation:composite numbers are numbers that have more factors than 1 and itself, factors are numbers you can multiply to get a number. 95 is a composite number since 1,95, AND 5 are all factors of 95 making it a composite number

Answer:

see explanation

Step-by-step explanation:

Given a quadratic equation in standard form

ax² + bx + c = 0 ( a ≠ 0 )

Then for the equation to have 2 real roots , the discriminant must be greater than zero , that is

b² - 4ac > 0

x² + x + c = 0 ← is in standard form

with a = 1, b = 1, c = c , then

b² - 4ac > 0

1² - (4 × 1 × c) > 0

1 - 4c > 0 ( subtract 1 from both sides )

- 4c > - 1

Divide both sides by - 4, reversing the inequality as a result of dividing by a negative quantity.

c < [tex]\frac{1}{4}[/tex]

The answer is A.

A negative x a negative equals a positive so the square root of a negative value cannot be a negative value.