All categories

2 years ago

Felipe fills an aquarium to a depth of 3/5 meters in 7 1/2 minutes.

Mathematics

2 answers:

dem82 [27]2 years ago

6 0

Answer:

2/25 meters per minute.

Step-by-step explanation:

I believe this is right please correct me if I'm wrong.

gogolik [260]2 years ago

6 0

3/5 divided by 450 seconds = 1/750 * 60= 2/25 meter per minutes

You might be interested in

I dont understand how to do this precalc question

Alexeev081 [22]

Answer:

x-intercept: (-0.1, 0)
Horizontal Asymptote: y = -3
Exponential <u>growth</u>

(First answer option)

Step-by-step explanation:

<u>General form of an exponential function</u>

$y=ab^x+c$

where:

a is the initial value (y-intercept).
b is the base (growth/decay factor) in decimal form:
If b > 1 then it is an increasing function.
If 0 < b < 1 then it is a decreasing function.
y=c is the horizontal asymptote.
x is the independent variable.
y is the dependent variable.

Given <u>exponential function</u>:

$y=4(10)^x-3$

<h3><u>x-intercept</u></h3>

The x-intercept is the point at which the curve crosses the x-axis, so when y = 0. To find the x-intercept, substitute y = 0 into the given equation and solve for x:

$\begin{aligned}& \textsf{Set the function to zero}:& 4(10)^x-3 &=0\\\\& \textsf{Add 3 to both sides}:& 4(10)^x &=3\\\\& \textsf{Divide both sides by 4}:& 10^x &=\dfrac{3}{4}\\\\& \textsf{Take natural logs of both sides}:& \ln 10^x &=\ln\left(\dfrac{3}{4}\right)\\\\& \textsf{Apply the power log law}:&x \ln 10 &=\ln\left(\dfrac{3}{4}\right)\\\\& \textsf{Divide both sides by }\ln 10:&x&=\dfrac{\ln\left(\dfrac{3}{4}\right)}{\ln 10} \\\\& \textsf{Simplify}:&x&=-0.1\:\:\sf(1\:d.p.)\end{aligned}$

Therefore, the x-intercept is (-0.1, 0) to the nearest tenth.

<h3><u>Asymptote</u></h3>

An <u>asymptote</u> is a line that the curve gets infinitely close to, but never touches.

The <u>parent function</u> of an <u>exponential function</u> is:

$f(x)=b^x$

As<em> </em>x approaches -∞ the function f(x) approaches zero, and as x approaches ∞ the function f(x) approaches ∞.

Therefore, there is a horizontal asymptote at y = 0.

This means that a function in the form $f(x) = ab^x+c$ always has a horizontal asymptote at y = c.

Therefore, the horizontal asymptote of the given function is y = -3.

<h3><u>Exponential Growth and Decay</u></h3>

A graph representing exponential growth will have a curve that shows an <u>increase</u> in y as x increases.

A graph representing exponential decay will have a curve that shows a <u>decrease</u> in y as x increases.

The part of an exponential function that shows the growth/decay factor is the base (b).

If b > 1 then it is an increasing function.
If 0 < b < 1 then it is a decreasing function.

The base of the given function is 10 and so this confirms that the function is increasing since 10 > 1.

Learn more about exponential functions here:

brainly.com/question/27466089

brainly.com/question/27955470

6 0

2 years ago

Define two terms, each containing the variables x and y, with exponents on each. (For example: 10x3y−5.) Find the quotient of th

Serjik [45]

Answer:Two such terms are 7x^3*y^9 and -3x*y^5

Their quotient is

7x^3*y^9

--------------

-3x*y^5

This can be simplified as follows:

The numerical coefficients become -7/3.

x^3/x = x^3*x^1 = x^(3 - 1) = x^2 (we subtract the exponent of x in the denominator from the exponent of x in the numerator).

Next, y^9*y^5 = y^4.

The quotient in final reduced form is then (-7/3)x^2*y^4

7 0

3 years ago

Need help with this homework question. Click on the picture for full screen.

larisa [96]

Check this attachment

5 0

3 years ago

It takes 0.250.25 cup of sugar to make a batch of chocolate chip cookies. I have 5.505.50 cups of sugar. How many batches of coo

RSB [31]

Answer:

a) 22 batches

c) 7.3 batches

Step-by-step explanation:

a) It takes 0.25 cup of sugar to make a batch of chocolate chip cookies. I have 5.50 cups of sugar. How many batches of cookies can I make?

0.25 cup = 1 batch

5.5 cup = x

Cross Multiply

0.25 cup × x = 5.5 cup × 1 batch

x = 5.5 cup × 1 batch/0.25 cup

x = 22

I can make 22 batches of chocolate chip cookies. You may use the scratchpad to show your work.

(b) Lemon Cookies It takes 0.75 cups of sugar to make a batch of lemon cookies. I have 5.5 cups of sugar. How many batches can I make?

0.75 cup = 1 batch

5.5 cup = x

Cross Multiply

0.75 cup × x = 5.5 cup × 1 batch

x = 5.5 cup × 1 batch/0.75 cup

x = 7.3 batches

I can make 7.3 batches of lemon cookies. You may use the scratchpad to show your work.

4 0

3 years ago

WHOEVER IS CORRECT GETS 55 POINTS!!! PLZ HELP FASTTTTT!!!!!!!martin throws a ball straight up in the air. the equation h(t)=-16t

weqwewe [10]

Given that Martin throws a ball straight up in the air.

The equation $h(t)=-16t^2+40t+5$ gives the height of the ball, in feet, t seconds after martin releases it.

We need to determine the time that it takes the ball to hit the ground.

<u>Time taken:</u>

To determine the time 't', let us equate h(t) = 0 in the equation $h(t)=-16t^2+40t+5$

Thus, we have;

$0=-16t^2+40t+5$

Switch sides, we get;

$-16 t^{2}+40 t+5=0$

Now, we shall solve the equation using the quadratic formula.

Thus, we have;

$t=\frac{-40 \pm \sqrt{40^{2}-4(-16) 5}}{2(-16)}$

Solving, we get,

$t=\frac{-40 \pm \sqrt{1600+320}}{-32}$

$t=\frac{-40 \pm \sqrt{1920}}{-32}$

$t=\frac{-40 \pm 8\sqrt{30}}{-32}$

$t=\frac{8(-5 \pm \sqrt{30})}{-32}$

Cancelling the common terms, we get,

$t=\frac{-5 \pm \sqrt{30}}{-4}$

Thus, the roots of the equation $t=\frac{-5 + \sqrt{30}}{-4}$ and $t=\frac{-5 - \sqrt{30}}{-4}$

Simplifying the roots, we get,

$t=\frac{-5 +5.477}{-4}$ and $t=\frac{-5 -5.477}{-4}$

$t=-0.119$ and $t=2.619$

Since, t cannot take negative values, then $t=2.619$

Hence, It takes 2.6 seconds for the ball to hit the ground.

8 0

4 years ago