The surface area of a rectangular prism

What change(s) should Sylvia make to the equation to find the value of t in the above scenario?

finlep [7]

Answer:

Option (D).

Step-by-step explanation:

Initial population of the deer $P_{0}$ = 4800

Decrease in the population of the deer after every 8 years = $\frac{1}{2}\times (\text{Initial population})$

Decrease in population is an exponential process, so the expression representing population will be,

$P_{t}=P_{0}(1-r)^x$

Where $P_{t}$ is the population after 'x' slots of 8 years.

r = fraction of decrease in the population

x = $\frac{\text{Number of years}}{8}$

By substituting the values of r and x in the expression,

$P_{t}=P_{0}(1-\frac{1}{2})^{\frac{t}{8}}$

$P_{t}=4800(\frac{1}{2})^{\frac{t}{8}}$

Therefore, Sylvia should do few corrections in her expression.

(8) should be replaced by ( $\frac{1}{2}$ ) and $\frac{t}{2}$ should be replaced by $\frac{t}{8}$ .

Option D. will be the answer.

5 0

2 years ago

Can someone help me

Slav-nsk [51]

9514 1404 393

Answer:

M = 7x² +21

Step-by-step explanation:

Subtract the unwanted terms on the left from both sides.

(-7x² +6x -16) + M = 6x +5

M = 6x +5 -(-7x² +6x -16)

M = 7x² +21 . . . . simplify

5 0

2 years ago

You are part of a rowing team. Every 1, miles you stop to take a drink of water. How many times will you stop to drink water if

musickatia [10]

Answer:

10 stops I think as the 0.2 is not a full mile so you dont stop

Step-by-step explanation:

4 0

2 years ago

Read 2 more answers

The perimeter of a rectangular baking sheet is 58 inches and its area is 201.25 in.2. What are the length and width of the bakin

anzhelika [568]

Answer:

$Length=17.5\ in\\\\Width=11.5\ in$

Step-by-step explanation:

The formula for calculate the Area of a rectangle is:

$A=lw$

Where "l" is the lenght and "w" is the width.

And the formula for calculate the peimeter of a rectangle is:

$P=2l+2w$

Where "l" is the lenght and "w" is the width.

We know that the perimeter of the rectangular baking sheet is 58 inches and its area is 201.25 in². Then:

$A=201.25\ in^2\\\\P=58\ in$

<u>The steps are:</u>

1. Solve for the "l" from the formula $A=lw$ :

$A=lw\\\\l=\frac{A}{w}\\\\\l=\frac{201.25}{w}$

2. Substitute $l=\frac{201.25}{w}$ into the formula $P=2l+2w$ and solve for "w":

$58=2(\frac{201.25}{w})+2w\\\\58=\frac{402.5}{w}+2w\\\\58=\frac{402.5+2w^2}{w}\\\\58w=402.5+2w^2\\\\2w^2-58w+402.5=0$

Applying the Quadratic formula $x=\frac{-b\±\sqrt{b^2-4ac}}{2a}$ , we get:

$x=w=\frac{-(-58)\±\sqrt{(-58)^2-4(2)(402.5)}}{2(2)}\\\\w_1=17.5\\\\w_2=11.5$

3. Substitute $w_1=17.5$ into $l=\frac{201.25}{w}$ :

$l=\frac{201.25}{17.5}=11.5$

4. Substitute $w_2=11.5$ into $l=\frac{201.25}{w}$ :

$l=\frac{201.25}{11.5}=17.5$

Therefore, since the value of the lenght of a rectangle must be greater that the value of the width, we can conclude that the lenght and the width of the rectangular baking sheet are:

$l=17.5\ in\\\\w=11.5\ in$

8 0

3 years ago

A plane took off at a point that is 42 meters from the control tower. The flight path takes the plane over the control tower tha

kodGreya [7K]

Answer:

D. The plane needs to be about 27 meters higher to clear the tower.

Step-by-step explanation:

In this scenario a triangle is being formed. The base the plane's takeoff point to the tower base which is 42 meters (x).

The hypothenus is the distance travelled by the plane which is 83 meters (h)

The height of the tower is 98 Meters

We want to calculate the height of our triangle (y) so we can guage if the plane scaled the tower.

According to Pythagorean theorem

(x^2) + (y^2) = h^2

y = √ (h^2) - (x^2)

y = √ (83^2) - (42^2)

y= √(6889 - 1764)

y= 71.59 Meters

The height from the plane's position to the top of the tower will be

Height difference = 98 - 71.59 = 26.41 Meters

So the plane should go about 27 Meters higher to clear the tower

5 0

2 years ago