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2 years ago

4

A professional baseball team won 84 games this season. The team won 14 more games than it lost. There were no ties. How many gam

es did the team lose? How many did they play?

1 answer:

GalinKa [24]2 years ago

4 0

I’m pretty sure the answer is 154

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For the equation ae^ct=d, solve for the variable t in terms of a,c, and d. Express your answer in terms of the natural logarithm

saveliy_v [14]

We have been given an equation $ae^{ct}=d$ . We are asked to solve the equation for t.

First of all, we will divide both sides of equation by a.

$\frac{ae^{ct}}{a}=\frac{d}{a}$

$e^{ct}=\frac{d}{a}$

Now we will take natural log on both sides.

$\text{ln}(e^{ct})=\text{ln}(\frac{d}{a})$

Using natural log property $\text{ln}(a^b)=b\cdot \text{ln}(a)$ , we will get:

$ct\cdot \text{ln}(e)=\text{ln}(\frac{d}{a})$

We know that $\text{ln}(e)=1$ , so we will get:

$ct\cdot 1=\text{ln}(\frac{d}{a})$

$ct=\text{ln}(\frac{d}{a})$

Now we will divide both sides by c as:

$\frac{ct}{c}=\frac{\text{ln}(\frac{d}{a})}{c}$

$t=\frac{\text{ln}(\frac{d}{a})}{c}$

Therefore, our solution would be $t=\frac{\text{ln}(\frac{d}{a})}{c}$ .

5 0

2 years ago

Consider the following problem: A farmer with 950 ft of fencing wants to enclose a rectangular area and then divide it into four

Alina [70]

Answer:

Step-by-step explanation:

(a)

Suppose we came up with an ideology whereby we pick a value for the length including the length dividing the inside into 4 parts(5 parallel sides), then we can get the value for breath by using the following process.

Let assume the length of the rectangle is 50;

Then, the breath can be calculated as follows:

= 50 × 5 = 250 ( since the breath is divided into 5 parallel sides)

The fencing is said to be 950 ft

So, 950 - 250 = 700

Then divided by 2, we get:

= 700/2

= 350

So for the first diagram; the length = 50 and the breath = 350

The area = 50 × 350 = 17500 ft²

Now, let's go up a little bit.

If the length increase to 100;

Then 100 × 5 = 500

⇒ 950 - 500 = 450

⇒ 450/2 = 225

The area = 225 × 100 = 22500 ft²

Suppose the length increases to 150

Then 150 × 5 = 750

⇒ 950 - 750 = 200

⇒ 200/2 = 100

The area = 150 × 100 = 15000 ft²

The diagrams for each of the outline above can be seen in the image attached below.

(b) The diagram illustrating the general solution can be seen in the second image provided below.

(c) The expression for the total area A in terms of both x and y is:

Area A = x×y

(d) Recall that:

The fencing is said to be 950 ft.

And the length is divided inside into 5 parallel sides;

Then:

5x + 2y = 950 (from the illustration in the second image below)

2y = 950 - 5x

$y = \dfrac{950}{2} - \dfrac{5}{2}x$

$y = 475- \dfrac{5}{2}x$

(e)

From (c); replace the value of y in (d) into (c)

Then:

Area A = x×y

$f(x)= x\times ( 475 -\dfrac{5}{2}x)$

Open brackets

$f(x)= ( 475 x-\dfrac{5}{2}x^2)$

(f)

By differentiating what we have in (e)

$f(x)= ( 475 x-\dfrac{5}{2}x^2)$

$f'(x)= ( 475 (1)-\dfrac{5}{2}(2x))$

$f'(x)= 475 -5x$

$\implies 475 = 5x$

x = 475/5

x = 95

From (d):

$y = 475- \dfrac{5}{2}x$

$y = 475- \dfrac{5}{2}(95)$

$y =237.5$

∴

Area A = x × y

Area A = 95 × 237.5

Area A = 22562.5 ft²

5 0

2 years ago

The vertices of ΔRST are R(–1,–1), S(–1,11) and T(4,11). Which could be the side lengths of a triangle that is similar but not c

Step2247 [10]

The side lengths could be 10, 24 and 26 units.

We must first find the side lengths. We use the distance formula to do this.

For RT:
$d=\sqrt{(11--1)^2+(-1--1)^2}
\\=\sqrt{(11+1)^2+(-1+1)^2}
\\=\sqrt{12^2+0^2}=\sqrt{144}=12$

For ST:
$d=\sqrt{(11-11)^2+(4--1)^2}
\\=\sqrt{0^2+(4+1)^2}=\sqrt{5^2}=\sqrt{25}=5$

For TR:
$d=\sqrt{(11--1)^2+(4--1)^2}
\\=\sqrt{(11+1)^2+(4+1)^2}=\sqrt{12^2+5^2}=\sqrt{144+25}=\sqrt{169}=13$

Our side lengths, from least to greatest, are 5, 12 and 13.

To be similar but not congruent, the side lengths must have the same ratio between corresponding sides but not be the same length. 10, 24 and 26 are all 2x the original side lengths, so this works.

5 0

2 years ago

“Great job, you've already earned 1300 points, but there are 5 more days in this month. How many points a day do you need to rea

sergiy2304 [10]

You would have to get 56 points everyday.
If you subtract 1300 from 1580 you get 280. divide 280/5 which equals 56.
56*5=280
280+1300=1580.
56 is the amount of points you need

6 0

2 years ago

Read 2 more answers

If the egress rate for a stadium is 5,500 fans per hour and it takes fans about one-third less time for fans to exit a game as i

Marina CMI [18]

Answer:

1833 fans per hour

Step-by-step explanation:

Ingress is entering and Egress is exiting.

Since exiting time is 1/3rd less than entering time, we have 5500 people exiting, so ingessing would be 1/3rd that.

Thus,

Ingress Rate = 5500/3 = 1833.33

Rounding to whole number, we have 1833 fans per hour

4 0

2 years ago

Read 2 more answers