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Ipatiy [6.2K]
3 years ago
9

Traveling with the current a certain boat went 16km/h. Against the same current it only went 6km/h. Find the current and the spe

ed of the boat if there were no current.
Mathematics
1 answer:
Aloiza [94]3 years ago
4 0

Answer:

Step-by-step explanation:

b and c are the speeds of the boat in stool water, and current, respectively.

Going with the current, the boat travels b+c=16 km/h.

Going against the current, the boat travels b-c=6 km/h

add the equations together

b+c = 16

b-c = 6

—————

2b = 22

b = 11

c = 16-b = 5

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Arturo purchased a package of 50 blank CDs. After he used “x” CDs, he had “x” less than 50 CDs remaining. How many CDs did he ha
Katarina [22]

Answer:

19 Cds left.

Step-by-step explanation:

The question said he used 31 Cds, so 50 minus 31 is 19.

4 0
2 years ago
The function y = x * ln(x + e) has two distinct x intercepts. One is at x = a and the other is at x = b. The value of a + b is
Snezhnost [94]
As points, x-intercepts take the form (x,0), so to find the intercepts we can set y=0 and solve for x.

x\ln(x+e)=0\implies\begin{cases}x=0\\\ln(x+e)=0\end{cases}

From the first equation alone, we already know that x=0 is a solution, which means one intercept is (0,0).

The second equation gives

\ln(x+e)=0\implies e^{\ln(x+e)}=e^0\implies x+e=1\implies x=1-e

so that the second intercept occurs at (1-e,0).

So if a=0 and b=1-e, we have a+b=1-e, giving C as the answer.
3 0
2 years ago
If it takes 10 seconds for 10 printers to print out 10 pages of paper, how many seconds will it take 50 printers to print out 50
Fed [463]

Lets use the formula RWT=J to solve this, where,

  • R is the rate
  • W is the number of workers/things
  • T is time
  • J is number of jobs/things

<em><u>"If it takes 10 seconds for 10 printers to print out 10 pages of paper"</u></em> - here -

W is 10 printers, T is 10 seconds,  and J is 10 pages. We can write:

R(10)(10)=10\\R(100)=10\\R=\frac{10}{100}\\R=0.1


<u><em>"how many seconds will it take 50 printers to print out 50 pages of paper"</em></u><em> - here we use R=0.1 (previously found) to figure out T.</em>

<em>RWT=J\\(0.1)(50)T=50\\5T=50\\T=\frac{50}{5}\\T=10</em>

So it will take 10 seconds for 50 printers to print 50 pages.


ANSWER: 10 seconds

4 0
3 years ago
Read 2 more answers
1 The prism-shaped roof has equilateral triangular bases. Use the model you created in question #1 to calculate the height of th
Diano4ka-milaya [45]

Answer:

Step-by-step explanation:

Step-by-step explanation:  As shown in the attached figure, the prism-shaped roof has equilateral triangular bases, one of which is ΔABC. We need to create an equation that models the height of one of the roof's triangular bases in terms of its sides. Let ii be AD.

See the figure attached herewith, ΔABC forms an equilateral triangle, in which AD is the height. So, D will be the mid-point of BC and ∠ADB = ∠ADC = 90°.

Now, in ΔADB, we have

AD^2=AB^2-BD^2

AD^2=AB^2-(1/2AB^2)^2

AD=√3/4AB^2

we can find the height of any one of the roof's triangular bases.

2.1. Check picture 1. Let the one side of the triangle be a, drop one perpendicular, CD. Then triangle ADB is a right triangle, with hypothenuse a and one side equal to 1/2a. By the Pythagorean theorem, as shown in the picture, the height is √3/2a

2. if a=25 ft, then the height is  √3/2a=√3/2*25=1.732/2*25=21.7(ft)

3. consider picture 2. Let the length of the roof be l feet.

one side of the prism (the roof) is a rectangle with dimensions a and l, so the area of one side is a*l

the lateral Area of the roof is 3a*l

the area of the equilateral surfaces is 2*(1/2*a*√3/2a)=√3/2a^2  

so the total area of the roof is  

4. The total area was the 2 triangular surfaces + the 3 equal lateral rectangular surfaces. Now instead of 3 lateral triangular surfaces, we have 2.

So the total area found previously will be decreased by al

5. so the area now is √3/2a^2 + 2al  

6. now a=25 and l=2a=50

Area= √3/2a^2+2al=√3/2*25^2+2*25*50=25^2(√3/2+4)=625*4.866

=3041.3 (ft squared)

6 0
3 years ago
The distance that a spring will stretch varies directly as the force applied to the spring. A force of 6060 pounds is needed to
Anestetic [448]

Answer:

Forced need to stretch 1414 inches = 129830.91 pounds

Step-by-step explanation:

Force ∝ Distance

F = KD where K is constant of proportionality

K = F/D = 6060/66 = 91.818182

Hence Force needed to stretch 1414 inches =

F = 6060/66 x 1414 = 129830.91 pounds

8 0
3 years ago
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