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satela [25.4K]
3 years ago
13

Hi guys . pls help me with this​

Mathematics
1 answer:
daser333 [38]3 years ago
6 0

Step-by-step explanation:

The upstream speed is S / t₁, and the downstream speed is S / t₂.

If we say f is the speed of the fish in calm water, and r is the speed of the river, then:

f − r = S / t₁

f + r = S / t₂

If we say T is the time it takes to cross the river, then the speed perpendicular to the river is ℓ/T, the speed parallel to the river is r, and the overall speed is f.

Using Pythagorean theorem:

f² = (ℓ/T)² + r²

f² − r² = (ℓ/T)²

(f − r) (f + r) = (ℓ/T)²

(S / t₁) (S / t₂) = (ℓ/T)²

S² / (t₁ t₂) = (ℓ/T)²

(t₁ t₂) / S² = (T/ℓ)²

√(t₁ t₂) / S = T/ℓ

T = ℓ√(t₁ t₂) / S

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3 years ago
Is​ f(x) continuous at x equals 4​? Why or why​ not? A. ​No, f(x) is not continuous at x equals 4 because ModifyingBelow lim Wit
soldier1979 [14.2K]

<u>Corrected Question</u>

Is the function given by:

f(x)=\left\{\begin{array}{ccc}\frac{1}{4}x+1 &x\leq 4\\4x-11&x>4\end{array}\right ​

continuous at x=4​? Why or why​ not? Choose the correct answer below.

Answer:

(D) ​Yes, f(x) is continuous at x = 4 because Lim_{x \to 4}f(x)=f(4)

Step-by-step explanation:

Given the function:

f(x)=\left\{\begin{array}{ccc}\frac{1}{4}x+1 &x\leq 4\\4x-11&x>4\end{array}\right

A function to be continuous  at some value c in its domain if the following condition holds:

  • f(c) exists and is defined.
  • Lim_{x \to c}$ f(x) exists.
  • f(c)=Lim_{x \to c}$ f(x)

At x=4

  • f(4)=\dfrac{1}{4}*4+1=2
  • Lim_{x \to 4}f(x)=2

Therefore: Lim_{x \to 4}f(x)=f(4)=2

By the above, the function satisfies the condition for continuity.

The correct option is D.

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The sum of two numbers is 2. If one number is subtracted from the​ other, their difference is -8. Find the numbers.
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5 and -3

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3 0
2 years ago
Someone help find surface area of a right rectangular prism
Bond [772]

Answer:

51 square units

Step-by-step explanation:

First you act like each side is it’s separate rectangle.

Then you would multiply 2 and 4 to get 8, the area of one of the sides. Then you would multiply 2 and 2.5 to get 5, the area of another side. Then 2.5 times 5 to get 12.5, the last side. Now sense every side has a side the same size of itself you would take each answer and multiply it by to to get 8x2=16, 5x2=10, and 12.5x2= 25. You would add together 16, 10, and 25 to get 51 square units, the surface area.

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spin [16.1K]

Answer:

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Step-by-step explanation:

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The coordinates of a point in the fourth quadrant is of the form (x,-y)

Considering the options, the vertex must have coordinates (h,k)=(8,-6) and a=1.


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