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natka813 [3]
3 years ago
15

An aquarium contained an equal number of horseshoe crabs and sea stars. After 15 horseshoe crabs were removed and 27 sea stars w

ere removed, the ratio of horseshoe crabs to sea stars was 5:3. How many horseshoe crabs and sea stars were there at first? Solve this problem and explain your reasoning.
Mathematics
1 answer:
KATRIN_1 [288]3 years ago
5 0

Answer:

45 horseshoe crabs and 45 sea stars

Step-by-step explanation:

The aquarium initially contained x crabs and x sea stars.

"After 15 horseshoe crabs and 27 sea stars are removed the ratio of horseshoe crabs to sea stars is 5:3"

(x-15):(x-27) = 5:3

(x-15)/(x-27) = 5/3

3(x-15) = 5(x-27)

3x-45 = 5x-135

90 = 2x

x = 45

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Attached as photo. Please help
Effectus [21]

By Euler's method the <em>numerical approximate</em> solution of the <em>definite</em> integral is 4.189 648.

<h3>How to estimate a definite integral by numerical methods</h3>

In this problem we must make use of Euler's method to estimate the upper bound of a <em>definite</em> integral. Euler's method is a <em>multi-step</em> method, related to Runge-Kutta methods, used to estimate <em>integral</em> values numerically. By integral theorems of calculus we know that definite integrals are defined as follows:

∫ f(x) dx = F(b) - F(a)     (1)

The steps of Euler's method are summarized below:

  1. Define the function seen in the statement by the label f(x₀, y₀).
  2. Determine the different variables by the following formulas:

    xₙ₊₁ = xₙ + (n + 1) · Δx     (2)
    yₙ₊₁ = yₙ + Δx · f(xₙ, yₙ)     (3)
  3. Find the integral.

The table for x, f(xₙ, yₙ) and y is shown in the image attached below. By direct subtraction we find that the <em>numerical</em> approximation of the <em>definite</em> integral is:

y(4) ≈ 4.189 648 - 0

y(4) ≈ 4.189 648

By Euler's method the <em>numerical approximate</em> solution of the <em>definite</em> integral is 4.189 648.

To learn more on Euler's method: brainly.com/question/16807646

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7 0
2 years ago
Is x - 8 a factor of the function f(x) = -2x3 + 17x2 - 64? Explain.
Oduvanchick [21]

we know that

If (x-8) is a factor of the function f(x)=-2x^{3}+17x^{2}-64

then

x=8 is a root of the function f(x)

therefore

For x=8 the value of the function must be zero

Verify

Substitute the value of x=8 in the function

f(8)=-2(8)^{3}+17(8)^{2}-64

f(8)=-2(512)+17(64)-64

f(8)=-1,024+1,088-64

f(8)=-1,088+1,088

f(8)=0

therefore

<u>the answer is</u>

Yes, (x-8) is a factor of the function f(x)

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3 years ago
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They should use 5 meters of tape since u syarted off but now u will use 2 and a half of wire i mean wire
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Write the fraction 2/10 in simplest form
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2/10 in simplest form is 0.2
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Find the standard equation of the parabola that satisfies the given conditions. Also, find the length of the latus rectum of eac
lakkis [162]

Answer:

The standard parabola

                                y² = -18 x +27

Length of Latus rectum = 4 a = 18

                         

Step-by-step explanation:

<u><em>Explanation:-</em></u>

Given focus : (-3 ,0) ,directrix  : x=6

Let P(x₁ , y₁) be the point on parabola

PM perpendicular to the the directrix L

                          SP² = PM²

                (x₁ +3)²+(y₁-0)²  = (\frac{x_{1}-6 }{\sqrt{1} } )^{2}

              x₁²+6 x₁ +9 + y₁² = x₁²-12 x₁ +36

                          y₁² = -18 x₁ +36 -9

                           y₁² = -18 x₁ +27

The standard parabola

                                y² = -18 x +27

    Length of Latus rectum = 4 a = 4 (18/4) = 18

                         

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