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Sergeeva-Olga [200]
3 years ago
6

Dale drove to the mountains last weekend. There was heavy traffic on the way there, and the trip took hours. When Dale drove hom

e, there was no traffic and the trip only took hours. If his average rate was miles per hour faster on the trip home, how far away does Dale live from the mountains?
Mathematics
1 answer:
IrinaK [193]3 years ago
4 0

Dale drove to the mountains last weekend. there was heavy traffic on the way there, and the trip took 7 hours. when dale drove home, there was no traffic and the trip only took 5 hours. if his average rate was 18 miles per hour faster on the trip home, how far away does dale live from the mountains? do not do any rounding.

Answer:

Dale live 315 miles from the mountains

Step-by-step explanation:

Let y be the speed  of Dale to the mountains

Time taken by Dale to the mountains=7 hrs

Therefore distance covered by dale to the mountain = speed × time = 7y ......eqn 1

Time taken by Dale back home = 5hours

Since it speed increased by 18 miles per hour back home it speed = y+18

So distance traveled home =speed × time = (y+18)5 ...... eqn 2

Since distance cover is same in both the eqn 1 and eqn 2.

Eqn 1 = eqn 2

7y = (y+18)5

7y = 5y + 90

7y - 5y = 90 (collection like terms)

2y = 90

Y = 45

Substitute for y in eqn 1 to get distance away from mountain

= 7y eqn 1

= 7×45

= 315 miles.

∴ Dale leave 315 miles from the mountains

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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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1 year ago
OH GOD PLEASE HELP ME MY BRAIN HURTS!
alukav5142 [94]
Your answer should be 71. :)
8 0
2 years ago
Solve using long division.
Mkey [24]

Answer:

Quotient is 3x-5 and remainder is 0.

Step-by-step explanation:

Given:

Dividend = 3x^2+7x-20

Divisor = x+4

The long division is shown in the attachment.

Step 1: we need to divide 3x^2+7x-20 with x+4 we first multiply x+4 with 3x we get the remainder as -5x-20

Quotient as 3x.

Step 2: Now the dividend is -5x-20 and divisor x+4 now we will multiply x+4 with -5 we get the remainder as 0 and Quotient as 3x-5

Hence Quotient is 3x-5 and remainder is 0.

6 0
3 years ago
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