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3 years ago

Courtney walked from her house to the beach at a constant speed of 4 kilometers per hour, and then walked

Mathematics

1 answer:

RUDIKE [14]3 years ago

8 0

The system of equations that represents this situation are:

q + p = 2

4q + 5p = 8

Solution:

Let q be the number of hours it took Courtney to walk from her house to the beach

Let p be the number of hours it took her to walk from the beach to the park

The entire walk took 2 hours

Therefore,

q + p = 2 ------- eqn 1

The total distance Courtney walked was 8 kilometers

Total distance = 8 km

Courtney walked from her house to the beach at a constant speed of 4 kilometers per hour

Then walked from the beach to the park at a constant speed of 5 kilometers per hour

Distance is given as:

$distance = speed \times time$

From her house to the beach:

$distance = 4 \times q = 4q$

From the beach to the park:

$distance = 5 \times p = 5p$

We know that,

Total distance = 8 km

Therefore,

4q + 5p = 8 ------ eqn 2

Thus the system of equations that represents this situation are:

q + p = 2

4q + 5p = 8

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Andre45 [30]

Answer:

2 : 3

Step-by-step explanation:

Given:

The two cylinders are similar. So, their corresponding dimensions must be in proportion.

$\frac{\textrm{Radius of small cylinder}}{\textrm{Radius of larger cyclinder}}=\frac{12}{18}=\frac{2}{3}=2:3$

$\frac{\textrm{Height of small cylinder}}{\textrm{Height of larger cylinder}}=\frac{20}{30}=\frac{2}{3}=2:3$

Therefore, the similarity ratio of the smaller to the larger similar cylinders is 2 : 3.

4 0

3 years ago

WILL GIVE BRAINLIEST!

lesya [120]

Answer:

425

Step-by-step explanation:

225/24 then multiply the answer by 40

6 0

2 years ago

jamerra received a $3,00 car loan. she plans on paying off the loan in 2 years. at the end of 2 years, jamerra will have paid $4

leonid [27]

The rate of interest is 75 % per year

Solution:

Given that, Jamerra received a $3,00 car loan

she plans on paying off the loan in 2 years

Jamerra will have paid $450 in interest

Therefore, we get

Principal = $ 300

Number of years = 2

Simple Interest = $ 450

Rate of interest = ?

The simple interest is given by formula:

$simple\ Interest = \frac{p \times n \times r}{100}$

Where,

"p" is the principal and "n" is the number of years and "r" is the rate of Interest

Substituting the given values we get,

$450 = \frac{300 \times 2 \times r}{100}\\\\450 = 3 \times 2 \times r\\\\6r = 450\\\\r = \frac{450}{6}\\\\r = 75$

Thus rate of interest is 75 % per year

5 0

2 years ago

Solve the equation 2x3 + 7x2 – 10x – 24 = 0 in the real number system.

Rom4ik [11]

Answer:

x = 2

x = -4

x = -3/2

Step-by-step explanation:

We need to find the roots of the equation

2x^3 + 7x^2 – 10x – 24 = 0

We can factorize the equation into

(x-2)(x+4)(2x + 3) = 0

Roots

x = 2

x = -4

x = -3/2

The answer to your question is also attached in the images below

4 0

2 years ago

Read 2 more answers

Use Simpson's Rule with n = 10 to approximate the area of the surface obtained by rotating the curve about the x-axis. Compare y

DiKsa [7]

The area of the surface is given exactly by the integral,

$\displaystyle\pi\int_0^5\sqrt{1+(y'(x))^2}\,\mathrm dx$

We have

$y(x)=\dfrac15x^5\implies y'(x)=x^4$

so the area is

$\displaystyle\pi\int_0^5\sqrt{1+x^8}\,\mathrm dx$

We split up the domain of integration into 10 subintervals,

[0, 1/2], [1/2, 1], [1, 3/2], ..., [4, 9/2], [9/2, 5]

where the left and right endpoints for the $i$ -th subinterval are, respectively,

$\ell_i=\dfrac{5-0}{10}(i-1)=\dfrac{i-1}2$

$r_i=\dfrac{5-0}{10}i=\dfrac i2$

with midpoint

$m_i=\dfrac{\ell_i+r_i}2=\dfrac{2i-1}4$

with $1\le i\le10$ .

Over each subinterval, we interpolate $f(x)=\sqrt{1+x^8}$ with the quadratic polynomial,

$p_i(x)=f(\ell_i)\dfrac{(x-m_i)(x-r_i)}{(\ell_i-m_i)(\ell_i-r_i)}+f(m_i)\dfrac{(x-\ell_i)(x-r_i)}{(m_i-\ell_i)(m_i-r_i)}+f(r_i)\dfrac{(x-\ell_i)(x-m_i)}{(r_i-\ell_i)(r_i-m_i)}$

Then

$\displaystyle\int_0^5f(x)\,\mathrm dx\approx\sum_{i=1}^{10}\int_{\ell_i}^{r_i}p_i(x)\,\mathrm dx$

It turns out that the latter integral reduces significantly to

$\displaystyle\int_0^5f(x)\,\mathrm dx\approx\frac56\left(f(0)+4f\left(\frac{0+5}2\right)+f(5)\right)=\frac56\left(1+\sqrt{390,626}+\dfrac{\sqrt{390,881}}4\right)$

which is about 651.918, so that the area is approximately $651.918\pi\approx\boxed{2048}$ .

Compare this to actual value of the integral, which is closer to 1967.

4 0

2 years ago