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Orlov [11]
2 years ago
13

Will give brainliest

Mathematics
1 answer:
serg [7]2 years ago
7 0

Answer:

c

Step-by-step explanation:

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Helen is 8 years older than Jane. Twenty years ago Helen was three times as old as Jane. How old is each now?
Ganezh [65]
Helen is 16 and Jane is 8
3 0
2 years ago
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a box or laundry detergent is on sale for $6.50. If this price represents a 40% discount from the original price, what is the or
Usimov [2.4K]
The discount is $2.60. $6.50 + $2.60 = $9.10. $9.10 is the original price.
4 0
3 years ago
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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
3 years ago
Pablo took out an 80/20 mortgage to buy a house that cost $140,000. The first (80%)
MArishka [77]

Answer:

$780.50

Step-by-step explanation:

I will update this if I figure how it's solved as well.

5 0
2 years ago
<img src="https://tex.z-dn.net/?f=%20%5Cfrac%7B1.107%7D%7B123%7D%20%20%5Ctimes%20%20%5Cfrac%7B1.998%7D%7B333%7D%20%20%3D%20" id=
pav-90 [236]

Answer:

<h2>45 </h2>

Step-by-step explanation:

\frac{1.107}{123} \times \frac{1.998}{333} =

=   > 9 \times 6

= 45

6 0
3 years ago
Read 2 more answers
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