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Kryger [21]
3 years ago
9

Can you help me solve this

Mathematics
2 answers:
irina [24]3 years ago
5 0
2 times the length of the midsegment equals the length of the base. That being said, your equation will be 2(x+21)=x+32.

First, use the distributive property on 2(x+21). You are left with 2x+42=x+32.
Subtract x from both sides. You are left with x+42=32.

Finally, subtract 42 from both sides of the equation. You are left with your answer: x=-10.

Check your work: -10+21=11 and -10+32=22
11 is half of 22.
fenix001 [56]3 years ago
4 0
The base is two times the midsegment.
2(x+21)=x+32
2x+42=x+32
Subtract x from both sides
x+ 42=32
Subtract 42 from both sides
x= -10
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Use Simpson's Rule with n = 10 to estimate the arc length of the curve. Compare your answer with the value of the integral produ
SOVA2 [1]

y=\ln(6+x^3)\implies y'=\dfrac{3x^2}{6+x^3}

The arc length of the curve is

\displaystyle\int_0^5\sqrt{1+\frac{9x^4}{(6+x^3)^2}}\,\mathrm dx

which has a value of about 5.99086.

Let f(x)=\sqrt{1+\frac{9x^4}{(6+x^3)^2}}. Split up the interval of integration into 10 subintervals,

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

The left and right endpoints are given respectively by the sequences,

\ell_i=\dfrac{i-1}2

r_i=\dfrac i2

with 1\le i\le10.

These subintervals have midpoints given by

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

Over each subinterval, we approximate f(x) 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)}

so that the integral we want to find can be estimated as

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

It turns out that

\displaystyle\int_{\ell_i}^{r_i}p_i(x)\,\mathrm dx=\frac{f(\ell_i)+4f(m_i)+f(r_i)}6

so that the arc length is approximately

\displaystyle\sum_{i=1}^{10}\frac{f(\ell_i)+4f(m_i)+f(r_i)}6\approx5.99086

5 0
3 years ago
Vanessa wants to buy a new iPod that costs $239.25. She earns $7.25 per hour at work.
kherson [118]

Answer:

She would have to work for 33 hours.

Step-by-step explanation:

239.25/7.25=33. Since we are going with hours, this would be 33.

5 0
3 years ago
Solve the equation-3y = 21 using inverse operations. What is the inverse operation step? What is the solution?
GaryK [48]

Answer:

-7

Step-by-step explanation:

You divide -3 on both sides to get the variable by itself, so -3 divided by 21 is -7

5 0
3 years ago
Read 2 more answers
5x = - 25x<br> Solve for x
Sunny_sXe [5.5K]
Subtract 5x from both sides
0=-30x

Divide both sides by -30
0=x

Final answer: x=0

Hope this helps!
8 0
2 years ago
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A youth group earns $600 for charity and decides to put it in a bank. Calculate the amount of money the group will have for each
igomit [66]

Based on the types of compounding and the interest rates, the following are true:

  • Part A - The group will have $750
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When using simple interest, the amount the group will have is:

<em>= Amount x ( 1 + rate x number of years )</em>

= 600 x ( 1 + 5% x 5)

= $750

When using compound interest, the group will have:

<em>= Amount x ( 1 + rate) ^ Number of years</em>

= 600 x ( 1 + 4%)⁶

= $759.19

In conclusion, compound interest yields more.

<em>Find out more about </em><em>compound interest </em><em>at brainly.com/question/25263325. </em>

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2 years ago
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