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3 years ago

Need help with this math question

Mathematics

1 answer:

dolphi86 [110]3 years ago

4 0

Answer:

x = 16

Step-by-step explanation:

From the first statement, we can say that:

Angle A is equal to angle D,

Angle B is equal to and E.

Since measure of Angle B and E are given and they are equal, we equate them and solve for x.

$B=E\\x+15=6x-65\\15+65=6x-x\\80=5x\\x=\frac{80}{5}\\x=16$

Hence x = 16

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The width of a rectangle measures (3s+t) centimeters,and it’s length measures (3s-9t) centimeters. Which expression represents t

andreyandreev [35.5K]

Answer:

12s - 16t

Step-by-step explanation:

2(3s + t) + 2(3s - 9t)

6s + 2t + 6s - 18t

12s + 2t - 18t

12s - 16t

3 0

2 years ago

Osvoldo has a goal of getting at least 30% of his grams of carbohydrates each day from whole grains. Today, he ate 220 grams of

pochemuha

Answer:

Answer: Osvoldo did not meet his goal.

Step-by-step explanation:

Total carbohydrate ate by Osvoldo = 220 g

carbohydrate from grains = 55 g

Percentage of carbohydrate of grain is

\begin{gathered}=\dfrac{\text { carbohydrate taken from grains}}{\text {Total carbohydrate}} \times 100\\\\= \dfrac{55}{220} \times 100= 25 \%\end{gathered}

Total carbohydrate

carbohydrate taken from grains

×100

220

×100=25%

Goal of getting carbohydrate from grains = at least 30%

but he ate only 25% of carbohydrate

Hence, Osvoldo did not meet his goal as he ate less carbohydrate than his goal.

8 0

3 years ago

Use the Trapezoidal Rule, the Midpoint Rule, and Simpson's Rule to approximate the given integral with the specified value of n.

Vera_Pavlovna [14]

Split up the integration interval into 4 subintervals:

$\left[0,\dfrac\pi8\right],\left[\dfrac\pi8,\dfrac\pi4\right],\left[\dfrac\pi4,\dfrac{3\pi}8\right],\left[\dfrac{3\pi}8,\dfrac\pi2\right]$

The left and right endpoints of the $i$ -th subinterval, respectively, are

$\ell_i=\dfrac{i-1}4\left(\dfrac\pi2-0\right)=\dfrac{(i-1)\pi}8$

$r_i=\dfrac i4\left(\dfrac\pi2-0\right)=\dfrac{i\pi}8$

for $1\le i\le4$ , and the respective midpoints are

$m_i=\dfrac{\ell_i+r_i}2=\dfrac{(2i-1)\pi}8$

Trapezoidal rule

We approximate the (signed) area under the curve over each subinterval by

$T_i=\dfrac{f(\ell_i)+f(r_i)}2(\ell_i-r_i)$

so that

$\displaystyle\int_0^{\pi/2}\frac3{1+\cos x}\,\mathrm dx\approx\sum_{i=1}^4T_i\approx\boxed{3.038078}$

Midpoint rule

We approximate the area for each subinterval by

$M_i=f(m_i)(\ell_i-r_i)$

so that

$\displaystyle\int_0^{\pi/2}\frac3{1+\cos x}\,\mathrm dx\approx\sum_{i=1}^4M_i\approx\boxed{2.981137}$

Simpson's rule

We first interpolate the integrand over each subinterval by a quadratic polynomial $p_i(x)$ , where

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

so that

$\displaystyle\int_0^{\pi/2}\frac3{1+\cos x}\,\mathrm dx\approx\sum_{i=1}^4\int_{\ell_i}^{r_i}p_i(x)\,\mathrm dx$

It so happens that the integral of $p_i(x)$ reduces nicely to the form you're probably more familiar with,

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

Then the integral is approximately

$\displaystyle\int_0^{\pi/2}\frac3{1+\cos x}\,\mathrm dx\approx\sum_{i=1}^4S_i\approx\boxed{3.000117}$

Compare these to the actual value of the integral, 3. I've included plots of the approximations below.

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2 years ago

Lindsey owes $5,381 on a credit card with a 24.9% interest rate compounded monthly. What is the monthly payment she should make

Digiron [165]

If you multiply .249*5381= 1339.87

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3 years ago

Find the area of the parallelogram

iogann1982 [59]

Answer:

The answer is 32.

Step-by-step explanation:

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