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lord [1]
2 years ago
6

What information do you need to write an equation in vertex form? Select all that

Mathematics
1 answer:
bulgar [2K]2 years ago
6 0

Answer:

an ordered pair anywhere on the parabola

the coordinates for the vertex

the formula for vertex form

Step-by-step explanation:

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Help I can’t figure this out
chubhunter [2.5K]

Answer:

3.74

Step-by-step explanation:

Use Pythagorean theorem

2.5^2=x^2=4.5^2

x=3.74

8 0
3 years ago
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BRAINLY CUP!!!! First to answer gets Brainliest and 50 points!
ArbitrLikvidat [17]
-np-4≤2(c-3)
-np-4≤2x-6
-np≤2x-2
-n≤(2x-2)/p
n≥-((2x-2)/p)
7 0
3 years ago
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At 12 noon, leslie recorded the temperature as 56 degrees f. The temperature had increased by 8 degrees f from 10am. The tempera
Marat540 [252]
Let the temperature at 10am be x, then
x + 8 = 56
x = 56 - 8 = 48 degrees F

Let y be the temperature at 8am, then
y - 2 = 48
y = 48 + 2 = 50 degrees.
4 0
3 years ago
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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.

3 0
3 years ago
A cube has an edge lengths of 5 cm. A rectangular prism has dimensions of 5 cm, 25 cm, and 1 cm. Which of the following statemen
murzikaleks [220]

The volume of cube and rectangular prism are same. Option B.

Step-by-step explanation:

Given,

The length of the edge of the cube (a) = 5 cm

The dimension of rectangular prism (l×b×h) = 5 cm×25 cm×1 cm

To find the relation between the volume of cube and rectangular prism.

Formula

The volume of a cube = a³ cube cm

The volume of rectangular prism = l×b×h cube cm

Now,

The volume of a cube = 5³ cube cm = 125 cube cm

The volume of rectangular prism = 5×25×1 cube cm = 125 cube cm

Hence,

The volume of cube and rectangular prism are same.

6 0
3 years ago
Read 2 more answers
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