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2 years ago

Need now for study guide

Mathematics

1 answer:

likoan [24]2 years ago

8 0

Answer:

17 cm.

Step-by-step explanation:

Because 12 cm + 5 cm. is 17 cm.

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Which of the following best describes the equation y= -2/7x +12

Lady bird [3.3K]

Linear, because the graph of the line is just a straight line without any curves, and the power of x is 1. If x was raised to the second, third, fourth, etc. power, it would be a nonlinear equation.

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2 years ago

PLZ HELP!!! Use limits to evaluate the integral.

Marrrta [24]

Split up the interval [0, 2] into n equally spaced subintervals:

$\left[0,\dfrac2n\right],\left[\dfrac2n,\dfrac4n\right],\left[\dfrac4n,\dfrac6n\right],\ldots,\left[\dfrac{2(n-1)}n,2\right]$

Let's use the right endpoints as our sampling points; they are given by the arithmetic sequence,

$r_i=\dfrac{2i}n$

where $1\le i\le n$ . Each interval has length $\Delta x_i=\frac{2-0}n=\frac2n$ .

At these sampling points, the function takes on values of

$f(r_i)=7{r_i}^3=7\left(\dfrac{2i}n\right)^3=\dfrac{56i^3}{n^3}$

We approximate the integral with the Riemann sum:

$\displaystyle\sum_{i=1}^nf(r_i)\Delta x_i=\frac{112}n\sum_{i=1}^ni^3$

Recall that

$\displaystyle\sum_{i=1}^ni^3=\frac{n^2(n+1)^2}4$

so that the sum reduces to

$\displaystyle\sum_{i=1}^nf(r_i)\Delta x_i=\frac{28n^2(n+1)^2}{n^4}$

Take the limit as n approaches infinity, and the Riemann sum converges to the value of the integral:

$\displaystyle\int_0^27x^3\,\mathrm dx=\lim_{n\to\infty}\frac{28n^2(n+1)^2}{n^4}=\boxed{28}$

Just to check:

$\displaystyle\int_0^27x^3\,\mathrm dx=\frac{7x^4}4\bigg|_0^2=\frac{7\cdot2^4}4=28$

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2 years ago

Let f(x) = 2x – 1 and g(x) = 3x Find g(f(x))

Gemiola [76]

6x-3

You have to put f(x) into g(x) to find the answer, so you rewrite it like this: 3(2x-1)

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2 years ago

It took Jimena 89 minutes to run a 15-kilometer race last weekend. If you know that 1 kilometer equals 0.621 mile, how many minu

Novosadov [1.4K]

The answer is 9.55 minutes

1. Turn 15 km into miles:
1 km = 0.621 mile
15 km = 15 * 0.621 mile = 9.315 miles
So, she ran 9.315 miles for 89 minutes

2. Calculate how many minutes it took Jimena to run 1 mile during the race:
She ran 9.315 miles for 89 minutes.
She ran 1 mile for x minutes.
9.315 mi : 89 min = 1 mi : x
x = 89 min * 1 mi / 9.315 mi
x = 9.55 min

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2 years ago

Find the length of the missing side in the figure below. a = _______ cm.

WITCHER [35]

Answer:

$\frac{2 \sqrt{177} }{5}$