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3 years ago

Please helppppppppppppp

Mathematics

1 answer:

maxonik [38]3 years ago

7 0

"He starts by sprinting 100 yards", so the first term is a_1 = 100

The common difference is d = 5 because he's adding 5 yards per day. The "21 days" info isn't going to be used at all

So because a_1 = 100 and d = 5, this means
a_n = a_1 + d*(n-1)
a_n = 100 + 5*(n-1)
a_n = 100 + (n-1)*5

Answer is choice D

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Express the integral as a limit of Riemann sums. Do not evaluate the limit. (Use the right endpoints of each subinterval as your

Darina [25.2K]

Answer:

Given definite integral as a limit of Riemann sums is:

$\lim_{n \to \infty} \sum^{n} _{i=1}3[\frac{9}{n^{3}}i^{3}+\frac{36}{n^{2}}i^{2}+\frac{97}{2n}i+22]$

Step-by-step explanation:

Given definite integral is:

$\int\limits^7_4 {\frac{x}{2}+x^{3}} \, dx \\f(x)=\frac{x}{2}+x^{3}---(1)\\\Delta x=\frac{b-a}{n}\\\\\Delta x=\frac{7-4}{n}=\frac{3}{n}\\\\x_{i}=a+\Delta xi\\a= Lower Limit=4\\\implies x_{i}=4+\frac{3}{n}i---(2)\\\\then\\f(x_{i})=\frac{x_{i}}{2}+x_{i}^{3}$

Substituting (2) in above

$f(x_{i})=\frac{1}{2}(4+\frac{3}{n}i)+(4+\frac{3}{n}i)^{3}\\\\f(x_{i})=(2+\frac{3}{2n}i)+(64+\frac{27}{n^{3}}i^{3}+3(16)\frac{3}{n}i+3(4)\frac{9}{n^{2}}i^{2})\\\\f(x_{i})=\frac{27}{n^{3}}i^{3}+\frac{108}{n^{2}}i^{2}+\frac{3}{2n}i+\frac{144}{n}i+66\\\\f(x_{i})=\frac{27}{n^{3}}i^{3}+\frac{108}{n^{2}}i^{2}+\frac{291}{2n}i+66\\\\f(x_{i})=3[\frac{9}{n^{3}}i^{3}+\frac{36}{n^{2}}i^{2}+\frac{97}{2n}i+22]$

Riemann sum is:

$= \lim_{n \to \infty} \sum^{n} _{i=1}3[\frac{9}{n^{3}}i^{3}+\frac{36}{n^{2}}i^{2}+\frac{97}{2n}i+22]$

4 0

4 years ago

Jimmy wants to buy a scooter and the price is 50 dollars when he goes to the store the second time it is marked down 20 % whats

Maru [420]

20% of $50 is:
$50* (20/100)= $10.

$50- $10= $40

The new price is $40.

Hope this helps~

6 0

4 years ago

Maya makes trail mix by combining 1/3 cup of mixed nuts, 1/4 cup of dried fruit, 1/6 cup of chocolate morsels. What is the total

Vaselesa [24]

Answer:

The total amount of trial mix made by Maya is $\frac{9}{12}\ \ \ Or\ \frac{3}{4}$ .

Step-by-step explanation:

Given,

Amount of mixed nuts = $\frac{1}{3}\ cup$

Amount of dry fruits = $\frac{1}{4}\ cup$

Amount of chocolate morsels = $\frac{1}{6}\ cup$

We have to find out the total amount of trial mix made by Maya.

Solution,

Total amount of trial mix is the sum of amount of mixed nuts, amount of dried fruit and amount of chocolate morsels.

So we can frame the above sentence in equation form as;

Total amount of trial mix = Amount of mixed nuts + Amount of dry fruits + Amount of chocolate morsels

On putting the given values, we get;

Total amount of trial mix = $\frac{1}{3}+\frac{1}{4}+\frac{1}{6}$

Here we have to add the fractions.

For this we will make the denominator same.

Total amount of trial mix = $\frac{1\times4}{3\times4}+\frac{1\times3}{4\times3}+\frac{1\times2}{6\times2}=\frac{4}{12}+\frac{3}{12}+\frac{2}{12}=\frac{9}{12}\ \ \ Or\ \frac{3}{4}$

Hence The total amount of trial mix made by Maya is $\frac{9}{12}\ \ \ Or\ \frac{3}{4}$ .

8 0

3 years ago

10,000 more than six hundred five thousand, four hundred seventy-two

dimaraw [331]

615,472 is the answer, just write that in word form (six hundred fifteen thousand, four hundred seventy two)

5 0

3 years ago

Once you you know the length of YX, find the length of the lower base, ZX. 14 units 10 + 4 StartRoot 3 EndRoot units 18 units 10

Natalija [7]

Given:

Consider the below figure attached with this equation.

To find:

Length of side ZX.

Solution:

From the figure it is clear that, WXY is a right angled triangle.

According the 30°-60°-90° theorem, the longer leg (opposite to 60° angle) of the right-angled triangle is $\sqrt{3}$ times of shorter leg (opposite to 30° angle).