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3 years ago

A triangle has an area of 100 square feet and a height of 5 feet

Mathematics

2 answers:

kodGreya [7K]3 years ago

6 0

500 is the answer since 100 times 5 equals 500

aleksandrvk [35]3 years ago

4 0

The length would be 40 feet... 100*2=200/5=40
hope this helps!

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Find the numbers b such that the average value of f(x) = 7 + 10x − 9x2 on the interval [0, b] is equal to 8.

barxatty [35]

Answer:

The numbers $b$ such that the average value of $f(x) = 7 +10\cdot x - 9\cdot x^{2}$ on the interval [0, b] is equal to 8 are $b_{1} \approx 1.434$ and $b_{2} \approx 0.232$ .

Step-by-step explanation:

The mean value of function within a given interval is given by the following integral:

$\bar f = \frac{1}{b-a}\cdot \int\limits^b_a {f(x)} \, dx$

If $f(x) = 7 +10\cdot x - 9\cdot x^{2}$ , $a = 0$ , $b = b$ and $\bar f = 8$ , then:

$\frac{1}{b}\cdot \int\limits^b_0 {7+10\cdot x -9\cdot x^{2}} \, dx = 8$

$\frac{7}{b}\int\limits^b_0 \, dx + \frac{10}{b} \int\limits^b_0 {x}\, dx - \frac{9}{b} \int\limits^b_0 {x^{2}}\, dx = 8$

$\left(\frac{7}{b} \right)\cdot b + \left(\frac{10}{b} \right)\cdot \left(\frac{b^{2}}{2} \right)-\left(\frac{9}{b} \right)\cdot \left(\frac{b^{3}}{3} \right) = 8$

$7 + 5\cdot b - 3\cdot b^{2} = 8$

$3\cdot b^{2}-5\cdot b +1 = 0$

The roots of this polynomial are determined by the Quadratic Formula:

$b_{1} \approx 1.434$ and $b_{2} \approx 0.232$ .

The numbers $b$ such that the average value of $f(x) = 7 +10\cdot x - 9\cdot x^{2}$ on the interval [0, b] is equal to 8 are $b_{1} \approx 1.434$ and $b_{2} \approx 0.232$ .

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4 years ago

Simplify the fraction completely.

k0ka [10]

Answer:

Step-by-step explanation:

40% means 40 parts out of 100. If we have made the numerator of the fraction 2, we have divided 40 by 20. To make this fraction equal to 40/100, we have to divide 100 by 20 as well, giving us 5.

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2 years ago

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Victor is making a recipe for smoothies. His first recipe requires 2 cups of strawberries for every 7 cups of other ingredients.

sweet-ann [11.9K]

Answer:

2/7 or 3/9

3/9 is greater so the recipe with 3 cups per 9 cup requires more

Step-by-step explanation:

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4 years ago

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