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3 years ago

HELP ME!!!

Mathematics

1 answer:

larisa [96]3 years ago

5 0

Answer:

-2, 8/3

Step-by-step explanation:

You can consider the area to be that of a trapezoid with parallel bases f(a) and f(4), and width (4-a). The area of that trapezoid is ...

A = (1/2)(f(a) +f(4))(4 -a)

= (1/2)((3a -1) +(3·4 -1))(4 -a)

= (1/2)(3a +10)(4 -a)

We want this area to be 12, so we can substitute that value for A and solve for "a".

12 = (1/2)(3a +10)(4 -a)

24 = (3a +10)(4 -a) = -3a² +2a +40

3a² -2a -16 = 0 . . . . . . subtract the right side

(3a -8)(a +2) = 0 . . . . . factor

Values of "a" that make these factors zero are ...

a = 8/3, a = -2

The values of "a" that make the area under the curve equal to 12 are -2 and 8/3.

_____

Alternate solution

The attachment shows a solution using the numerical integration function of a graphing calculator. The area under the curve of function f(x) on the interval [a, 4] is the integral of f(x) on that interval. Perhaps confusingly, we have called that area f(a). As we have seen above, the area is a quadratic function of "a". I find it convenient to use a calculator's functions to solve problems like this where possible.

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Solve 250 ÷ 5 ÷ 10 making sure to divide in the proper order.

Pavlova-9 [17]

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2 years ago

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A rectangle garden has a width that is 8 feet less than twice the length. Find the dimensions if the perimeter is 20 feet

Lana71 [14]

Width = 4ft

Length = 6ft

Explanation:

Let length = l ,

So, width = 2l-8

Perimeter of rectangle = 2x(length + width)

According to the question,

$20ft = 2X(l + 2l-8)\\20ft = 2X(3l -8)\\ 10ft = 3l-8\\18ft = 3l \\ l = 6ft$

Hence,

Width = 4ft

Length = 6ft

6 0

3 years ago

Evaluate the integral. (Assume a ≠ b. Remember to use absolute values where appropriate. Use C for the constant of integration.)

Bess [88]

Answer:

F(x)= 5*[ $\frac{x^{3} }{3}$ + (a*b)* $\frac{x^{2} }{2}$ + a*b*x + C.

Step-by-step explanation:

First step we aplicate distributive property to the function.

5*(x+a)*(x+b)= 5*[ $x^{2}$ +x*b+a*x+a*b]

5*[ $x^{2}$ +x*(b+a)+a*b]= f(x), where a, b are constant and a≠b

integrating we find ⇒∫f(x)*dx= F(x) + C, where C= integration´s constant

∫^5*[ $x^{2}$ +x*(a+b)+a*b]*dx, apply integral´s property

5*[∫ $x^{2}$ dx+∫(a*b)*x*dx + ∫a*b*dx], resolving the integrals

5*[ $\frac{x^{3} }{3}$ + (a*b)* $\frac{x^{2} }{2}$ + a*b*x

Finally we can write the function F(x)

F(x)= 5*[ $\frac{x^{3} }{3}$ + (a*b)* $\frac{x^{2} }{2}$ + a*b*x ]+ C.

4 0

3 years ago

Help help help help help

aleksklad [387]

Answer:

<h2>Toothpaste</h2>

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Bright = $0.19875 per ounce

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Bronze Smart = $0.23625 per ounce

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Step-by-step explanation:

divide the cost by the ounces and you will get the cost per ounce

Have a nice day! :-)

3 0

3 years ago

the value of n is both 5 times as much as the value of m and 36 more than the value of m. what are the values of n and m? explai

xenn [34]

We have to find the values of m and n. We know that the value of n is 5 times as much as the value of m : n = 5 m. Also n is 36 more than the value of m : n = m + 36. This is a system of equations. Of we substitute n = 5 m into the second equation: 5 m = m + 36; 5 m - m = 36; 4 m = 36; m = 36 : 4; m = 9. Finally: n = 5 * 9 ; n = 45. Answer: The values are n = 45 and m = 9.

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3 years ago