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1 year ago

Simplify 2/3 +9-1/24

Mathematics

2 answers:

WITCHER [35]1 year ago

8 0

Answer:

$9 \frac{5}{8}$

Step-by-step explanation:

$1. \: lcd = 24 \\ 2. \: \frac{2 \times 8}{3 \times 8} + 9 \times \frac{24}{24} - \frac{1}{24} \\ 3. \: \frac{16}{24} + \frac{216}{24} - \frac{1}{24} \\ 4. \: \frac{16 + 216 - 1}{24} \\ 5. \: \frac{231}{24} \\ 6. \: \frac{77}{8} \\ 7. \: 9 \frac{5}{8}$

Natalka [10]1 year ago

7 0

2/3 + 9 - 1/24

LCM is 72

2/3 * 24/24 = 48/72
9/1 * 72/72 = 648 / 72
1/24 * 3/3 = 3/72

48/72 + 648/72 - 3/72
693/72
231/24

77/8

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The graph of f is given in the figure to the right. Let A(x)equals=Integral from 0 to x f left parenthesis t right parenthesis

Tpy6a [65]

Answer:

$A(4)=-4\pi$

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$A(12)=-4\pi +16$

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Step-by-step explanation:

we are given

$A(x)=\int\limits^x_0 f{x} \, dx$

Calculation of A(4):

we can plug x=4

$A(4)=\int\limits^4_0 f{x} \, dx$

Since, this curve is below x-axis

so, the value of integral must be negative

and it is quarter of circle

so, we can find area of quarter circle

radius =4

$A(4)=-\frac{1}{4}\times \pi \times (4)^2$

$A(4)=-4\pi$

Calculation of A(8):

we can plug x=8

$A(8)=\int\limits^8_0 f{x} \, dx$

we can break into two parts

$A(8)=\int\limits^4_0 f{x} \, dx+\int\limits^8_4 f{x} \, dx$

now, we can find area and then combine them

$A(8)=-4\pi +\frac{1}{2}\times 4\times 4$

$A(8)=-4\pi +8$

Calculation of A(12):

we can plug x=12

$A(12)=\int\limits^12_0 f{x} \, dx$

we can break into two parts

$A(12)=\int\limits^4_0 f{x} \, dx+\int\limits^8_4 f{x} \, dx+\int\limits^12_8 f{x} \, dx$

now, we can find area and then combine them

$A(12)=-4\pi +\frac{1}{2}\times 8\times 4$

$A(12)=-4\pi +16$

Calculation of A(14):

we can plug x=14

$A(14)=\int\limits^14_0 f{x} \, dx$

we can break into two parts

$A(14)=\int\limits^4_0 f{x} \, dx+\int\limits^8_4 f{x} \, dx+\int\limits^12_8 f{x} \, dx+\int\limits^14_12 f{x} \, dx$

now, we can find area and then combine them

$A(14)=-4\pi +\frac{1}{2}\times 8\times 4-\frac{1}{2}\times 1\times 2$

$A(14)=-4\pi +16-1$

$A(14)=-4\pi +15$

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