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3 years ago

Find the surface area of a grapefruit with circumference of 14 cm

Mathematics

2 answers:

Lisa [10]3 years ago

8 0

The answer is 62 cm^2!

malfutka [58]3 years ago

6 0

The circumference of the grape fruit is $2\pi r=14$ , where $r$ is the radius. Solving for r,

$r=\frac{7}{\pi}$ .

The surface area of a sphere with radius r is $S=4 \pi r^2$ . Substituting numerical value of r,

$S=4 \pi r^2 =4 \pi (\frac{7}{\pi} )^2 =62.39$ .

The surface area of the grape fruit is $62.39\;cm^2$ .

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Tash conducted a survey of the students in her school.

Rasek [7]

Answer:

The total number of students in the school is 750. You can use algebraic equation to calculate the number of the students. Let x be the total number of students in the school. Hope this helps.

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3 years ago

What is the area of a rectangle that has side lengths of 3/4 yard and 5/6 yard

Ahat [919]

We are asked to find the area of the rectangle that has side lengths of 3/4 yard and 5/6 yard.

We know that area of rectangle is width times length.

To find the area of the given rectangle we will multiply both side lengths as:

$\text{Area of rectangle}=\text{Width}\times \text{Length}$

$\text{Area of rectangle}=\frac{3}{4}\text{ yard}\times\frac{5}{6}\text{ yard}$

$\text{Area of rectangle}=\frac{3}{4}\times\frac{5}{6}\text{ yard}^2$

$\text{Area of rectangle}=\frac{1}{4}\times\frac{5}{2}\text{ yard}^2$

$\text{Area of rectangle}=\frac{1\times5}{4\times2}\text{ yard}^2$

$\text{Area of rectangle}=\frac{5}{8}\text{ yard}^2$

Therefore, the area of the given rectangle would be $\frac{5}{8}$ square yards.

5 0

3 years ago

Find the remainder when x^5-x-1 is divided by (x-1)(x-2)<br>

Elina [12.6K]

Answer:

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Step-by-step explanation:

6 0

3 years ago

Express 3/10 + 45/100 as a fraction with denominator 100

AlladinOne [14]

3/10 + 45/100
= 30/100 + 45/100
= 75/100

6 0

3 years ago

A fraction becomes 4÷5 if 1 is added to both numerator and denominator. If, however, 5 is subtracted from both numerator and den

tia_tia [17]

Answer:

$\dfrac{7}{9}$

Step-by-step explanation:

$\dfrac{x+1}{y+1}=\dfrac{4}{5}\\\Rightarrow 5x-4y=-1$

$\dfrac{x-5}{y-5}=\dfrac{1}{2}\\\Rightarrow 2x-y=5$

Putting it in matrix form

$\begin{bmatrix}a_{1}&b_{1}\\a_{2}&b_{2}\end{bmatrix}{\begin{bmatrix}x\\y\end{bmatrix}=\begin{bmatrix}{c_{1}}\\{c_{2}}\end{bmatrix}\\\Rightarrow\begin{bmatrix}5 & -4\\2 & -1\end{bmatrix}\begin{bmatrix}x\\ y\end{bmatrix}=\begin{bmatrix}-1\\ 5\end{bmatrix}$

From Cramer's rule we have

$x=\dfrac{\begin{vmatrix}c_1 &b_1 \\ c_2 & b_2\end{vmatrix}}{\begin{vmatrix}a_1 &b_1 \\ a_2& b_2\end{vmatrix}}\\\Rightarrow x=\dfrac{\begin{vmatrix}-1 &-4 \\ 5 & -1\end{vmatrix}}{\begin{vmatrix}5 &-4 \\ 2& -1\end{vmatrix}}\\\Rightarrow x=\dfrac{1+20}{-5+8}\\\Rightarrow x=7$

$y=\dfrac{\begin{vmatrix}a_1 &c_1 \\ a_2 & c_1\end{vmatrix}}{\begin{vmatrix}a_1 &b_1 \\ a_2& b_2\end{vmatrix}}\\\Rightarrow y=\dfrac{\begin{vmatrix}5 &-1 \\ 2 & 5\end{vmatrix}}{\begin{vmatrix}5 &-4 \\ 2& -1 \end{vmatrix}}\\\Rightarrow y=\dfrac{25+2}{-5+8}\\\Rightarrow y=9$

Verifying the results

$\dfrac{7+1}{9+1}=\dfrac{8}{10}=\dfrac{4}{5}$

$\dfrac{7-5}{9-5}=\dfrac{2}{4}=\dfrac{1}{2}$

Hence, the fraction is $\dfrac{7}{9}$ .

6 0

3 years ago