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1 year ago

Emily is entering a bicycle race for charity. Her mother pledges $0.40 for every 0.25 mile she bikes. If Emily

Mathematics

1 answer:

Olin [163]1 year ago

5 0

Her mother will donate $6 to Emily
Step by Step:
If emily’s mom pledges $0.40 every .25 miles u multiply .40*15

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The perimeter of the base of a regular quadrilateral prism is 60 cm, the area of one of the lateral faces is 105 cm2.

yawa3891 [41]

For a better understanding of the solution, please follow the diagram in the attached file.

A regular quadrilateral is basically a square.

So, if the base of the prism has a perimeter of 60 cm, then the length of the side of the square will be $\frac{60}{4}=15 cm$ . It is shown of the diagram.

Now, from the diagram, it is clear that the lateral face area, which is given as 105 cm^2, is the product of the side of the square, which is known, and the unknown height, let us call it h. Thus, we will get the following equation:

$15\times h=105$

$\therefore h=\frac{105}{15}=7 cm$

This is depicted on the diagram.

Now, all our required parameters are in place. Thus, let us find what has been asked.

<u>SURFACE AREA</u>

Surface Area (SA) will be the sum of the areas of the two bases (squares) and the areas of the four lateral faces.

Since the side of one square base is 15 cm, therefore, the area of one square base will be $15^2$ .

Likewise, the area of one lateral surface is actually the area of a rectangle with length 15 cm and height 7 cm. Thus, it's area will be given as: $15\times 7$ .

Thus, our equation will be:

$SA=2\times 15^2+4\times 15\times 7=870 cm^2$

Therefore, Surface Area=870 cm^2

<u>VOLUME OF THE PRISM</u>

The volume of the prism will simply be the area of the base times the height of the prism.

Thus, the volume is:

$Volume=15^2\times 7=1575 cm^3$

5 0

2 years ago

M(t)M, left parenthesis, t, right parenthesis models the distance (in millions of \text{km}kmstart text, k, m, end text) from Ma

lana [24]

Answer:

214

Step-by-step explanation:

5 0

2 years ago

An expression is given: 2 open parentheses square root of k minus 1 close parenthesis plus square root of 8. If on adding negati

neonofarm [45]

Answer:

Possible value of k is √2

Step-by-step explanation:

The information given are;

The expression, 2·(√k - 1) + √8 to which may be added -6·√2 to obtain a rational number, we therefore have;

2·(√k - 1) + √8 - 6·√2 = R

Therefore, simplifying gives;

2·√k - 2 + 2·√2 - 6·√2 = 2·√k - 2 - 4·√2 = R

2·√k - 2 - 4·√2 + 2= R + 2 = R

2·√k - 2+ 2 - 4·√2 = R

2·√k + 0 - 4·√2 = 2·√k - 4·√2 = 2·(√k - 2·√2) = R

(√k - 2·√2) = R/2 = R

Therefore, √2 is a factor of √k such that √k - 2·√2 = R

Which gives k = x·√2, where x = a rational number

When x = 1, k = √2.

Therefore, a possible value of k is √2

3 0

1 year ago

Name the value of each 2 in 222,222?

Eva8 [605]

Hundred thousand,ten thousand,hundred,ten,ones

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1 year ago

The volume inside of a sphere is V=4πr33 where r is the radius of the sphere. Your group has been asked to rearrange the formula

Semmy [17]

Answer:

Therefore,

$r=\sqrt[3]{\frac{3V}{4\pi }}$

is the required r

Step-by-step explanation:

Given:

Volume of inside of the sphere is given as

$V=\frac{4}{3} \pi r^{3}$

where r is the radius of the sphere

To Find:

r =?

Solution:

We have

$V=\frac{4}{3} \pi r^{3}$ ......Given

$3\times V=4\pi r^{3} \\\\\therefore r^{3}=\frac{3V}{4\pi } \\\\\therefore r=\sqrt[3]{\frac{3V}{4\pi }} \textrm{which is the expression for r}$

Therefore,

$r=\sqrt[3]{\frac{3V}{4\pi }}$

is the required r

5 0

1 year ago