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3 years ago

R=p/4(c+k) for k, please help, thank you!

Mathematics

1 answer:

White raven [17]3 years ago

8 0

Answer:

$k=\frac{-cp+4r}{p}$

Step-by-step explanation:

$r=p/4(c+k)$

$\frac{r}{p/4} =c+k$

$\frac{r}{p/4} -c=k$

$-cp+4r=kp$

$\frac{-cp+4r}{p} =k$

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Find the total area for the regular pyramid.

hram777 [196]

Answer:

Option B

Step-by-step explanation:

Given is the hexagonal pyramid.

We know the radius of the base is same as its side.

Find the base area:

A = 3√3/2a²
A = 3√3/2*6² = 54√3

Given the height and radius, find the side of the lateral triangular faces:

$\sqrt{8^2+6^2} =\sqrt{100} =10$

Each of 6 triangles have sides 10, 10 and 6 units.

Find the area using heron's formula:

s = P/2 = (10*2 + 6)/2 = 13
s - a = s - b = 13 - 10 = 3
s - c = 13 - 6 = 7
$A = \sqrt{s(s-a)(s-b)(s-c)} =\sqrt{13*3*3*7} =3\sqrt{91}$

Total surface area:

$S = 6*3\sqrt{91}+54\sqrt{3} =18\sqrt{91}+54\sqrt{3}$

Correct choice is B

3 0

2 years ago

If the endpoints of the diameter of a circle are (−8, −6) and (−4, −14), what is the standard form equation of the circle?

kondaur [170]

Equation of the circle is $(x+6)^{2}+(y+10)^{2}=20$ .

Solution:

The endpoints of the diameter of a circle are (–8, –6) and (–4, –14).

Center of the circle = Mid point of the diameter

Mid point formula:

$$P(x, y)=\left(\frac{x_{1}+x_{2}}{2}, \frac{y_{1}+y_{2}}{2}\right)$

Here, $x_1=-8, y_1=-6, x_2=-4, y_2=-14$

$$P(x, y) =\left(\frac{-8-4}{2}, \frac{-6-14}{2}\right)$

$$P(x, y) =\left(\frac{-12}{2}, \frac{-20}{2}\right)$

$$P(x, y) =(-6, -10)$

Center of the circle = (–6, –10)

Radius is the distance between center and any endpoint of the diameter.

To calculate the radius using distance formula.

$r=\sqrt{\left(x_{2}-x_{1}\right)^{2}+\left(y_{2}-y_{1}\right)^{2}}$

Here, $x_1=-6, y_1=-10, x_2=-8, y_2=-6$

$r=\sqrt{\left(-8-(-6)\right)^{2}+\left(-6-(-10)}\right)^{2}}$

$r=\sqrt{(-8+6)^{2}+(-6+10)^{2}}$

$r=\sqrt{(-2)^{2}+(4)^{2}}$

$r=\sqrt{20}$ units

The standard form of the equation of a circle is

$(x-a)^{2}+(y-b)^{2}=r^{2}$ , where (a, b) are center and r is the radius.

Here, center = (–6, –10) and $r=\sqrt{20}$

$(x-(-6))^{2}+(y-(-10))^{2}={(\sqrt{20})} ^{2}$

$(x+6)^{2}+(y+10)^{2}=20$

Equation of the circle is $(x+6)^{2}+(y+10)^{2}=20$ .

4 0

2 years ago

What is 5r^2 = 80 It says solve each equation with the quadratic formula.

katovenus [111]

$5r^2 = 80 \ \ /:5\\ \\r^2=\frac{80}{5}\\ \\r^2=16\\ \\r^2-16=0\\ \\ r^2 - 4^2 =0 \\ \\(r-4)(r+4)=0$

$r-4=0 \ \ \vee \ \ r+4 =0 \\ \\r=4 \ \ \vee \ \ r = -4 \\ \\ \\ a^2-b^2 = (a- b)(a+b)$

5 0

3 years ago

0.175 as a percentage

Paul [167]

Answer: 17.5%

To convert from decimal to percent, just multiply the decimal value by 100. In this example we have: 0.175 × 100 = 17.5% (answer).

➥ The ease way:

1) Move the decimal point two places to the right: 0.175 → 1.75 → 17.5.

2) Add a % sign: 17.5%

Answer: 17.5%

3 0

2 years ago

Read 2 more answers

A bag contains 6 red balls and 3 blue balls. 4 balls are selected at random. find the probability of selecting 4 red balls.

geniusboy [140]

Assuming that the balls are not replaced;

$\frac{6}{9}* \frac{5}{8}* \frac{4}{7}* \frac{3}{6}$ = 5/42

(the numbers are decreasing in the denominator as you are presumably taking out the red balls. In the denominator, there is one less ball each time since you took out a red one).

Therefore, the probability of selected 4 red balls consecutively without replacement is 5/42.

Hope I Helped :)

4 0

3 years ago