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Sunny_sXe [5.5K]
3 years ago
14

A regular pentagon is created using the bases of five congruent isosceles triangles, joined at a common vertex. The total number

of degrees in the center is 360°. If all five vertex angles meeting at the center are congruent, what is the measure of a base angle of one of the triangles? 54° 72° 108° 144°

Mathematics
2 answers:
KonstantinChe [14]3 years ago
6 0

Answer:

54\°

Step-by-step explanation:

we know that

An isosceles triangle has two equal sides and two equal angles

The two equal angles are the base angles and the third angle is the vertex angle

In this problem

The vertex angle of one of the isosceles triangle is equal to

360\°/5=72\°

The sum of the internal angles of the triangle is equal to 180\°

Let

x------> the measure of a base angle of one of the isosceles triangle

so

2x+72\°=180\°

solve for x

2x=180\°-72\°

2x=108\°

x=54\°

Gala2k [10]3 years ago
4 0
It's 54 degrees.

The internet is a wonderful friend. Type in "Pentagon split into triangles" on google images and you will find a diagram that finds it.
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ruslelena [56]

For the first one it is 5 x10^{8}  

and for the second one it is 0.0005 = 5 × 0.0001 = 5 × 10−4

6 0
3 years ago
A particle moves so that r(t) = ati + b sin atj. Show that the magnitude of the acceleration of the particle is proportional to
ValentinkaMS [17]

Answer:

Step-by-step explanation:

Given

Position of particle is r(t)=at\hat{i}+b\sin (at)\hat{j}

i.e. distance from x axis is b\sin (at)---1

Distance from y axis at

velocity is given by v=\frac{\mathrm{d} r}{\mathrm{d} t}

v=a\hat{i}+ba\cos (at)\hat{j}

Similarly acceleration is given by

a=\frac{\mathrm{d} v}{\mathrm{d} t}

a=0\hat{i}-a^2b\sin (at)\hat{j}

Magnitude of acceleration is =\sqrt{(-a^2b\sin (at))^2}

=a^2b\sin (at)----2

From 1 and 2 we can see that

Magnitude of acceleration is proportional to distance from x axis

a\propto distance\ from\ x-axis

5 0
3 years ago
Read 2 more answers
Assume that the profit generated by a product is given by where x is the number of units sold. If the profit keeps changing at a
scoray [572]

Answer:

21794.495 units/month

Step-by-step explanation:

Some data are missing which i can assume as per requirement of the Question.

Let us consider that profit generated by a product is given by

p(x) =4√x

Also, consider that the profit keeps changing at a rate of $1000 per month.

Now, Using the chain rule we can write

dp/dx=(dp/dt)÷(dx/dt).

So, we  can calculate

dp/dx=2x^(-1/2)=2/√x.

As per  question we have to find out  dx/dt

Since, dx/dt= (dp/dt)/(dp/dx),

so plugging  x=1900  we get 1000√1900/2=21794.495 units/month increase in sales.

6 0
3 years ago
URGENT PLEASE HELP!!!! GIVING BRAINLIEST!! If you answer this correctly ill answer some of your questions you have posted! (39pt
Musya8 [376]

Answer:

ΔMNO= 90°, <em>m </em>= 7.316 cm, <em>n</em> = 16.69 cm

Step-by-step explanation:

The little square in the corner tells you that the angle is 90°

<u><em>Calculating the length of m</em></u>

We know that the Tangent of an angle is gotten by dividing the <u>opposite</u> side by the <u>adjacent</u> side, i.e,

Tan Ф = Opposite ÷ Adjacent

hence:

Tan 26° = <em>m </em>÷ 15

0.4877 = <em>m </em>/ 15

make <em>m </em>the subject and multiply both sides by 15

0.4877 × 15 = <em>m </em>/ 15 × 15

7.3155 = <em>m</em>

∴ <em>m </em>= 7.316 cm

<u><em>Calculating the length of n</em></u>

For this we can use the Pythagoras theorem that states, a² + b² = c² where <em>m </em>= <em>a</em><em>, </em><em>b </em>=<em> </em>15 cm and <em>c</em> = <em>n</em>. Hence:

7.316² + 15² = <em>c </em>²

53.52 + 225 = <em>c ²</em>

278·52 = <em>c ²</em>

<em>c</em> = √278·52

<em>c</em> = 16.69

∴ <em>n </em>= 16.69 cm

We could also use the Cosine of ΔOMN to get length <em>n </em>i.e,

The Cosine of an angle is equal to the adjacent side divided by the hypotenuse.

Cosine Ф = Adjacent ÷ Hypotenuse

Cosine 26° = 15 cm ÷ <em>n</em>

0.8987 = 15 / <em>n</em>

Make 15 the subject and multiply both sides by <em>n</em>

0.8987 × <em>n  </em>= 15 / <em>n </em>× <em>n</em>

0.8987 <em>n </em>= 15

Divide both sides by 0.8987

0.8987 <em>n </em>÷ 0.8987 = 15 ÷ 0.8987

∴ <em>n </em>= 16.69 cm

Hope this helps!

8 0
3 years ago
If f(x) = x2 + 3x - 4, find f(4).
Nat2105 [25]

Answer:

f(4) = 24

Step-by-step explanation:

Plug in 4 for x in the equation:

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f(4) = (4)² + 3(4) - 4

Remember to follow PEMDAS. PEMDAS =

Parenthesis

Exponents (&  Roots)

Multiplication

Division

Addition

Subtraction

and is the order of operation.

First, solve the power:

(4)² = 4 * 4 = 16

Next, multiply 3 with 4:

3 * 4 = 12

Next, combine the terms:

f(4) = 16 + 12 - 4

f(4) = (16 + 12) - 4

f(4) = 28 - 4

f(4) = 24

f(4) = 24 is your answer.

~

8 0
3 years ago
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