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Anestetic [448]
3 years ago
14

a parallelogram has side lenghts 20 cm and 25 cm. the diagonal opposite the obtuse angle measures 38 cm. what is the measure of

the obtuse angle?
Mathematics
2 answers:
Gelneren [198K]3 years ago
7 0

9514 1404 393

Answer:

  114.8°

Step-by-step explanation:

The angles can be found using the Law of Cosines. It tells you ...

  c² = a² +b² -2ab·cos(C)

Then angle C can be found to be ...

  C = arccos((a² +b² -c²)/(2ab)) = arccos((20² +25² -38²)/(2·20·25))

  C = arccos(-419/1000) ≈ 114.77°

The measure of the obtuse angle is about 114.8°.

Nady [450]3 years ago
3 0

Step-by-step explanation:

1. draw the parallelogram with side 20cm and 25cm respectively and also the diagonal as well.

2.Clearly it forms a triangle in the parallelogram with three known lengths of side.

3.Using the cosine rule : c^2=b^2+c^2 -2bc cos c to find the obtuse angle.

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Write the first four terms of a sequence given the recursive rule below:
777dan777 [17]

Answer:

The first four terms of the sequence is : A)   7, 17, 37, 77.

Step-by-step explanation:

The given function f(n) = 2 x  f(n − 1) + 3

Also, f(1)= 7

<u>FOR n= 2</u>

f(2) = 2 x f(2-1) + 3  = 2 x f(1)  + 3

      = (2 x 7) + 3 = 14 + 3 = 17

⇒f(2) = 17

<u>FOR n= 3</u>

f(3) = 2 x f(3-1) + 3  = 2 x f(2)  + 3

      = (2 x 17) + 3 = 34 + 3 = 37

⇒f(3) = 37

<u>FOR n= 4</u>

f(4) = 2 x f(4-1) + 3  = 2 x f(3)  + 3

      = (2 x 37) + 3 = 74 + 3 = 77

⇒f(4) =77

So, the first four terms of the sequence are 7, 17, 37, 77.

A) is the correct option.

5 0
3 years ago
The dimensions of a triangular prism are
natulia [17]

Answer:

192 cubic centimeters

Step-by-step explanation:

The first step is to find the area of the triangular base. The formula for the area of a triangle is bh/2, where b is the length of the base and h is the length of the height. Plugging in the dimensions you are given, you get 6*4/2=12 square centimeters. Multiplying this by the height of the prism, or 16, you get 12*16=192. Hope this helps!

3 0
4 years ago
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A car traveled 63 miles on 3 gallons of gas. What proportion can you set up to determine how many miles, m, the car can travel o
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Answer:Let x be the number of miles driven on 60 gallons of gas. By setting up and solving a proportion involving x, find the value of x for the car that you have chosen. State the type of car, the mileage, and show both the set up of the proportion and the steps

Step-by-step explanation:

5 0
4 years ago
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Paul hit the golf ball 85 yards.
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Paul hit the golf ball 255 feet.  
Danika hit the golf ball 80 yards.  
Paul hit the golf ball 1080 inches farther than Billy.
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4 years ago
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I DON’T UNDERSTAND! PLEASE HELP!
Brums [2.3K]

Answer:

The height of the water is 60.5\ ft

Step-by-step explanation:

step 1

Find the volume of the tank

The volume of the inverted right circular cone is equal to

V=\frac{1}{3}\pi R^{2} H

we have

R=16\ ft

H=96\ ft

substitute

V=\frac{1}{3}\pi (16)^{2} (96)

V=8,192\pi\ ft^{3}

step 2

Find the 25% of the tank’s capacity  

V=(0.25)*8,192\pi=2,048\pi\ ft^{3}

step 3

Find the height, of the water in the tank  

Let

h ----> the height of the water  

we know that

If two figures are similar, then the ratio of its corresponding sides is proportional

\frac{R}{H}=\frac{r}{h}

substitute

\frac{16}{96}=\frac{r}{h}\\ \\r= \frac{h}{6}

where

r is the radius of the smaller cone of the figure

h is the height of the smaller cone of the figure

R is the radius of the circular base of tank

H is the height of the tank

we  have

V=2,048\pi\ ft^{3} -----> volume of the smaller cone

substitute

2,048\pi=\frac{1}{3}\pi (\frac{h}{6})^{2}h

Simplify

221,184=h^{3}

h=60.5\ ft

6 0
3 years ago
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