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2 years ago

Can a triangle have two obtuse angles? please Justify your answer.

Mathematics

2 answers:

Scrat [10]2 years ago

8 0

Answer:

No, a triangle cannot have 2 obtuse angles. The definition of an obtuse angle is an angle with a measure that is greater than 90°.

Step-by-step explanation:

Lostsunrise [7]2 years ago

6 0

Answer:

No, because if the triangle have two obtuse angles i.e., more than 90° angle, then the sum of all three angles of a triangle will not be equal to 180°.

Step-by-step explanation:

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I need help on 1-6 and If you can, can you explain how to do these? I'm not entirely sure how to.

gayaneshka [121]

1. Using c=2pi(r), plug in 7 for r and solve. Then using a=pi(r)^2, plug in 7 for r once again and solve.

2. First, the diameter (d) is 12 so to get the radius (r), divide 12 by 2 and you should get 6. Then use c=2pi(r) for circumference and a=pi(r)^2 for area to solve.

3. To get the area of the semicircle, divide 16 by 2 to get the radius (r), plug it into a=pi(r)^2, and divide the answer you get for a by 2. To get the area of the triangle, use a=1/2bh, plugging in 16 for b and 10 for h. Finally, add your two answers (the a's from the semicircle and triangle problems).

4. Multiply 20 by 5.5 to get the area of the triangle. Then multiply 4.5 by 20 to get the area of the parallelogram and add your two quotients.

5. Use a=1/2bh and plug in 4 for b and 3 for h and solve. Then multiply the quotient by 10 and there's your volume. To find the surface area, solve SA=(10×4)+(10×3)+(10×5)+12. All I did there was find the area of all the sides and added them together.

6. To find the triangle's volume, use a=1/2bh (b=4, h=1.5) and then multiply the quotient of that by 2.5. To find the rectangle's volume, use v=lwh (l=4, w=2.5, h=2) and solve. Finally, add the triangle's volume and the rectangle's volume to get the total volume. To get its surface area, start with the rectangle. Find the areas of all the sides and add them together but then subtract the 2.5×4 rectangle as it is not on the surface. It should look like this: SA=2(4×2)+2(2.5×2)+10. Again, all I did was find the areas of all the rectangle's sides on the surface and added them. Next, find the triangle's areas on the surface and it should look like this: SA=2(1.5×4)+2(2.5×2.5). Finally, add both values of SA from the triangle and rectangle and there's your surface area.

7 0

3 years ago

The base of an aquarium with given volume V is made of slate and the sides are made of glass. If the slate costs seven times as

Olin [163]

Answer:

x = ∛(2V/7)

y = ∛(2V/7)

z = 3.5 [∛(2V/7)]

{x,y,z} = { ∛(2V/7), ∛(2V/7), 3.5[∛(2V/7)] }

Step-by-step explanation:

The aquarium is a cuboid open at the top.

Let the dimensions of the base of the aquarium be x and y.

The height of the aquarium is then z.

The volume of the aquarium is then

V = xyz

Area of the base of the aquarium = xy

Area of the other faces = 2xz + 2yz

The problem is to now minimize the value of the cost function.

The cost of the area of the base per area is seven times the cost of any other face per area.

With the right assumption that the cost of the other faces per area is 1 currency units, then, the cost of the base of the aquarium per area would then be 7 currency units.

Cost of the base of the aquarium = 7xy

cost of the other faces = 2xz + 2yz

Total cost function = 7xy + 2xz + 2yz

C(x,y,z) = 7xy + 2xz + 2yz

We're to minimize this function subject to the constraint that

xyz = V

The constraint can be rewritten as

xyz - V = 0

Using Lagrange multiplier, we then write the equation in Lagrange form

Lagrange function = Function - λ(constraint)

where λ = Lagrange factor, which can be a function of x, y and z

L(x,y,z) = 7xy + 2xz + 2yz - λ(xyz - V)

We then take the partial derivatives of the Lagrange function with respect to x, y, z and λ. Because these are turning points and at the turning point, each of the partial derivatives is equal to 0.

(∂L/∂x) = 7y + 2z - λyz = 0

λ = (7y + 2z)/yz = (7/z) + (2/y) (eqn 1)

(∂L/∂y) = 7x + 2z - λxz = 0

λ = (7x + 2z)/xz = (7/z) + (2/x) (eqn 2)

(∂L/∂z) = 2x + 2y - λxy = 0

λ = (2x + 2y)/xy = (2/y) + (2/x) (eqn 3)

(∂L/∂λ) = xyz - V = 0

We can then equate the values of λ from the first 3 partial derivatives and solve for the values of x, y and z

(eqn 1) = (eqn 2)

(7/z) + (2/y) = (7/z) + (2/x)

(2/y) = (2/x)

y = x

Also,

(eqn 1) = (eqn 3)

(7/z) + (2/x) = (2/y) + (2/x)

(7/z) = (2/y)

z = (7y/2)

Hence, at the point where the box has minimal area,

y = x,

z = (7y/2) = (7x/2)

We can then substitute those into the constraint equation for y and z

xyz = V

x(x)(7x/2) = V

(7x³/2) = V

x³ = (2V/7)

x = ∛(2V/7)

y = x = ∛(2V/7)

z = (7x/2) = 3.5 [∛(2V/7)]

The values of x, y and z in terms of the volume that minimizes the cost function are

{x,y,z} = {∛(2V/7), ∛(2V/7), 3.5[∛(2V/7)]}

Hope this Helps!!!

7 0

3 years ago

If there are 18 boxes with 12 caculators in each box how many caculators are there in total

Dahasolnce [82]

The number of calculators
= Number of boxes * calculators in each box
=18* 12
= 216 calculators

7 0

3 years ago

Kaylee has 1 1/2 cups of yogurt to make smoothies. Each smoothie uses 1/2 cup of yogurt. How many smoothies can Kaylee make wi

ANTONII [103]

Answer:

3 smoothies

Step-by-step explanation:

1/2 goes into 1 1/2 3 times

6 0

2 years ago

Read 2 more answers

The disk enclosed by the circle x+y = 4 is revoived about the y-axis to generate solid sphere. A hele of diameter 2 units is the

Vesnalui [34]

Step-by-step explanation:

Suppose we have a curve, y = f(x).

y = f(x)

x = a x = b

Imagine that the part of the curve between the ordinates x = a and x = b is rotated about the

x-axis through 360◦

. The curve would then map out the surface of a solid as it rotated. Such

solids are called solids of revolution. Thus if the curve was a circle, we would obtain the surface

of a sphere. If the curve was a straight line through the origin, we would obtain the surface of

a cone. Now we already know what the formulae for the volumes of a sphere and a cone are,

but where did they come from? How can they calculated? If we could find a general method

for calculating the volumes of the solids of revolution then we would be able to calculate, for

example, the volume of a sphere and the volume of a cone, as well as the volumes of more

complex solids.

To see how to carry out these calculations we look first at the curve, together with the solid it

maps out when rotated through 360◦

y = f(x)

Now if we take a cross-section of the solid, parallel to the y-axis, this cross-section will be a

circle. But rather than take a cross-section, let us take a thin disc of thickness δx, with the face

of the disc nearest the y-axis at a distance x from the origin.

www.mathcentre.ac.uk 2

6 0

3 years ago