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1 year ago

Dan invests £1200 into his bank account.

Mathematics

2 answers:

tresset_1 [31]1 year ago

6 0

Answer:

300 euros

Step-by-step explanation:

1200 x 5 x 5=30000/100=300

Lina20 [59]1 year ago

4 0

Answer:

£1531.53

Step-by-step explanation:

Times 1200 by 1.05 then times the new answer by 1.05 until done 5 times

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2 inches 3 inches Pivot. If 60 lbs. of force must be applied to the valve for it to open, how much upward force must push rod X

tresset_1 [31]

We can solve this problem by stating that the summation of momentums must be zero. That is, the momentum at one end of the pivot must be equal to the momentum at the other end.

Momentum 1 = Momentum 2

Since Momentum is the product of Force and Distance, and with this rule created, we can say that:

F1 * d1 = F2 * d2

Where,

F1 = 60 lbs

d1 = 2 inches from the pivot

F2 = unknown X

d2 = 3 inches from the pivot

Substituting to the equation to find for F2:

60 lbs * 2 inches = F2 * 3 inches

F2 = 40 lbs

Therefore 40 lbs of upward force must be pushed to open the valve.

Answer: B

3 0

1 year ago

A container has the shape of an open right circular cone, as shown. The height of the container is 10 cm and the diameter of the

SVETLANKA909090 [29]

A) Volume = (1/12)pi*h^3, with height = 5cm.

b) You should be able to differentiate V = (1/12)pi*h^3 with respect to h, and you were given dh/dt = -0.3 cm/hr.

does that make sense?

5 0

1 year ago

Sum of positive roots of the equation (x2 - 12x + 35) (x2 + 10x + 24) = 504 is

Digiron [165]

Answer:

(3)11

Step-by-step explanation:

We are given that

$(x^2-12x+35)(x^2+10x+24)=504$

We have to find the sum of positive roots of the equation.

$x^2(x^2+10x+24)-12x(x^2+10x+24)+35(x^2+10x+24)=504$

$x^4+10x^3+24x^2-12x^3-120x^2-288x+35x^2+350x+840=504$

$x^4-2x^3-61x^2+62x+840-504=0$

$x^4-2x^3-61x^2+62x+336=0$

Factor of 336

2,3,4,6,8,7,

Let x=2

$2^4-2^4-61(2^2)+62(2)+336\neq0$

x=2 is not the root of equation

x=-2

$(-2)^4-2(-2)^3-61(-2)^2+62(-2)+336=0$

Hence x=-2 is the root of equation.

x+2 is a factor of equation.

x=3

$3^4-2(3^3)-61(3^2)+62(3)+336=0$

Therefore, x=3 is the root of equation.

$(x+2)(x-3)(x^2-x-56)=0$

$(x+2)(x-3)(x^2-8x+7x-56)=0$

$(x+2)(x-3)(x(x-8)+7(x-8))=0$

$(x+2)(x-3)(x-8)(x+7)=0$

$x-8=0\implies x=8$

$x+7=0\implies x=-7$

Positive roots are 3 and 8

Sum of positive roots=3+8=11

Option (3) is true.

4 0

1 year ago

Which of the following could be the ratio of the length of the longer leg of a 30-60-90 triangle to the length of its hypotenuse

Aliun [14]

Answer:

Option C is correct.

Ratio of longer leg to hypotenuse is; $\sqrt{3} : 2$

Step-by-step explanation:

This is the special right angle triangle 30°-60°-90° as shown below in the figure.

The side opposite the 30° angle is always the shortest because 30 degrees is the smallest angle.

The side opposite the 60° angle will be the longer leg, because 60 degrees is the mid-sized degree angle in this triangle.

Finally , the side opposite the 90° angle will always be the largest side(Hypotenuse) because 90 degrees is the largest angle.

In 30°−60°−90° right triangle,

the length of the hypotenuse is twice the length of the shorter leg,also
the length of the longer leg is $\sqrt{3}$ times the length of the shorter leg.

Then:

the sides are in proportion i.e, $1:\sqrt{3} :2$

Therefore, the ratio of the length of the longer leg to the length of its hypotenuse is: $\sqrt{3} : 2$

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