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rjkz [21]
3 years ago
12

The first three towers in a sequence are shown. The nth tower is formed by stacking n blocks on top of an n times n square of bl

ocks. How many blocks are in the 99th tower?

Mathematics
1 answer:
erik [133]3 years ago
7 0

Answer:

The 99th tower contains 9900 blocks.

Step-by-step explanation:

From the question given, we were told that the nth tower is formed by stacking n blocks on top of an n times n square of blocks. This implies that the number of blocks in n tower will be:

n + n²

Now let us use the diagram to validate the idea.

Tower 1:

n = 1

Number of blocks = 1 + 1² = 2

Tower 2:

Number of blocks = 2 + 2² = 6

Tower 3:

Number of blocks = 3 + 3² = 12

Using same idea, we can obtain the number of blocks in the 99th tower as follow:

Tower 99:

n = 99

Number of blocks = 99 + 99² = 9900

Therefore, the 99th tower contains 9900 blocks.

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A ball is thrown vertically upwards with an initial velocity of 22 m/s. When will its speed be 10
gogolik [260]

Answer:

<em>The ball's speed will be 10 m/s at t=1.22 seconds</em>

Step-by-step explanation:

The vertical motion of an object is controlled by the force of gravity. This means that there is a non-zero net force acting on the object that makes it accelerate downwards.

If the object is thrown upwards at speed vo, its speed at time t is:

v_f=v_o-g.t

Where g is the acceleration of gravity g=9.8 m/s^2.

Our ball is thrown upwards with v0=22 m/s. We need to calculate the time when its speed is vf=10 m/s.

Solving the above equation for t:

\displaystyle t=\frac{v_o-v_f}{g}

Substituting:

\displaystyle t=\frac{22-10}{9.8}=\frac{12}{9.8}

t=1.22 seconds

The ball's speed will be 10 m/s at t=1.22 seconds

8 0
3 years ago
Penny is counting the days until her grandma comes to visit. There are 98 days left. How many weeks are left until Penny's grand
Burka [1]
98 divided by 7

98/7 = 14

Answer: There are 14 weeks left.
3 0
4 years ago
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Positive because you will said that has the charged is about $2.50
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Write an equation in the form y = mx + b that represents this line.
kondaur [170]

Answer:

Step-by-step explanation:

The form, y = mx + b is the slope intercept form of a straight line.

Where b = intercept

m = slope = (change in the value of y in the vertical axis) / (change in the value of x in the horizontal axis.

Slope = (y2 - y1)/(x2 - x1)

y2 represents final value of y = - 3

y1 represents initial value of y = 3

x2 represents final value of x = 3

x1 represents initial value of x = 0

Therefore,

slope = (- 3 - 3)/(3 - 0) = - 6/3 = - 2

To determine the intercept, we would substitute m = - 2, x = 3 and y = -3 into y = mx + b. It becomes

- 3 = - 2 × 3 + b = - 6 + b

b = - 3 + 6 = 3

The equation becomes

y = - 3x + 3

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Snezhnost [94]

Answer: it’s answer c

Step-by-step explanation:

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